A study of numerical methods for hyperbolic conservation laws with stiff source terms

NASA Technical Reports Server (NTRS)

Leveque, R. J.; Yee, H. C.

1988-01-01

The proper modeling of nonequilibrium gas dynamics is required in certain regimes of hypersonic flow. For inviscid flow this gives a system of conservation laws coupled with source terms representing the chemistry. Often a wide range of time scales is present in the problem, leading to numerical difficulties as in stiff systems of ordinary differential equations. Stability can be achieved by using implicit methods, but other numerical difficulties are observed. The behavior of typical numerical methods on a simple advection equation with a parameter-dependent source term was studied. Two approaches to incorporate the source term were utilized: MacCormack type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. Various comparisons over a wide range of parameter values were made. In the stiff case where the solution contains discontinuities, incorrect numerical propagation speeds are observed with all of the methods considered. This phenomenon is studied and explained.

Efficient numerical method for analyzing optical bistability in photonic crystal microcavities.

PubMed

Yuan, Lijun; Lu, Ya Yan

2013-05-20

Nonlinear optical effects can be enhanced by photonic crystal microcavities and be used to develop practical ultra-compact optical devices with low power requirements. The finite-difference time-domain method is the standard numerical method for simulating nonlinear optical devices, but it has limitations in terms of accuracy and efficiency. In this paper, a rigorous and efficient frequency-domain numerical method is developed for analyzing nonlinear optical devices where the nonlinear effect is concentrated in the microcavities. The method replaces the linear problem outside the microcavities by a rigorous and numerically computed boundary condition, then solves the nonlinear problem iteratively in a small region around the microcavities. Convergence of the iterative method is much easier to achieve since the size of the problem is significantly reduced. The method is presented for a specific two-dimensional photonic crystal waveguide-cavity system with a Kerr nonlinearity, using numerical methods that can take advantage of the geometric features of the structure. The method is able to calculate multiple solutions exhibiting the optical bistability phenomenon in the strongly nonlinear regime.

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

An efficient numerical technique for calculating thermal spreading resistance

NASA Technical Reports Server (NTRS)

Gale, E. H., Jr.

1977-01-01

An efficient numerical technique for solving the equations resulting from finite difference analyses of fields governed by Poisson's equation is presented. The method is direct (noniterative)and the computer work required varies with the square of the order of the coefficient matrix. The computational work required varies with the cube of this order for standard inversion techniques, e.g., Gaussian elimination, Jordan, Doolittle, etc.

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

Dual domain material point method for multiphase flows

NASA Astrophysics Data System (ADS)

Zhang, Duan

2017-11-01

Although the particle-in-cell method was first invented in the 60's for fluid computations, one of its later versions, the material point method, is mostly used for solid calculations. Recent development of the multi-velocity formulations for multiphase flows and fluid-structure interactions requires the Lagrangian capability of the method be combined with Eulerian calculations for fluids. Because of different numerical representations of the materials, additional numerical schemes are needed to ensure continuity of the materials. New applications of the method to compute fluid motions have revealed numerical difficulties in various versions of the method. To resolve these difficulties, the dual domain material point method is introduced and improved. Unlike other particle based methods, the material point method uses both Lagrangian particles and Eulerian mesh, therefore it avoids direct communication between particles. With this unique property and the Lagrangian capability of the method, it is shown that a multiscale numerical scheme can be efficiently built based on the dual domain material point method. In this talk, the theoretical foundation of the method will be introduced. Numerical examples will be shown. Work sponsored by the next generation code project of LANL.

Formulation of a dynamic analysis method for a generic family of hoop-mast antenna systems

NASA Technical Reports Server (NTRS)

Gabriele, A.; Loewy, R.

1981-01-01

Analytical studies of mast-cable-hoop-membrane type antennas were conducted using a transfer matrix numerical analysis approach. This method, by virtue of its specialization and the inherently easy compartmentalization of the formulation and numerical procedures, can be significantly more efficient in computer time required and in the time needed to review and interpret the results.

Numerical methods for stochastic differential equations

NASA Astrophysics Data System (ADS)

Kloeden, Peter; Platen, Eckhard

1991-06-01

The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations due to the peculiarities of stochastic calculus. This book provides an introduction to stochastic calculus and stochastic differential equations, both theory and applications. The main emphasise is placed on the numerical methods needed to solve such equations. It assumes an undergraduate background in mathematical methods typical of engineers and physicists, through many chapters begin with a descriptive summary which may be accessible to others who only require numerical recipes. To help the reader develop an intuitive understanding of the underlying mathematicals and hand-on numerical skills exercises and over 100 PC Exercises (PC-personal computer) are included. The stochastic Taylor expansion provides the key tool for the systematic derivation and investigation of discrete time numerical methods for stochastic differential equations. The book presents many new results on higher order methods for strong sample path approximations and for weak functional approximations, including implicit, predictor-corrector, extrapolation and variance-reduction methods. Besides serving as a basic text on such methods. the book offers the reader ready access to a large number of potential research problems in a field that is just beginning to expand rapidly and is widely applicable.

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.

Bayesian-based estimation of acoustic surface impedance: Finite difference frequency domain approach.

PubMed

Bockman, Alexander; Fackler, Cameron; Xiang, Ning

2015-04-01

Acoustic performance for an interior requires an accurate description of the boundary materials' surface acoustic impedance. Analytical methods may be applied to a small class of test geometries, but inverse numerical methods provide greater flexibility. The parameter estimation problem requires minimizing prediction vice observed acoustic field pressure. The Bayesian-network sampling approach presented here mitigates other methods' susceptibility to noise inherent to the experiment, model, and numerics. A geometry agnostic method is developed here and its parameter estimation performance is demonstrated for an air-backed micro-perforated panel in an impedance tube. Good agreement is found with predictions from the ISO standard two-microphone, impedance-tube method, and a theoretical model for the material. Data by-products exclusive to a Bayesian approach are analyzed to assess sensitivity of the method to nuisance parameters.

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.

Nonclassicality thresholds for multiqubit states: Numerical analysis

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

Gruca, Jacek; Zukowski, Marek; Laskowski, Wieslaw

2010-07-15

States that strongly violate Bell's inequalities are required in many quantum-informational protocols as, for example, in cryptography, secret sharing, and the reduction of communication complexity. We investigate families of such states with a numerical method which allows us to reveal nonclassicality even without direct knowledge of Bell's inequalities for the given problem. An extensive set of numerical results is presented and discussed.

Method of and Apparatus for Histological Human Tissue Characterization Using Ultrasound

NASA Technical Reports Server (NTRS)

Yost, William T. (Inventor); Cantrell, John H. (Inventor); TalEr, George A. (Inventor)

1999-01-01

A method and apparatus for determining important histological characteristics of tissue, including a determination of the tissue's health. Electrical pulses are converted into meaningful numerical representations through the use of Fourier Transforms. These numerical representations are then used to determine important histological characteristics of tissue. This novel invention does not require rectification and thus provides for detailed information from the ultrasonic scan.

Method of and Apparatus for Histological Human Tissue Characterization Using Ultrasound

NASA Technical Reports Server (NTRS)

Yost, William T. (Inventor); Cantrell, John H. (Inventor); Taler, George A. (Inventor)

1998-01-01

A method and apparatus for determining important histological characteristics of tissue, including a determination of the tissue's health is discussed. Electrical pulses are converted into meaningful numerical representations through the use of Fourier Transforms. These numerical representations are then used to determine important histological characteristics of tissue. This novel invention does not require rectification and thus provides for detailed information from the ultrasonic scan.

A Density Perturbation Method to Study the Eigenstructure of Two-Phase Flow Equation Systems

NASA Astrophysics Data System (ADS)

Cortes, J.; Debussche, A.; Toumi, I.

1998-12-01

Many interesting and challenging physical mechanisms are concerned with the mathematical notion of eigenstructure. In two-fluid models, complex phasic interactions yield a complex eigenstructure which may raise numerous problems in numerical simulations. In this paper, we develop a perturbation method to examine the eigenvalues and eigenvectors of two-fluid models. This original method, based on the stiffness of the density ratio, provides a convenient tool to study the relevance of pressure momentum interactions and allows us to get precise approximations of the whole flow eigendecomposition for minor requirements. Roe scheme is successfully implemented and some numerical tests are presented.

Hierarchical matrices implemented into the boundary integral approaches for gravity field modelling

NASA Astrophysics Data System (ADS)

Čunderlík, Róbert; Vipiana, Francesca

2017-04-01

Boundary integral approaches applied for gravity field modelling have been recently developed to solve the geodetic boundary value problems numerically, or to process satellite observations, e.g. from the GOCE satellite mission. In order to obtain numerical solutions of "cm-level" accuracy, such approaches require very refined level of the disretization or resolution. This leads to enormous memory requirements that need to be reduced. An implementation of the Hierarchical Matrices (H-matrices) can significantly reduce a numerical complexity of these approaches. A main idea of the H-matrices is based on an approximation of the entire system matrix that is split into a family of submatrices. Large submatrices are stored in factorized representation, while small submatrices are stored in standard representation. This allows reducing memory requirements significantly while improving the efficiency. The poster presents our preliminary results of implementations of the H-matrices into the existing boundary integral approaches based on the boundary element method or the method of fundamental solution.

Numerical simulation of immiscible viscous fingering using adaptive unstructured meshes

NASA Astrophysics Data System (ADS)

Adam, A.; Salinas, P.; Percival, J. R.; Pavlidis, D.; Pain, C.; Muggeridge, A. H.; Jackson, M.

2015-12-01

Displacement of one fluid by another in porous media occurs in various settings including hydrocarbon recovery, CO2 storage and water purification. When the invading fluid is of lower viscosity than the resident fluid, the displacement front is subject to a Saffman-Taylor instability and is unstable to transverse perturbations. These instabilities can grow, leading to fingering of the invading fluid. Numerical simulation of viscous fingering is challenging. The physics is controlled by a complex interplay of viscous and diffusive forces and it is necessary to ensure physical diffusion dominates numerical diffusion to obtain converged solutions. This typically requires the use of high mesh resolution and high order numerical methods. This is computationally expensive. We demonstrate here the use of a novel control volume - finite element (CVFE) method along with dynamic unstructured mesh adaptivity to simulate viscous fingering with higher accuracy and lower computational cost than conventional methods. Our CVFE method employs a discontinuous representation for both pressure and velocity, allowing the use of smaller control volumes (CVs). This yields higher resolution of the saturation field which is represented CV-wise. Moreover, dynamic mesh adaptivity allows high mesh resolution to be employed where it is required to resolve the fingers and lower resolution elsewhere. We use our results to re-examine the existing criteria that have been proposed to govern the onset of instability.Mesh adaptivity requires the mapping of data from one mesh to another. Conventional methods such as consistent interpolation do not readily generalise to discontinuous fields and are non-conservative. We further contribute a general framework for interpolation of CV fields by Galerkin projection. The method is conservative, higher order and yields improved results, particularly with higher order or discontinuous elements where existing approaches are often excessively diffusive.

Detection of Orbital Debris Collision Risks for the Automated Transfer Vehicle

NASA Technical Reports Server (NTRS)

Peret, L.; Legendre, P.; Delavault, S.; Martin, T.

2007-01-01

In this paper, we present a general collision risk assessment method, which has been applied through numerical simulations to the Automated Transfer Vehicle (ATV) case. During ATV ascent towards the International Space Station, close approaches between the ATV and objects of the USSTRACOM catalog will be monitored through collision rosk assessment. Usually, collision risk assessment relies on an exclusion volume or a probability threshold method. Probability methods are more effective than exclusion volumes but require accurate covariance data. In this work, we propose to use a criterion defined by an adaptive exclusion area. This criterion does not require any probability calculation but is more effective than exclusion volume methods as demonstrated by our numerical experiments. The results of these studies, when confirmed and finalized, will be used for the ATV operations.

Variational Algorithms for Test Particle Trajectories

NASA Astrophysics Data System (ADS)

Ellison, C. Leland; Finn, John M.; Qin, Hong; Tang, William M.

2015-11-01

The theory of variational integration provides a novel framework for constructing conservative numerical methods for magnetized test particle dynamics. The retention of conservation laws in the numerical time advance captures the correct qualitative behavior of the long time dynamics. For modeling the Lorentz force system, new variational integrators have been developed that are both symplectic and electromagnetically gauge invariant. For guiding center test particle dynamics, discretization of the phase-space action principle yields multistep variational algorithms, in general. Obtaining the desired long-term numerical fidelity requires mitigation of the multistep method's parasitic modes or applying a discretization scheme that possesses a discrete degeneracy to yield a one-step method. Dissipative effects may be modeled using Lagrange-D'Alembert variational principles. Numerical results will be presented using a new numerical platform that interfaces with popular equilibrium codes and utilizes parallel hardware to achieve reduced times to solution. This work was supported by DOE Contract DE-AC02-09CH11466.

The generalized scattering coefficient method for plane wave scattering in layered structures

NASA Astrophysics Data System (ADS)

Liu, Yu; Li, Chao; Wang, Huai-Yu; Zhou, Yun-Song

2017-02-01

The generalized scattering coefficient (GSC) method is pedagogically derived and employed to study the scattering of plane waves in homogeneous and inhomogeneous layered structures. The numerical stabilities and accuracies of this method and other commonly used numerical methods are discussed and compared. For homogeneous layered structures, concise scattering formulas with clear physical interpretations and strong numerical stability are obtained by introducing the GSCs. For inhomogeneous layered structures, three numerical methods are employed: the staircase approximation method, the power series expansion method, and the differential equation based on the GSCs. We investigate the accuracies and convergence behaviors of these methods by comparing their predictions to the exact results. The conclusions are as follows. The staircase approximation method has a slow convergence in spite of its simple and intuitive implementation, and a fine stratification within the inhomogeneous layer is required for obtaining accurate results. The expansion method results are sensitive to the expansion order, and the treatment becomes very complicated for relatively complex configurations, which restricts its applicability. By contrast, the GSC-based differential equation possesses a simple implementation while providing fast and accurate results.

A modified form of conjugate gradient method for unconstrained optimization problems

NASA Astrophysics Data System (ADS)

Ghani, Nur Hamizah Abdul; Rivaie, Mohd.; Mamat, Mustafa

2016-06-01

Conjugate gradient (CG) methods have been recognized as an interesting technique to solve optimization problems, due to the numerical efficiency, simplicity and low memory requirements. In this paper, we propose a new CG method based on the study of Rivaie et al. [7] (Comparative study of conjugate gradient coefficient for unconstrained Optimization, Aus. J. Bas. Appl. Sci. 5(2011) 947-951). Then, we show that our method satisfies sufficient descent condition and converges globally with exact line search. Numerical results show that our proposed method is efficient for given standard test problems, compare to other existing CG methods.

Rapid analysis of scattering from periodic dielectric structures using accelerated Cartesian expansions.

PubMed

Baczewski, Andrew D; Miller, Nicholas C; Shanker, Balasubramaniam

2012-04-01

The analysis of fields in periodic dielectric structures arise in numerous applications of recent interest, ranging from photonic bandgap structures and plasmonically active nanostructures to metamaterials. To achieve an accurate representation of the fields in these structures using numerical methods, dense spatial discretization is required. This, in turn, affects the cost of analysis, particularly for integral-equation-based methods, for which traditional iterative methods require O(N2) operations, N being the number of spatial degrees of freedom. In this paper, we introduce a method for the rapid solution of volumetric electric field integral equations used in the analysis of doubly periodic dielectric structures. The crux of our method is the accelerated Cartesian expansion algorithm, which is used to evaluate the requisite potentials in O(N) cost. Results are provided that corroborate our claims of acceleration without compromising accuracy, as well as the application of our method to a number of compelling photonics applications.

The convolutional differentiator method for numerical modelling of acoustic and elastic wavefields

NASA Astrophysics Data System (ADS)

Zhang, Zhong-Jie; Teng, Ji-Wen; Yang, Ding-Hui

1996-02-01

Based on the techniques of forward and inverse Fourier transformation, the authors discussed the design scheme of ordinary differentiator used and applied in the simulation of acoustic and elastic wavefields in isotropic media respectively. To compress Gibbs effects by truncation effectively, Hanning window is introduced in. The model computation shows that, the convolutional differentiator method has the advantages of rapidity, low requirements of computer’s inner storage and high precision, which is a potential method of numerical simulation.

Numerical Simulation of Chemically Reacting Flows

DTIC Science & Technology

2015-09-03

62 (1986) 1-25. 6. O.L. Burchett, M.R. Birnbaum, and C.T. Oien, “ Compaction studies of palladium/aluminum powder ,” Sandia National Laboratories...interest to the Air Force. 15. SUBJECT TERMS Numerical methods, Diffusion Flames, Adaptive Gridding, Velocity-Vorticity, Compact Methods 16...discussed ab ot require th sure mass c mputational city formula e spectrum soot forma formulation lent agreem ing MC-Sm ork will lik ith compact iled

Analytical, Numerical, and Experimental Investigation on a Non-Contact Method for the Measurements of Creep Properties of Ultra-High-Temperature Materials

NASA Technical Reports Server (NTRS)

Lee, Jonghyun; Hyers, Robert W.; Rogers, Jan R.; Rathz, Thomas J.; Choo, Hahn; Liaw, Peter

2006-01-01

Responsive access to space requires re-use of components such as rocket nozzles that operate at extremely high temperatures. For such applications, new ultra-hightemperature materials that can operate over 2,000 C are required. At the temperatures higher than the fifty percent of the melting temperature, the characterization of creep properties is indispensable. Since conventional methods for the measurement of creep is limited below 1,700 C, a new technique that can be applied at higher temperatures is strongly demanded. This research develops a non-contact method for the measurement of creep at the temperatures over 2,300 C. Using the electrostatic levitator in NASA MSFC, a spherical sample was rotated to cause creep deformation by centrifugal acceleration. The deforming sample was captured with a digital camera and analyzed to measure creep deformation. Numerical and analytical analyses have also been conducted to compare the experimental results. Analytical, numerical, and experimental results showed a good agreement with one another.

Modified harmonic balance method for the solution of nonlinear jerk equations

NASA Astrophysics Data System (ADS)

Rahman, M. Saifur; Hasan, A. S. M. Z.

2018-03-01

In this paper, a second approximate solution of nonlinear jerk equations (third order differential equation) can be obtained by using modified harmonic balance method. The method is simpler and easier to carry out the solution of nonlinear differential equations due to less number of nonlinear equations are required to solve than the classical harmonic balance method. The results obtained from this method are compared with those obtained from the other existing analytical methods that are available in the literature and the numerical method. The solution shows a good agreement with the numerical solution as well as the analytical methods of the available literature.

5 CFR 302.401 - Selection and appointment.

Code of Federal Regulations, 2010 CFR

2010-01-01

... reemployment, reemployment, or regular list on which candidates have not received numerical scores, an agency... candidates have received numerical scores, the agency must make its selection for each vacancy from not more... method, an agency is not required to— (1) Accord an applicant on its priority reemployment or...

Some problems of the calculation of three-dimensional boundary layer flows on general configurations

NASA Technical Reports Server (NTRS)

Cebeci, T.; Kaups, K.; Mosinskis, G. J.; Rehn, J. A.

1973-01-01

An accurate solution of the three-dimensional boundary layer equations over general configurations such as those encountered in aircraft and space shuttle design requires a very efficient, fast, and accurate numerical method with suitable turbulence models for the Reynolds stresses. The efficiency, speed, and accuracy of a three-dimensional numerical method together with the turbulence models for the Reynolds stresses are examined. The numerical method is the implicit two-point finite difference approach (Box Method) developed by Keller and applied to the boundary layer equations by Keller and Cebeci. In addition, a study of some of the problems that may arise in the solution of these equations for three-dimensional boundary layer flows over general configurations.

Random element method for numerical modeling of diffusional processes

NASA Technical Reports Server (NTRS)

Ghoniem, A. F.; Oppenheim, A. K.

1982-01-01

The random element method is a generalization of the random vortex method that was developed for the numerical modeling of momentum transport processes as expressed in terms of the Navier-Stokes equations. The method is based on the concept that random walk, as exemplified by Brownian motion, is the stochastic manifestation of diffusional processes. The algorithm based on this method is grid-free and does not require the diffusion equation to be discritized over a mesh, it is thus devoid of numerical diffusion associated with finite difference methods. Moreover, the algorithm is self-adaptive in space and explicit in time, resulting in an improved numerical resolution of gradients as well as a simple and efficient computational procedure. The method is applied here to an assortment of problems of diffusion of momentum and energy in one-dimension as well as heat conduction in two-dimensions in order to assess its validity and accuracy. The numerical solutions obtained are found to be in good agreement with exact solution except for a statistical error introduced by using a finite number of elements, the error can be reduced by increasing the number of elements or by using ensemble averaging over a number of solutions.

A new implementation of the CMRH method for solving dense linear systems

NASA Astrophysics Data System (ADS)

Heyouni, M.; Sadok, H.

2008-04-01

The CMRH method [H. Sadok, Methodes de projections pour les systemes lineaires et non lineaires, Habilitation thesis, University of Lille1, Lille, France, 1994; H. Sadok, CMRH: A new method for solving nonsymmetric linear systems based on the Hessenberg reduction algorithm, Numer. Algorithms 20 (1999) 303-321] is an algorithm for solving nonsymmetric linear systems in which the Arnoldi component of GMRES is replaced by the Hessenberg process, which generates Krylov basis vectors which are orthogonal to standard unit basis vectors rather than mutually orthogonal. The iterate is formed from these vectors by solving a small least squares problem involving a Hessenberg matrix. Like GMRES, this method requires one matrix-vector product per iteration. However, it can be implemented to require half as much arithmetic work and less storage. Moreover, numerical experiments show that this method performs accurately and reduces the residual about as fast as GMRES. With this new implementation, we show that the CMRH method is the only method with long-term recurrence which requires not storing at the same time the entire Krylov vectors basis and the original matrix as in the GMRES algorithmE A comparison with Gaussian elimination is provided.

Comparison of methods for developing the dynamics of rigid-body systems

NASA Technical Reports Server (NTRS)

Ju, M. S.; Mansour, J. M.

1989-01-01

Several approaches for developing the equations of motion for a three-degree-of-freedom PUMA robot were compared on the basis of computational efficiency (i.e., the number of additions, subtractions, multiplications, and divisions). Of particular interest was the investigation of the use of computer algebra as a tool for developing the equations of motion. Three approaches were implemented algebraically: Lagrange's method, Kane's method, and Wittenburg's method. Each formulation was developed in absolute and relative coordinates. These six cases were compared to each other and to a recursive numerical formulation. The results showed that all of the formulations implemented algebraically required fewer calculations than the recursive numerical algorithm. The algebraic formulations required fewer calculations in absolute coordinates than in relative coordinates. Each of the algebraic formulations could be simplified, using patterns from Kane's method, to yield the same number of calculations in a given coordinate system.

A numeric investigation of co-flowing liquid streams using the Lattice Boltzmann Method

NASA Astrophysics Data System (ADS)

Somogyi, Andy; Tagg, Randall

2007-11-01

We present a numerical investigation of co-flowing immiscible liquid streams using the Lattice Boltzmann Method (LBM) for multi component, dissimilar viscosity, immiscible fluid flow. When a liquid is injected into another immiscible liquid, the flow will eventually transition from jetting to dripping due to interfacial tension. Our implementation of LBM models the interfacial tension through a variety of techniques. Parallelization is also straightforward for both single and multi component models as only near local interaction is required. We compare the results of our numerical investigation using LBM to several recent physical experiments.

A methodology for highway asset valuation in Indiana.

DOT National Transportation Integrated Search

2012-11-01

The Government Accounting Standards Board (GASB) requires transportation agencies to report the values of their tangible assets. : Numerous valuation methods exist which use different underlying concepts and data items. These traditional methods have...

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.

A numerical study of adaptive space and time discretisations for Gross–Pitaevskii equations

PubMed Central

Thalhammer, Mechthild; Abhau, Jochen

2012-01-01

As a basic principle, benefits of adaptive discretisations are an improved balance between required accuracy and efficiency as well as an enhancement of the reliability of numerical computations. In this work, the capacity of locally adaptive space and time discretisations for the numerical solution of low-dimensional nonlinear Schrödinger equations is investigated. The considered model equation is related to the time-dependent Gross–Pitaevskii equation arising in the description of Bose–Einstein condensates in dilute gases. The performance of the Fourier-pseudo spectral method constrained to uniform meshes versus the locally adaptive finite element method and of higher-order exponential operator splitting methods with variable time stepsizes is studied. Numerical experiments confirm that a local time stepsize control based on a posteriori local error estimators or embedded splitting pairs, respectively, is effective in different situations with an enhancement either in efficiency or reliability. As expected, adaptive time-splitting schemes combined with fast Fourier transform techniques are favourable regarding accuracy and efficiency when applied to Gross–Pitaevskii equations with a defocusing nonlinearity and a mildly varying regular solution. However, the numerical solution of nonlinear Schrödinger equations in the semi-classical regime becomes a demanding task. Due to the highly oscillatory and nonlinear nature of the problem, the spatial mesh size and the time increments need to be of the size of the decisive parameter 0<ε≪1, especially when it is desired to capture correctly the quantitative behaviour of the wave function itself. The required high resolution in space constricts the feasibility of numerical computations for both, the Fourier pseudo-spectral and the finite element method. Nevertheless, for smaller parameter values locally adaptive time discretisations facilitate to determine the time stepsizes sufficiently small in order that the numerical approximation captures correctly the behaviour of the analytical solution. Further illustrations for Gross–Pitaevskii equations with a focusing nonlinearity or a sharp Gaussian as initial condition, respectively, complement the numerical study. PMID:25550676

A numerical study of adaptive space and time discretisations for Gross-Pitaevskii equations.

PubMed

Thalhammer, Mechthild; Abhau, Jochen

2012-08-15

As a basic principle, benefits of adaptive discretisations are an improved balance between required accuracy and efficiency as well as an enhancement of the reliability of numerical computations. In this work, the capacity of locally adaptive space and time discretisations for the numerical solution of low-dimensional nonlinear Schrödinger equations is investigated. The considered model equation is related to the time-dependent Gross-Pitaevskii equation arising in the description of Bose-Einstein condensates in dilute gases. The performance of the Fourier-pseudo spectral method constrained to uniform meshes versus the locally adaptive finite element method and of higher-order exponential operator splitting methods with variable time stepsizes is studied. Numerical experiments confirm that a local time stepsize control based on a posteriori local error estimators or embedded splitting pairs, respectively, is effective in different situations with an enhancement either in efficiency or reliability. As expected, adaptive time-splitting schemes combined with fast Fourier transform techniques are favourable regarding accuracy and efficiency when applied to Gross-Pitaevskii equations with a defocusing nonlinearity and a mildly varying regular solution. However, the numerical solution of nonlinear Schrödinger equations in the semi-classical regime becomes a demanding task. Due to the highly oscillatory and nonlinear nature of the problem, the spatial mesh size and the time increments need to be of the size of the decisive parameter [Formula: see text], especially when it is desired to capture correctly the quantitative behaviour of the wave function itself. The required high resolution in space constricts the feasibility of numerical computations for both, the Fourier pseudo-spectral and the finite element method. Nevertheless, for smaller parameter values locally adaptive time discretisations facilitate to determine the time stepsizes sufficiently small in order that the numerical approximation captures correctly the behaviour of the analytical solution. Further illustrations for Gross-Pitaevskii equations with a focusing nonlinearity or a sharp Gaussian as initial condition, respectively, complement the numerical study.

Direct imaging of small scatterers using reduced time dependent data

NASA Astrophysics Data System (ADS)

Cakoni, Fioralba; Rezac, Jacob D.

2017-06-01

We introduce qualitative methods for locating small objects using time dependent acoustic near field waves. These methods have reduced data collection requirements compared to typical qualitative imaging techniques. In particular, we only collect scattered field data in a small region surrounding the location from which an incident field was transmitted. The new methods are partially theoretically justified and numerical simulations demonstrate their efficacy. We show that these reduced data techniques give comparable results to methods which require full multistatic data and that these time dependent methods require less scattered field data than their time harmonic analogs.

A fast quadrature-based numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage.

PubMed

Stuebner, Michael; Haider, Mansoor A

2010-06-18

A new and efficient method for numerical solution of the continuous spectrum biphasic poroviscoelastic (BPVE) model of articular cartilage is presented. Development of the method is based on a composite Gauss-Legendre quadrature approximation of the continuous spectrum relaxation function that leads to an exponential series representation. The separability property of the exponential terms in the series is exploited to develop a numerical scheme that can be reduced to an update rule requiring retention of the strain history at only the previous time step. The cost of the resulting temporal discretization scheme is O(N) for N time steps. Application and calibration of the method is illustrated in the context of a finite difference solution of the one-dimensional confined compression BPVE stress-relaxation problem. Accuracy of the numerical method is demonstrated by comparison to a theoretical Laplace transform solution for a range of viscoelastic relaxation times that are representative of articular cartilage. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

An Improved Neutron Transport Algorithm for HZETRN

NASA Technical Reports Server (NTRS)

Slaba, Tony C.; Blattnig, Steve R.; Clowdsley, Martha S.; Walker, Steven A.; Badavi, Francis F.

2010-01-01

Long term human presence in space requires the inclusion of radiation constraints in mission planning and the design of shielding materials, structures, and vehicles. In this paper, the numerical error associated with energy discretization in HZETRN is addressed. An inadequate numerical integration scheme in the transport algorithm is shown to produce large errors in the low energy portion of the neutron and light ion fluence spectra. It is further shown that the errors result from the narrow energy domain of the neutron elastic cross section spectral distributions, and that an extremely fine energy grid is required to resolve the problem under the current formulation. Two numerical methods are developed to provide adequate resolution in the energy domain and more accurately resolve the neutron elastic interactions. Convergence testing is completed by running the code for various environments and shielding materials with various energy grids to ensure stability of the newly implemented method.

Numerical solutions of the macroscopic Maxwell equations for scattering by non-spherical particles: A tutorial review

NASA Astrophysics Data System (ADS)

Kahnert, Michael

2016-07-01

Numerical solution methods for electromagnetic scattering by non-spherical particles comprise a variety of different techniques, which can be traced back to different assumptions and solution strategies applied to the macroscopic Maxwell equations. One can distinguish between time- and frequency-domain methods; further, one can divide numerical techniques into finite-difference methods (which are based on approximating the differential operators), separation-of-variables methods (which are based on expanding the solution in a complete set of functions, thus approximating the fields), and volume integral-equation methods (which are usually solved by discretisation of the target volume and invoking the long-wave approximation in each volume cell). While existing reviews of the topic often tend to have a target audience of program developers and expert users, this tutorial review is intended to accommodate the needs of practitioners as well as novices to the field. The required conciseness is achieved by limiting the presentation to a selection of illustrative methods, and by omitting many technical details that are not essential at a first exposure to the subject. On the other hand, the theoretical basis of numerical methods is explained with little compromises in mathematical rigour; the rationale is that a good grasp of numerical light scattering methods is best achieved by understanding their foundation in Maxwell's theory.

A Numerical Method for Calculating the Wave Drag of a Configuration from the Second Derivative of the Area Distribution of a Series of Equivalent Bodies of Revolution

NASA Technical Reports Server (NTRS)

Levy, Lionel L., Jr.; Yoshikawa, Kenneth K.

1959-01-01

A method based on linearized and slender-body theories, which is easily adapted to electronic-machine computing equipment, is developed for calculating the zero-lift wave drag of single- and multiple-component configurations from a knowledge of the second derivative of the area distribution of a series of equivalent bodies of revolution. The accuracy and computational time required of the method to calculate zero-lift wave drag is evaluated relative to another numerical method which employs the Tchebichef form of harmonic analysis of the area distribution of a series of equivalent bodies of revolution. The results of the evaluation indicate that the total zero-lift wave drag of a multiple-component configuration can generally be calculated most accurately as the sum of the zero-lift wave drag of each component alone plus the zero-lift interference wave drag between all pairs of components. The accuracy and computational time required of both methods to calculate total zero-lift wave drag at supersonic Mach numbers is comparable for airplane-type configurations. For systems of bodies of revolution both methods yield similar results with comparable accuracy; however, the present method only requires up to 60 percent of the computing time required of the harmonic-analysis method for two bodies of revolution and less time for a larger number of bodies.

Numerical Simulation of Transit-Time Ultrasonic Flowmeters by a Direct Approach.

PubMed

Luca, Adrian; Marchiano, Regis; Chassaing, Jean-Camille

2016-06-01

This paper deals with the development of a computational code for the numerical simulation of wave propagation through domains with a complex geometry consisting in both solids and moving fluids. The emphasis is on the numerical simulation of ultrasonic flowmeters (UFMs) by modeling the wave propagation in solids with the equations of linear elasticity (ELE) and in fluids with the linearized Euler equations (LEEs). This approach requires high performance computing because of the high number of degrees of freedom and the long propagation distances. Therefore, the numerical method should be chosen with care. In order to minimize the numerical dissipation which may occur in this kind of configuration, the numerical method employed here is the nodal discontinuous Galerkin (DG) method. Also, this method is well suited for parallel computing. To speed up the code, almost all the computational stages have been implemented to run on graphical processing unit (GPU) by using the compute unified device architecture (CUDA) programming model from NVIDIA. This approach has been validated and then used for the two-dimensional simulation of gas UFMs. The large contrast of acoustic impedance characteristic to gas UFMs makes their simulation a real challenge.

A unified convergence theory of a numerical method, and applications to the replenishment policies.

PubMed

Mi, Xiang-jiang; Wang, Xing-hua

2004-01-01

In determining the replenishment policy for an inventory system, some researchers advocated that the iterative method of Newton could be applied to the derivative of the total cost function in order to get the optimal solution. But this approach requires calculation of the second derivative of the function. Avoiding this complex computation we use another iterative method presented by the second author. One of the goals of this paper is to present a unified convergence theory of this method. Then we give a numerical example to show the application of our theory.

A Lagrangian meshfree method applied to linear and nonlinear elasticity.

PubMed

Walker, Wade A

2017-01-01

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code.

Elastic Differential Cross Sections

NASA Technical Reports Server (NTRS)

Werneth, Charles M.; Maung, Khin M.; Ford, William P.; Norbury, John W.; Vera, Michael D.

2014-01-01

The eikonal, partial wave (PW) Lippmann-Schwinger, and three-dimensional Lippmann-Schwinger (LS3D) methods are compared for nuclear reactions that are relevant for space radiation applications. Numerical convergence of the eikonal method is readily achieved when exact formulas of the optical potential are used for light nuclei (A less than or equal to 16) and the momentum-space optical potential is used for heavier nuclei. The PW solution method is known to be numerically unstable for systems that require a large number of partial waves, and, as a result, the LS3D method is employed. The effect of relativistic kinematics is studied with the PW and LS3D methods and is compared to eikonal results. It is recommended that the LS3D method be used for high energy nucleon- nucleus reactions and nucleus-nucleus reactions at all energies because of its rapid numerical convergence and stability.

Nuclear Cross Sections for Space Radiation Applications

NASA Technical Reports Server (NTRS)

Werneth, C. M.; Maung, K. M.; Ford, W. P.; Norbury, J. W.; Vera, M. D.

2015-01-01

The eikonal, partial wave (PW) Lippmann-Schwinger, and three-dimensional Lippmann-Schwinger (LS3D) methods are compared for nuclear reactions that are relevant for space radiation applications. Numerical convergence of the eikonal method is readily achieved when exact formulas of the optical potential are used for light nuclei (A = 16) and the momentum-space optical potential is used for heavier nuclei. The PW solution method is known to be numerically unstable for systems that require a large number of partial waves, and, as a result, the LS3D method is employed. The effect of relativistic kinematics is studied with the PW and LS3D methods and is compared to eikonal results. It is recommended that the LS3D method be used for high energy nucleon-nucleus reactions and nucleus-nucleus reactions at all energies because of its rapid numerical convergence and stability for both non-relativistic and relativistic kinematics.

A Lagrangian meshfree method applied to linear and nonlinear elasticity

PubMed Central

2017-01-01

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code. PMID:29045443

Robust and Accurate Shock Capturing Method for High-Order Discontinuous Galerkin Methods

NASA Technical Reports Server (NTRS)

Atkins, Harold L.; Pampell, Alyssa

2011-01-01

A simple yet robust and accurate approach for capturing shock waves using a high-order discontinuous Galerkin (DG) method is presented. The method uses the physical viscous terms of the Navier-Stokes equations as suggested by others; however, the proposed formulation of the numerical viscosity is continuous and compact by construction, and does not require the solution of an auxiliary diffusion equation. This work also presents two analyses that guided the formulation of the numerical viscosity and certain aspects of the DG implementation. A local eigenvalue analysis of the DG discretization applied to a shock containing element is used to evaluate the robustness of several Riemann flux functions, and to evaluate algorithm choices that exist within the underlying DG discretization. A second analysis examines exact solutions to the DG discretization in a shock containing element, and identifies a "model" instability that will inevitably arise when solving the Euler equations using the DG method. This analysis identifies the minimum viscosity required for stability. The shock capturing method is demonstrated for high-speed flow over an inviscid cylinder and for an unsteady disturbance in a hypersonic boundary layer. Numerical tests are presented that evaluate several aspects of the shock detection terms. The sensitivity of the results to model parameters is examined with grid and order refinement studies.

32 CFR 701.106 - Collecting information about individuals.

Code of Federal Regulations, 2010 CFR

2010-07-01

... their SSN. E.O. 9397 requires Federal Agencies to use SSNs as numerical identifiers for individuals in... provide their SSNs. In many instances, this becomes the individual's numerical identifier and is used to... in a system of records, a PAS must be provided to the individual, regardless of the method used to...

Computational procedure for finite difference solution of one-dimensional heat conduction problems reduces computer time

NASA Technical Reports Server (NTRS)

Iida, H. T.

1966-01-01

Computational procedure reduces the numerical effort whenever the method of finite differences is used to solve ablation problems for which the surface recession is large relative to the initial slab thickness. The number of numerical operations required for a given maximum space mesh size is reduced.

Using the Multilayer Free-Surface Flow Model to Solve Wave Problems

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

Prokof’ev, V. A., E-mail: ProkofyevVA@vniig.ru

2017-01-15

A method is presented for changing over from a single-layer shallow-water model to a multilayer model with hydrostatic pressure profile and, then, to a multilayer model with nonhydrostatic pressure profile. The method does not require complex procedures for solving the discrete Poisson’s equation and features high computation efficiency. The results of validating the algorithm against experimental data critical for the numerical dissipation of the numerical scheme are presented. Examples are considered.

40 CFR 63.1188 - What performance test requirements must I meet?

Code of Federal Regulations, 2010 CFR

2010-07-01

... Performance Tests and Methods § 63.1188 What performance test requirements must I meet? You must meet the... numerical emission limit for PM, CO, or formaldehyde, or at the inlet and outlet of the control device if...

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.

Lattice Boltzmann modeling of transport phenomena in fuel cells and flow batteries

NASA Astrophysics Data System (ADS)

Xu, Ao; Shyy, Wei; Zhao, Tianshou

2017-06-01

Fuel cells and flow batteries are promising technologies to address climate change and air pollution problems. An understanding of the complex multiscale and multiphysics transport phenomena occurring in these electrochemical systems requires powerful numerical tools. Over the past decades, the lattice Boltzmann (LB) method has attracted broad interest in the computational fluid dynamics and the numerical heat transfer communities, primarily due to its kinetic nature making it appropriate for modeling complex multiphase transport phenomena. More importantly, the LB method fits well with parallel computing due to its locality feature, which is required for large-scale engineering applications. In this article, we review the LB method for gas-liquid two-phase flows, coupled fluid flow and mass transport in porous media, and particulate flows. Examples of applications are provided in fuel cells and flow batteries. Further developments of the LB method are also outlined.

Design of two-dimensional channels with prescribed velocity distributions along the channel walls

NASA Technical Reports Server (NTRS)

Stanitz, John D

1953-01-01

A general method of design is developed for two-dimensional unbranched channels with prescribed velocities as a function of arc length along the channel walls. The method is developed for both compressible and incompressible, irrotational, nonviscous flow and applies to the design of elbows, diffusers, nozzles, and so forth. In part I solutions are obtained by relaxation methods; in part II solutions are obtained by a Green's function. Five numerical examples are given in part I including three elbow designs with the same prescribed velocity as a function of arc length along the channel walls but with incompressible, linearized compressible, and compressible flow. One numerical example is presented in part II for an accelerating elbow with linearized compressible flow, and the time required for the solution by a Green's function in part II was considerably less than the time required for the same solution by relaxation methods in part I.

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...

Numerical solution of the quantum Lenard-Balescu equation for a non-degenerate one-component plasma

DOE PAGES

Scullard, Christian R.; Belt, Andrew P.; Fennell, Susan C.; ...

2016-09-01

We present a numerical solution of the quantum Lenard-Balescu equation using a spectral method, namely an expansion in Laguerre polynomials. This method exactly conserves both particles and kinetic energy and facilitates the integration over the dielectric function. To demonstrate the method, we solve the equilibration problem for a spatially homogeneous one-component plasma with various initial conditions. Unlike the more usual Landau/Fokker-Planck system, this method requires no input Coulomb logarithm; the logarithmic terms in the collision integral arise naturally from the equation along with the non-logarithmic order-unity terms. The spectral method can also be used to solve the Landau equation andmore » a quantum version of the Landau equation in which the integration over the wavenumber requires only a lower cutoff. We solve these problems as well and compare them with the full Lenard-Balescu solution in the weak-coupling limit. Finally, we discuss the possible generalization of this method to include spatial inhomogeneity and velocity anisotropy.« less

Rapid analysis of scattering from periodic dielectric structures using accelerated Cartesian expansions

DOE PAGES

Baczewski, Andrew David; Miller, Nicholas C.; Shanker, Balasubramaniam

2012-03-22

Here, the analysis of fields in periodic dielectric structures arise in numerous applications of recent interest, ranging from photonic bandgap structures and plasmonically active nanostructures to metamaterials. To achieve an accurate representation of the fields in these structures using numerical methods, dense spatial discretization is required. This, in turn, affects the cost of analysis, particularly for integral-equation-based methods, for which traditional iterative methods require Ο(Ν 2) operations, Ν being the number of spatial degrees of freedom. In this paper, we introduce a method for the rapid solution of volumetric electric field integral equations used in the analysis of doubly periodicmore » dielectric structures. The crux of our method is the accelerated Cartesian expansion algorithm, which is used to evaluate the requisite potentials in Ο(Ν) cost. Results are provided that corroborate our claims of acceleration without compromising accuracy, as well as the application of our method to a number of compelling photonics applications.« less

Numerical techniques for the solution of the compressible Navier-Stokes equations and implementation of turbulence models. [separated turbulent boundary layer flow problems

NASA Technical Reports Server (NTRS)

Baldwin, B. S.; Maccormack, R. W.; Deiwert, G. S.

1975-01-01

The time-splitting explicit numerical method of MacCormack is applied to separated turbulent boundary layer flow problems. Modifications of this basic method are developed to counter difficulties associated with complicated geometry and severe numerical resolution requirements of turbulence model equations. The accuracy of solutions is investigated by comparison with exact solutions for several simple cases. Procedures are developed for modifying the basic method to improve the accuracy. Numerical solutions of high-Reynolds-number separated flows over an airfoil and shock-separated flows over a flat plate are obtained. A simple mixing length model of turbulence is used for the transonic flow past an airfoil. A nonorthogonal mesh of arbitrary configuration facilitates the description of the flow field. For the simpler geometry associated with the flat plate, a rectangular mesh is used, and solutions are obtained based on a two-equation differential model of turbulence.

Numerical modeling of the radiative transfer in a turbid medium using the synthetic iteration.

PubMed

Budak, Vladimir P; Kaloshin, Gennady A; Shagalov, Oleg V; Zheltov, Victor S

2015-07-27

In this paper we propose the fast, but the accurate algorithm for numerical modeling of light fields in the turbid media slab. For the numerical solution of the radiative transfer equation (RTE) it is required its discretization based on the elimination of the solution anisotropic part and the replacement of the scattering integral by a finite sum. The solution regular part is determined numerically. A good choice of the method of the solution anisotropic part elimination determines the high convergence of the algorithm in the mean square metric. The method of synthetic iterations can be used to improve the convergence in the uniform metric. A significant increase in the solution accuracy with the use of synthetic iterations allows applying the two-stream approximation for the regular part determination. This approach permits to generalize the proposed method in the case of an arbitrary 3D geometry of the medium.

Combining existing numerical models with data assimilation using weighted least-squares finite element methods.

PubMed

Rajaraman, Prathish K; Manteuffel, T A; Belohlavek, M; Heys, Jeffrey J

2017-01-01

A new approach has been developed for combining and enhancing the results from an existing computational fluid dynamics model with experimental data using the weighted least-squares finite element method (WLSFEM). Development of the approach was motivated by the existence of both limited experimental blood velocity in the left ventricle and inexact numerical models of the same flow. Limitations of the experimental data include measurement noise and having data only along a two-dimensional plane. Most numerical modeling approaches do not provide the flexibility to assimilate noisy experimental data. We previously developed an approach that could assimilate experimental data into the process of numerically solving the Navier-Stokes equations, but the approach was limited because it required the use of specific finite element methods for solving all model equations and did not support alternative numerical approximation methods. The new approach presented here allows virtually any numerical method to be used for approximately solving the Navier-Stokes equations, and then the WLSFEM is used to combine the experimental data with the numerical solution of the model equations in a final step. The approach dynamically adjusts the influence of the experimental data on the numerical solution so that more accurate data are more closely matched by the final solution and less accurate data are not closely matched. The new approach is demonstrated on different test problems and provides significantly reduced computational costs compared with many previous methods for data assimilation. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Spectrum analysis on quality requirements consideration in software design documents.

PubMed

Kaiya, Haruhiko; Umemura, Masahiro; Ogata, Shinpei; Kaijiri, Kenji

2013-12-01

Software quality requirements defined in the requirements analysis stage should be implemented in the final products, such as source codes and system deployment. To guarantee this meta-requirement, quality requirements should be considered in the intermediate stages, such as the design stage or the architectural definition stage. We propose a novel method for checking whether quality requirements are considered in the design stage. In this method, a technique called "spectrum analysis for quality requirements" is applied not only to requirements specifications but also to design documents. The technique enables us to derive the spectrum of a document, and quality requirements considerations in the document are numerically represented in the spectrum. We can thus objectively identify whether the considerations of quality requirements in a requirements document are adapted to its design document. To validate the method, we applied it to commercial software systems with the help of a supporting tool, and we confirmed that the method worked well.

A practically unconditionally gradient stable scheme for the N-component Cahn-Hilliard system

NASA Astrophysics Data System (ADS)

Lee, Hyun Geun; Choi, Jeong-Whan; Kim, Junseok

2012-02-01

We present a practically unconditionally gradient stable conservative nonlinear numerical scheme for the N-component Cahn-Hilliard system modeling the phase separation of an N-component mixture. The scheme is based on a nonlinear splitting method and is solved by an efficient and accurate nonlinear multigrid method. The scheme allows us to convert the N-component Cahn-Hilliard system into a system of N-1 binary Cahn-Hilliard equations and significantly reduces the required computer memory and CPU time. We observe that our numerical solutions are consistent with the linear stability analysis results. We also demonstrate the efficiency of the proposed scheme with various numerical experiments.

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

Kaurov, Alexander A., E-mail: kaurov@uchicago.edu

The methods for studying the epoch of cosmic reionization vary from full radiative transfer simulations to purely analytical models. While numerical approaches are computationally expensive and are not suitable for generating many mock catalogs, analytical methods are based on assumptions and approximations. We explore the interconnection between both methods. First, we ask how the analytical framework of excursion set formalism can be used for statistical analysis of numerical simulations and visual representation of the morphology of ionization fronts. Second, we explore the methods of training the analytical model on a given numerical simulation. We present a new code which emergedmore » from this study. Its main application is to match the analytical model with a numerical simulation. Then, it allows one to generate mock reionization catalogs with volumes exceeding the original simulation quickly and computationally inexpensively, meanwhile reproducing large-scale statistical properties. These mock catalogs are particularly useful for cosmic microwave background polarization and 21 cm experiments, where large volumes are required to simulate the observed signal.« less

Efficient analytical implementation of the DOT Riemann solver for the de Saint Venant-Exner morphodynamic model

NASA Astrophysics Data System (ADS)

Carraro, F.; Valiani, A.; Caleffi, V.

2018-03-01

Within the framework of the de Saint Venant equations coupled with the Exner equation for morphodynamic evolution, this work presents a new efficient implementation of the Dumbser-Osher-Toro (DOT) scheme for non-conservative problems. The DOT path-conservative scheme is a robust upwind method based on a complete Riemann solver, but it has the drawback of requiring expensive numerical computations. Indeed, to compute the non-linear time evolution in each time step, the DOT scheme requires numerical computation of the flux matrix eigenstructure (the totality of eigenvalues and eigenvectors) several times at each cell edge. In this work, an analytical and compact formulation of the eigenstructure for the de Saint Venant-Exner (dSVE) model is introduced and tested in terms of numerical efficiency and stability. Using the original DOT and PRICE-C (a very efficient FORCE-type method) as reference methods, we present a convergence analysis (error against CPU time) to study the performance of the DOT method with our new analytical implementation of eigenstructure calculations (A-DOT). In particular, the numerical performance of the three methods is tested in three test cases: a movable bed Riemann problem with analytical solution; a problem with smooth analytical solution; a test in which the water flow is characterised by subcritical and supercritical regions. For a given target error, the A-DOT method is always the most efficient choice. Finally, two experimental data sets and different transport formulae are considered to test the A-DOT model in more practical case studies.

Numerical integration of discontinuous functions: moment fitting and smart octree

NASA Astrophysics Data System (ADS)

Hubrich, Simeon; Di Stolfo, Paolo; Kudela, László; Kollmannsberger, Stefan; Rank, Ernst; Schröder, Andreas; Düster, Alexander

2017-11-01

A fast and simple grid generation can be achieved by non-standard discretization methods where the mesh does not conform to the boundary or the internal interfaces of the problem. However, this simplification leads to discontinuous integrands for intersected elements and, therefore, standard quadrature rules do not perform well anymore. Consequently, special methods are required for the numerical integration. To this end, we present two approaches to obtain quadrature rules for arbitrary domains. The first approach is based on an extension of the moment fitting method combined with an optimization strategy for the position and weights of the quadrature points. In the second approach, we apply the smart octree, which generates curved sub-cells for the integration mesh. To demonstrate the performance of the proposed methods, we consider several numerical examples, showing that the methods lead to efficient quadrature rules, resulting in less integration points and in high accuracy.

An analytically based numerical method for computing view factors in real urban environments

NASA Astrophysics Data System (ADS)

Lee, Doo-Il; Woo, Ju-Wan; Lee, Sang-Hyun

2018-01-01

A view factor is an important morphological parameter used in parameterizing in-canyon radiative energy exchange process as well as in characterizing local climate over urban environments. For realistic representation of the in-canyon radiative processes, a complete set of view factors at the horizontal and vertical surfaces of urban facets is required. Various analytical and numerical methods have been suggested to determine the view factors for urban environments, but most of the methods provide only sky-view factor at the ground level of a specific location or assume simplified morphology of complex urban environments. In this study, a numerical method that can determine the sky-view factors ( ψ ga and ψ wa ) and wall-view factors ( ψ gw and ψ ww ) at the horizontal and vertical surfaces is presented for application to real urban morphology, which are derived from an analytical formulation of the view factor between two blackbody surfaces of arbitrary geometry. The established numerical method is validated against the analytical sky-view factor estimation for ideal street canyon geometries, showing a consolidate confidence in accuracy with errors of less than 0.2 %. Using a three-dimensional building database, the numerical method is also demonstrated to be applicable in determining the sky-view factors at the horizontal (roofs and roads) and vertical (walls) surfaces in real urban environments. The results suggest that the analytically based numerical method can be used for the radiative process parameterization of urban numerical models as well as for the characterization of local urban climate.

Numerical solution of the electron transport equation

NASA Astrophysics Data System (ADS)

Woods, Mark

The electron transport equation has been solved many times for a variety of reasons. The main difficulty in its numerical solution is that it is a very stiff boundary value problem. The most common numerical methods for solving boundary value problems are symmetric collocation methods and shooting methods. Both of these types of methods can only be applied to the electron transport equation if the boundary conditions are altered with unrealistic assumptions because they require too many points to be practical. Further, they result in oscillating and negative solutions, which are physically meaningless for the problem at hand. For these reasons, all numerical methods for this problem to date are a bit unusual because they were designed to try and avoid the problem of extreme stiffness. This dissertation shows that there is no need to introduce spurious boundary conditions or invent other numerical methods for the electron transport equation. Rather, there already exists methods for very stiff boundary value problems within the numerical analysis literature. We demonstrate one such method in which the fast and slow modes of the boundary value problem are essentially decoupled. This allows for an upwind finite difference method to be applied to each mode as is appropriate. This greatly reduces the number of points needed in the mesh, and we demonstrate how this eliminates the need to define new boundary conditions. This method is verified by showing that under certain restrictive assumptions, the electron transport equation has an exact solution that can be written as an integral. We show that the solution from the upwind method agrees with the quadrature evaluation of the exact solution. This serves to verify that the upwind method is properly solving the electron transport equation. Further, it is demonstrated that the output of the upwind method can be used to compute auroral light emissions.

Numerical solution of boundary-integral equations for molecular electrostatics.

PubMed

Bardhan, Jaydeep P

2009-03-07

Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The analysis emphasizes boundary-element method simulations of the integral-equation formulation known as the apparent-surface-charge (ASC) method or polarizable-continuum model (PCM). In many numerical implementations of the ASC/PCM model, one forces the integral equation to be satisfied exactly at a set of discrete points on the boundary. We demonstrate in this paper that this approach to discretization, known as point collocation, is significantly less accurate than an alternative approach known as qualocation. Furthermore, the qualocation method offers this improvement in accuracy without increasing simulation time. Numerical examples demonstrate that electrostatic part of the solvation free energy, when calculated using the collocation and qualocation methods, can differ significantly; for a polypeptide, the answers can differ by as much as 10 kcal/mol (approximately 4% of the total electrostatic contribution to solvation). The applicability of the qualocation discretization to other integral-equation formulations is also discussed, and two equivalences between integral-equation methods are derived.

Sensitivity of Simulated Warm Rain Formation to Collision and Coalescence Efficiencies, Breakup, and Turbulence: Comparison of Two Bin-Resolved Numerical Models

NASA Technical Reports Server (NTRS)

Fridlind, Ann; Seifert, Axel; Ackerman, Andrew; Jensen, Eric

2004-01-01

Numerical models that resolve cloud particles into discrete mass size distributions on an Eulerian grid provide a uniquely powerful means of studying the closely coupled interaction of aerosols, cloud microphysics, and transport that determine cloud properties and evolution. However, such models require many experimentally derived paramaterizations in order to properly represent the complex interactions of droplets within turbulent flow. Many of these parameterizations remain poorly quantified, and the numerical methods of solving the equations for temporal evolution of the mass size distribution can also vary considerably in terms of efficiency and accuracy. In this work, we compare results from two size-resolved microphysics models that employ various widely-used parameterizations and numerical solution methods for several aspects of stochastic collection.

A Quantitative Investigation of Entrainment and Detrainment in Numerically Simulated Convective Clouds. Pt. 1; Model Development

NASA Technical Reports Server (NTRS)

Cohen, Charles

1998-01-01

A method is developed which uses numerical tracers to make accurate diagnoses of entraimnent and detrainment rates and of the properties of the entrained and detrained air in numerically simulated clouds. The numerical advection scheme is modified to make it nondispersive, as required by the use of the tracers. Tests of the new method are made, and an appropriate definition of clouds is selected. Distributions of mixing fractions in the model consistently show maximums at the end points, for nearly undilute environmental air or nearly undilute cloud air, with a uniform distribution between. The cumulonimbus clouds simulated here entrain air that had been substantially changed by the clouds, and detrained air that is not necessarily representative of the cloud air at the same level.

Infinite occupation number basis of bosons: Solving a numerical challenge

NASA Astrophysics Data System (ADS)

Geißler, Andreas; Hofstetter, Walter

2017-06-01

In any bosonic lattice system, which is not dominated by local interactions and thus "frozen" in a Mott-type state, numerical methods have to cope with the infinite size of the corresponding Hilbert space even for finite lattice sizes. While it is common practice to restrict the local occupation number basis to Nc lowest occupied states, the presence of a finite condensate fraction requires the complete number basis for an exact representation of the many-body ground state. In this work we present a truncation scheme to account for contributions from higher number states. By simply adding a single coherent-tail state to this common truncation, we demonstrate increased numerical accuracy and the possible increase in numerical efficiency of this method for the Gutzwiller variational wave function and within dynamical mean-field theory.

Fast and high-order numerical algorithms for the solution of multidimensional nonlinear fractional Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Mohebbi, Akbar

2018-02-01

In this paper we propose two fast and accurate numerical methods for the solution of multidimensional space fractional Ginzburg-Landau equation (FGLE). In the presented methods, to avoid solving a nonlinear system of algebraic equations and to increase the accuracy and efficiency of method, we split the complex problem into simpler sub-problems using the split-step idea. For a homogeneous FGLE, we propose a method which has fourth-order of accuracy in time component and spectral accuracy in space variable and for nonhomogeneous one, we introduce another scheme based on the Crank-Nicolson approach which has second-order of accuracy in time variable. Due to using the Fourier spectral method for fractional Laplacian operator, the resulting schemes are fully diagonal and easy to code. Numerical results are reported in terms of accuracy, computational order and CPU time to demonstrate the accuracy and efficiency of the proposed methods and to compare the results with the analytical solutions. The results show that the present methods are accurate and require low CPU time. It is illustrated that the numerical results are in good agreement with the theoretical ones.

Nonequilibrium hypersonic flows simulations with asymptotic-preserving Monte Carlo methods

NASA Astrophysics Data System (ADS)

Ren, Wei; Liu, Hong; Jin, Shi

2014-12-01

In the rarefied gas dynamics, the DSMC method is one of the most popular numerical tools. It performs satisfactorily in simulating hypersonic flows surrounding re-entry vehicles and micro-/nano- flows. However, the computational cost is expensive, especially when Kn → 0. Even for flows in the near-continuum regime, pure DSMC simulations require a number of computational efforts for most cases. Albeit several DSMC/NS hybrid methods are proposed to deal with this, those methods still suffer from the boundary treatment, which may cause nonphysical solutions. Filbet and Jin [1] proposed a framework of new numerical methods of Boltzmann equation, called asymptotic preserving schemes, whose computational costs are affordable as Kn → 0. Recently, Ren et al. [2] realized the AP schemes with Monte Carlo methods (AP-DSMC), which have better performance than counterpart methods. In this paper, AP-DSMC is applied in simulating nonequilibrium hypersonic flows. Several numerical results are computed and analyzed to study the efficiency and capability of capturing complicated flow characteristics.

Efficient calculation of the polarizability: a simplified effective-energy technique

NASA Astrophysics Data System (ADS)

Berger, J. A.; Reining, L.; Sottile, F.

2012-09-01

In a recent publication [J.A. Berger, L. Reining, F. Sottile, Phys. Rev. B 82, 041103(R) (2010)] we introduced the effective-energy technique to calculate in an accurate and numerically efficient manner the GW self-energy as well as the polarizability, which is required to evaluate the screened Coulomb interaction W. In this work we show that the effective-energy technique can be used to further simplify the expression for the polarizability without a significant loss of accuracy. In contrast to standard sum-over-state methods where huge summations over empty states are required, our approach only requires summations over occupied states. The three simplest approximations we obtain for the polarizability are explicit functionals of an independent- or quasi-particle one-body reduced density matrix. We provide evidence of the numerical accuracy of this simplified effective-energy technique as well as an analysis of our method.

Simulation of violent free surface flow by AMR method

NASA Astrophysics Data System (ADS)

Hu, Changhong; Liu, Cheng

2018-05-01

A novel CFD approach based on adaptive mesh refinement (AMR) technique is being developed for numerical simulation of violent free surface flows. CIP method is applied to the flow solver and tangent of hyperbola for interface capturing with slope weighting (THINC/SW) scheme is implemented as the free surface capturing scheme. The PETSc library is adopted to solve the linear system. The linear solver is redesigned and modified to satisfy the requirement of the AMR mesh topology. In this paper, our CFD method is outlined and newly obtained results on numerical simulation of violent free surface flows are presented.

A Novel Polygonal Finite Element Method: Virtual Node Method

NASA Astrophysics Data System (ADS)

Tang, X. H.; Zheng, C.; Zhang, J. H.

2010-05-01

Polygonal finite element method (PFEM), which can construct shape functions on polygonal elements, provides greater flexibility in mesh generation. However, the non-polynomial form of traditional PFEM, such as Wachspress method and Mean Value method, leads to inexact numerical integration. Since the integration technique for non-polynomial functions is immature. To overcome this shortcoming, a great number of integration points have to be used to obtain sufficiently exact results, which increases computational cost. In this paper, a novel polygonal finite element method is proposed and called as virtual node method (VNM). The features of present method can be list as: (1) It is a PFEM with polynomial form. Thereby, Hammer integral and Gauss integral can be naturally used to obtain exact numerical integration; (2) Shape functions of VNM satisfy all the requirements of finite element method. To test the performance of VNM, intensive numerical tests are carried out. It found that, in standard patch test, VNM can achieve significantly better results than Wachspress method and Mean Value method. Moreover, it is observed that VNM can achieve better results than triangular 3-node elements in the accuracy test.

Adapted all-numerical correlator for face recognition applications

NASA Astrophysics Data System (ADS)

Elbouz, M.; Bouzidi, F.; Alfalou, A.; Brosseau, C.; Leonard, I.; Benkelfat, B.-E.

2013-03-01

In this study, we suggest and validate an all-numerical implementation of a VanderLugt correlator which is optimized for face recognition applications. The main goal of this implementation is to take advantage of the benefits (detection, localization, and identification of a target object within a scene) of correlation methods and exploit the reconfigurability of numerical approaches. This technique requires a numerical implementation of the optical Fourier transform. We pay special attention to adapt the correlation filter to this numerical implementation. One main goal of this work is to reduce the size of the filter in order to decrease the memory space required for real time applications. To fulfil this requirement, we code the reference images with 8 bits and study the effect of this coding on the performances of several composite filters (phase-only filter, binary phase-only filter). The saturation effect has for effect to decrease the performances of the correlator for making a decision when filters contain up to nine references. Further, an optimization is proposed based for an optimized segmented composite filter. Based on this approach, we present tests with different faces demonstrating that the above mentioned saturation effect is significantly reduced while minimizing the size of the learning data base.

Simple numerical method for predicting steady compressible flows

NASA Technical Reports Server (NTRS)

Vonlavante, Ernst; Nelson, N. Duane

1986-01-01

A numerical method for solving the isenthalpic form of the governing equations for compressible viscous and inviscid flows was developed. The method was based on the concept of flux vector splitting in its implicit form. The method was tested on several demanding inviscid and viscous configurations. Two different forms of the implicit operator were investigated. The time marching to steady state was accelerated by the implementation of the multigrid procedure. Its various forms very effectively increased the rate of convergence of the present scheme. High quality steady state results were obtained in most of the test cases; these required only short computational times due to the relative efficiency of the basic method.

A technique for increasing the accuracy of the numerical inversion of the Laplace transform with applications

NASA Technical Reports Server (NTRS)

Berger, B. S.; Duangudom, S.

1973-01-01

A technique is introduced which extends the range of useful approximation of numerical inversion techniques to many cycles of an oscillatory function without requiring either the evaluation of the image function for many values of s or the computation of higher-order terms. The technique consists in reducing a given initial value problem defined over some interval into a sequence of initial value problems defined over a set of subintervals. Several numerical examples demonstrate the utility of the method.

Boundary particle method for Laplace transformed time fractional diffusion equations

NASA Astrophysics Data System (ADS)

Fu, Zhuo-Jia; Chen, Wen; Yang, Hai-Tian

2013-02-01

This paper develops a novel boundary meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation in Laplace space and then employs a truly boundary-only meshless boundary particle method (BPM) to solve this Laplace-transformed problem. Unlike the other boundary discretization methods, the BPM does not require any inner nodes, since the recursive composite multiple reciprocity technique (RC-MRM) is used to convert the inhomogeneous problem into the higher-order homogeneous problem. Finally, the Stehfest numerical inverse Laplace transform (NILT) is implemented to retrieve the numerical solutions of time fractional diffusion equations from the corresponding BPM solutions. In comparison with finite difference discretization, the LTBPM introduces Laplace transform and Stehfest NILT algorithm to deal with time fractional derivative term, which evades costly convolution integral calculation in time fractional derivation approximation and avoids the effect of time step on numerical accuracy and stability. Consequently, it can effectively simulate long time-history fractional diffusion systems. Error analysis and numerical experiments demonstrate that the present LTBPM is highly accurate and computationally efficient for 2D and 3D time fractional diffusion equations.

Reliability-Based Stability Analysis of Rock Slopes Using Numerical Analysis and Response Surface Method

NASA Astrophysics Data System (ADS)

Dadashzadeh, N.; Duzgun, H. S. B.; Yesiloglu-Gultekin, N.

2017-08-01

While advanced numerical techniques in slope stability analysis are successfully used in deterministic studies, they have so far found limited use in probabilistic analyses due to their high computation cost. The first-order reliability method (FORM) is one of the most efficient probabilistic techniques to perform probabilistic stability analysis by considering the associated uncertainties in the analysis parameters. However, it is not possible to directly use FORM in numerical slope stability evaluations as it requires definition of a limit state performance function. In this study, an integrated methodology for probabilistic numerical modeling of rock slope stability is proposed. The methodology is based on response surface method, where FORM is used to develop an explicit performance function from the results of numerical simulations. The implementation of the proposed methodology is performed by considering a large potential rock wedge in Sumela Monastery, Turkey. The accuracy of the developed performance function to truly represent the limit state surface is evaluated by monitoring the slope behavior. The calculated probability of failure is compared with Monte Carlo simulation (MCS) method. The proposed methodology is found to be 72% more efficient than MCS, while the accuracy is decreased with an error of 24%.

High Performance Computing of Meshless Time Domain Method on Multi-GPU Cluster

NASA Astrophysics Data System (ADS)

Ikuno, Soichiro; Nakata, Susumu; Hirokawa, Yuta; Itoh, Taku

2015-01-01

High performance computing of Meshless Time Domain Method (MTDM) on multi-GPU using the supercomputer HA-PACS (Highly Accelerated Parallel Advanced system for Computational Sciences) at University of Tsukuba is investigated. Generally, the finite difference time domain (FDTD) method is adopted for the numerical simulation of the electromagnetic wave propagation phenomena. However, the numerical domain must be divided into rectangle meshes, and it is difficult to adopt the problem in a complexed domain to the method. On the other hand, MTDM can be easily adept to the problem because MTDM does not requires meshes. In the present study, we implement MTDM on multi-GPU cluster to speedup the method, and numerically investigate the performance of the method on multi-GPU cluster. To reduce the computation time, the communication time between the decomposed domain is hided below the perfect matched layer (PML) calculation procedure. The results of computation show that speedup of MTDM on 128 GPUs is 173 times faster than that of single CPU calculation.

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.

Numerical methods for engine-airframe integration

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

Murthy, S.N.B.; Paynter, G.C.

1986-01-01

Various papers on numerical methods for engine-airframe integration are presented. The individual topics considered include: scientific computing environment for the 1980s, overview of prediction of complex turbulent flows, numerical solutions of the compressible Navier-Stokes equations, elements of computational engine/airframe integrations, computational requirements for efficient engine installation, application of CAE and CFD techniques to complete tactical missile design, CFD applications to engine/airframe integration, and application of a second-generation low-order panel methods to powerplant installation studies. Also addressed are: three-dimensional flow analysis of turboprop inlet and nacelle configurations, application of computational methods to the design of large turbofan engine nacelles, comparison ofmore » full potential and Euler solution algorithms for aeropropulsive flow field computations, subsonic/transonic, supersonic nozzle flows and nozzle integration, subsonic/transonic prediction capabilities for nozzle/afterbody configurations, three-dimensional viscous design methodology of supersonic inlet systems for advanced technology aircraft, and a user's technology assessment.« less

On numerical model of one-dimensional time-dependent gas flows through bed of encapsulated phase change material

NASA Astrophysics Data System (ADS)

Lutsenko, N. A.; Fetsov, S. S.

2017-10-01

Mathematical model and numerical method are proposed for investigating the one-dimensional time-dependent gas flows through a packed bed of encapsulated Phase Change Material (PCM). The model is based on the assumption of interacting interpenetrating continua and includes equations of state, continuity, momentum conservation and energy for PCM and gas. The advantage of the method is that it does not require predicting the location of phase transition zone and can define it automatically as in a usual shock-capturing method. One of the applications of the developed numerical model is the simulation of novel Adiabatic Compressed Air Energy Storage system (A-CAES) with Thermal Energy Storage subsystem (TES) based on using the encapsulated PCM in packed bed. Preliminary test calculations give hope that the method can be effectively applied in the future for modelling the charge and discharge processes in such TES with PCM.

An adaptive gridless methodology in one dimension

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

Snyder, N.T.; Hailey, C.E.

1996-09-01

Gridless numerical analysis offers great potential for accurately solving for flow about complex geometries or moving boundary problems. Because gridless methods do not require point connection, the mesh cannot twist or distort. The gridless method utilizes a Taylor series about each point to obtain the unknown derivative terms from the current field variable estimates. The governing equation is then numerically integrated to determine the field variables for the next iteration. Effects of point spacing and Taylor series order on accuracy are studied, and they follow similar trends of traditional numerical techniques. Introducing adaption by point movement using a spring analogymore » allows the solution method to track a moving boundary. The adaptive gridless method models linear, nonlinear, steady, and transient problems. Comparison with known analytic solutions is given for these examples. Although point movement adaption does not provide a significant increase in accuracy, it helps capture important features and provides an improved solution.« less

The application of the large particles method of numerical modeling of the process of carbonic nanostructures synthesis in plasma

NASA Astrophysics Data System (ADS)

Abramov, G. V.; Gavrilov, A. N.

2018-03-01

The article deals with the numerical solution of the mathematical model of the particles motion and interaction in multicomponent plasma by the example of electric arc synthesis of carbon nanostructures. The high order of the particles and the number of their interactions requires a significant input of machine resources and time for calculations. Application of the large particles method makes it possible to reduce the amount of computation and the requirements for hardware resources without affecting the accuracy of numerical calculations. The use of technology of GPGPU parallel computing using the Nvidia CUDA technology allows organizing all General purpose computation on the basis of the graphical processor graphics card. The comparative analysis of different approaches to parallelization of computations to speed up calculations with the choice of the algorithm in which to calculate the accuracy of the solution shared memory is used. Numerical study of the influence of particles density in the macro particle on the motion parameters and the total number of particle collisions in the plasma for different modes of synthesis has been carried out. The rational range of the coherence coefficient of particle in the macro particle is computed.

Validation Methods Research for Fault-Tolerant Avionics and Control Systems Sub-Working Group Meeting. CARE 3 peer review

NASA Technical Reports Server (NTRS)

Trivedi, K. S. (Editor); Clary, J. B. (Editor)

1980-01-01

A computer aided reliability estimation procedure (CARE 3), developed to model the behavior of ultrareliable systems required by flight-critical avionics and control systems, is evaluated. The mathematical models, numerical method, and fault-tolerant architecture modeling requirements are examined, and the testing and characterization procedures are discussed. Recommendations aimed at enhancing CARE 3 are presented; in particular, the need for a better exposition of the method and the user interface is emphasized.

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.

Numerical implementation of complex orthogonalization, parallel transport on Stiefel bundles, and analyticity

NASA Astrophysics Data System (ADS)

Avitabile, Daniele; Bridges, Thomas J.

2010-06-01

Numerical integration of complex linear systems of ODEs depending analytically on an eigenvalue parameter are considered. Complex orthogonalization, which is required to stabilize the numerical integration, results in non-analytic systems. It is shown that properties of eigenvalues are still efficiently recoverable by extracting information from a non-analytic characteristic function. The orthonormal systems are constructed using the geometry of Stiefel bundles. Different forms of continuous orthogonalization in the literature are shown to correspond to different choices of connection one-form on the Stiefel bundle. For the numerical integration, Gauss-Legendre Runge-Kutta algorithms are the principal choice for preserving orthogonality, and performance results are shown for a range of GLRK methods. The theory and methods are tested by application to example boundary value problems including the Orr-Sommerfeld equation in hydrodynamic stability.

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.

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

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.

APPLICATION OF A FINITE-DIFFERENCE TECHNIQUE TO THE HUMAN RADIOFREQUENCY DOSIMETRY PROBLEM

EPA Science Inventory

A powerful finite difference numerical technique has been applied to the human radiofrequency dosimetry problem. The method possesses inherent advantages over the method of moments approach in that its implementation requires much less computer memory. Consequently, it has the ca...

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

NASA Astrophysics Data System (ADS)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

Advanced nodal neutron diffusion method with space-dependent cross sections: ILLICO-VX

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

Rajic, H.L.; Ougouag, A.M.

1987-01-01

Advanced transverse integrated nodal methods for neutron diffusion developed since the 1970s require that node- or assembly-homogenized cross sections be known. The underlying structural heterogeneity can be accurately accounted for in homogenization procedures by the use of heterogeneity or discontinuity factors. Other (milder) types of heterogeneity, burnup-induced or due to thermal-hydraulic feedback, can be resolved by explicitly accounting for the spatial variations of material properties. This can be done during the nodal computations via nonlinear iterations. The new method has been implemented in the code ILLICO-VX (ILLICO variable cross-section method). Numerous numerical tests were performed. As expected, the convergence ratemore » of ILLICO-VX is lower than that of ILLICO, requiring approx. 30% more outer iterations per k/sub eff/ computation. The methodology has also been implemented as the NOMAD-VX option of the NOMAD, multicycle, multigroup, two- and three-dimensional nodal diffusion depletion code. The burnup-induced heterogeneities (space dependence of cross sections) are calculated during the burnup steps.« less

14 CFR 221.41 - Routing.

Code of Federal Regulations, 2010 CFR

2010-01-01

...) Individually stated routings—Method of publication. The routing required by paragraph (a) of this section shall... with their respective explanations of the applicable routings shall be arranged in numerical order in...

Wavenumber-extended high-order oscillation control finite volume schemes for multi-dimensional aeroacoustic computations

NASA Astrophysics Data System (ADS)

Kim, Sungtae; Lee, Soogab; Kim, Kyu Hong

2008-04-01

A new numerical method toward accurate and efficient aeroacoustic computations of multi-dimensional compressible flows has been developed. The core idea of the developed scheme is to unite the advantages of the wavenumber-extended optimized scheme and M-AUSMPW+/MLP schemes by predicting a physical distribution of flow variables more accurately in multi-space dimensions. The wavenumber-extended optimization procedure for the finite volume approach based on the conservative requirement is newly proposed for accuracy enhancement, which is required to capture the acoustic portion of the solution in the smooth region. Furthermore, the new distinguishing mechanism which is based on the Gibbs phenomenon in discontinuity, between continuous and discontinuous regions is introduced to eliminate the excessive numerical dissipation in the continuous region by the restricted application of MLP according to the decision of the distinguishing function. To investigate the effectiveness of the developed method, a sequence of benchmark simulations such as spherical wave propagation, nonlinear wave propagation, shock tube problem and vortex preservation test problem are executed. Also, throughout more realistic shock-vortex interaction and muzzle blast flow problems, the utility of the new method for aeroacoustic applications is verified by comparing with the previous numerical or experimental results.

A multi-scalar PDF approach for LES of turbulent spray combustion

NASA Astrophysics Data System (ADS)

Raman, Venkat; Heye, Colin

2011-11-01

A comprehensive joint-scalar probability density function (PDF) approach is proposed for large eddy simulation (LES) of turbulent spray combustion and tests are conducted to analyze the validity and modeling requirements. The PDF method has the advantage that the chemical source term appears closed but requires models for the small scale mixing process. A stable and consistent numerical algorithm for the LES/PDF approach is presented. To understand the modeling issues in the PDF method, direct numerical simulation of a spray flame at three different fuel droplet Stokes numbers and an equivalent gaseous flame are carried out. Assumptions in closing the subfilter conditional diffusion term in the filtered PDF transport equation are evaluated for various model forms. In addition, the validity of evaporation rate models in high Stokes number flows is analyzed.

Preconditioning the Helmholtz Equation for Rigid Ducts

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1998-01-01

An innovative hyperbolic preconditioning technique is developed for the numerical solution of the Helmholtz equation which governs acoustic propagation in ducts. Two pseudo-time parameters are used to produce an explicit iterative finite difference scheme. This scheme eliminates the large matrix storage requirements normally associated with numerical solutions to the Helmholtz equation. The solution procedure is very fast when compared to other transient and steady methods. Optimization and an error analysis of the preconditioning factors are present. For validation, the method is applied to sound propagation in a 2D semi-infinite hard wall duct.

Explicit evaluation of discontinuities in 2-D unsteady flows solved by the method of characteristics

NASA Astrophysics Data System (ADS)

Osnaghi, C.

When shock waves appear in the numerical solution of flows, a choice is necessary between shock capturing techniques, possible when equations are written in conservative form, and shock fitting techniques. If the second one is preferred, e.g. in order to obtain better definition and more physical description of the shock evolution in time, the method of characteristics is advantageous in the vicinity of the shock and it seems natural to use this method everywhere. This choice requires to improve the efficiency of the numerical scheme in order to produce competitive codes, preserving accuracy and flexibility, which are intrinsic features of the method: this is the goal of the present work.

Fast focus estimation using frequency analysis in digital holography.

PubMed

Oh, Seungtaik; Hwang, Chi-Young; Jeong, Il Kwon; Lee, Sung-Keun; Park, Jae-Hyeung

2014-11-17

A novel fast frequency-based method to estimate the focus distance of digital hologram for a single object is proposed. The focus distance is computed by analyzing the distribution of intersections of smoothed-rays. The smoothed-rays are determined by the directions of energy flow which are computed from local spatial frequency spectrum based on the windowed Fourier transform. So our method uses only the intrinsic frequency information of the optical field on the hologram and therefore does not require any sequential numerical reconstructions and focus detection techniques of conventional photography, both of which are the essential parts in previous methods. To show the effectiveness of our method, numerical results and analysis are presented as well.

The CE/SE Method: a CFD Framework for the Challenges of the New Millennium

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Yu, Sheng-Tao

2001-01-01

The space-time conservation element and solution element (CE/SE) method, which was originated and is continuously being developed at NASA Glenn Research Center, is a high-resolution, genuinely multidimensional and unstructured-mesh compatible numerical method for solving conservation laws. Since its inception in 1991, the CE/SE method has been used to obtain highly accurate numerical solutions for 1D, 2D and 3D flow problems involving shocks, contact discontinuities, acoustic waves, vortices, shock/acoustic waves/vortices interactions, shock/boundary layers interactions and chemical reactions. Without the aid of preconditioning or other special techniques, it has been applied to both steady and unsteady flows with speeds ranging from Mach number = 0.00288 to 10. In addition, the method has unique features that allow for (i) the use of very simple non-reflecting boundary conditions, and (ii) a unified wall boundary treatment for viscous and inviscid flows. The CE/SE method was developed with the conviction that, with a solid foundation in physics, a robust, coherent and accurate numerical framework can be built without involving overly complex mathematics. As a result, the method was constructed using a set of design principles that facilitate simplicity, robustness and accuracy. The most important among them are: (i) enforcing both local and global flux conservation in space and time, with flux evaluation at an interface being an integral part of the solution procedure and requiring no interpolation or extrapolation; (ii) unifying space and time and treating them as a single entity; and (iii) requiring that a numerical scheme be built from a nondissipative core scheme such that the numerical dissipation can be effectively controlled and, as a result, will not overwhelm the physical dissipation. Part I of the workshop will be devoted to a discussion of these principles along with a description of how the ID, 2D and 3D CE/SE schemes are constructed. In Part II, various applications of the CE/SE method, particularly those involving chemical reactions and acoustics, will be presented. The workshop will be concluded with a sketch of the future research directions.

Forebody and base region real gas flow in severe planetary entry by a factored implicit numerical method. II - Equilibrium reactive gas

NASA Technical Reports Server (NTRS)

Davy, W. C.; Green, M. J.; Lombard, C. K.

1981-01-01

The factored-implicit, gas-dynamic algorithm has been adapted to the numerical simulation of equilibrium reactive flows. Changes required in the perfect gas version of the algorithm are developed, and the method of coupling gas-dynamic and chemistry variables is discussed. A flow-field solution that approximates a Jovian entry case was obtained by this method and compared with the same solution obtained by HYVIS, a computer program much used for the study of planetary entry. Comparison of surface pressure distribution and stagnation line shock-layer profiles indicates that the two solutions agree well.

Application of symbolic/numeric matrix solution techniques to the NASTRAN program

NASA Technical Reports Server (NTRS)

Buturla, E. M.; Burroughs, S. H.

1977-01-01

The matrix solving algorithm of any finite element algorithm is extremely important since solution of the matrix equations requires a large amount of elapse time due to null calculations and excessive input/output operations. An alternate method of solving the matrix equations is presented. A symbolic processing step followed by numeric solution yields the solution very rapidly and is especially useful for nonlinear problems.

Application of artificial intelligence to impulsive orbital transfers

NASA Technical Reports Server (NTRS)

Burns, Rowland E.

1987-01-01

A generalized technique for the numerical solution of any given class of problems is presented. The technique requires the analytic (or numerical) solution of every applicable equation for all variables that appear in the problem. Conditional blocks are employed to rapidly expand the set of known variables from a minimum of input. The method is illustrated via the use of the Hohmann transfer problem from orbital mechanics.

Scalar self-force on eccentric geodesics in Schwarzschild spacetime: A time-domain computation

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

Haas, Roland

2007-06-15

We calculate the self-force acting on a particle with scalar charge moving on a generic geodesic around a Schwarzschild black hole. This calculation requires an accurate computation of the retarded scalar field produced by the moving charge; this is done numerically with the help of a fourth-order convergent finite-difference scheme formulated in the time domain. The calculation also requires a regularization procedure, because the retarded field is singular on the particle's world line; this is handled mode-by-mode via the mode-sum regularization scheme first introduced by Barack and Ori. This paper presents the numerical method, various numerical tests, and a samplemore » of results for mildly eccentric orbits as well as ''zoom-whirl'' orbits.« less

Assessment of sub-grid scale dispersion closure with regularized deconvolution method in a particle-laden turbulent jet

NASA Astrophysics Data System (ADS)

Wang, Qing; Zhao, Xinyu; Ihme, Matthias

2017-11-01

Particle-laden turbulent flows are important in numerous industrial applications, such as spray combustion engines, solar energy collectors etc. It is of interests to study this type of flows numerically, especially using large-eddy simulations (LES). However, capturing the turbulence-particle interaction in LES remains challenging due to the insufficient representation of the effect of sub-grid scale (SGS) dispersion. In the present work, a closure technique for the SGS dispersion using regularized deconvolution method (RDM) is assessed. RDM was proposed as the closure for the SGS dispersion in a counterflow spray that is studied numerically using finite difference method on a structured mesh. A presumed form of LES filter is used in the simulations. In the present study, this technique has been extended to finite volume method with an unstructured mesh, where no presumption on the filter form is required. The method is applied to a series of particle-laden turbulent jets. Parametric analyses of the model performance are conducted for flows with different Stokes numbers and Reynolds numbers. The results from LES will be compared against experiments and direct numerical simulations (DNS).

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.

On a modified streamline curvature method for the Euler equations

NASA Technical Reports Server (NTRS)

Cordova, Jeffrey Q.; Pearson, Carl E.

1988-01-01

A modification of the streamline curvature method leads to a quasilinear second-order partial differential equation for the streamline coordinate function. The existence of a stream function is not required. The method is applied to subsonic and supersonic nozzle flow, and to axially symmetric flow with swirl. For many situations, the associated numerical method is both fast and accurate.

On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes

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

Rembiasz, Tomasz; Obergaulinger, Martin; Cerdá-Durán, Pablo

2017-06-01

We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfvén waves, and the tearing mode (TM) instability using the MHD code Aenus. By comparing the simulation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of TMs, we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast magnetosonic speed and wavelength are the characteristic velocity and length, respectively, ofmore » the aforementioned (relatively simple) systems. We also determine the dependence of the numerical viscosity and resistivity on the time integration method, the spatial reconstruction scheme and (to a lesser extent) the Riemann solver employed in the simulations. From the measured results, we infer the numerical resolution (as a function of the spatial reconstruction method) required to properly resolve the growth and saturation level of the magnetic field amplified by the magnetorotational instability in the post-collapsed core of massive stars. Our results show that it is most advantageous to resort to ultra-high-order methods (e.g., the ninth-order monotonicity-preserving method) to tackle this problem properly, in particular, in three-dimensional simulations.« less

Simple Criteria to Determine the Set of Key Parameters of the DRPE Method by a Brute-force Attack

NASA Astrophysics Data System (ADS)

Nalegaev, S. S.; Petrov, N. V.

Known techniques of breaking Double Random Phase Encoding (DRPE), which bypass the resource-intensive brute-force method, require at least two conditions: the attacker knows the encryption algorithm; there is an access to the pairs of source and encoded images. Our numerical results show that for the accurate recovery by numerical brute-force attack, someone needs only some a priori information about the source images, which can be quite general. From the results of our numerical experiments with optical data encryption DRPE with digital holography, we have proposed four simple criteria for guaranteed and accurate data recovery. These criteria can be applied, if the grayscale, binary (including QR-codes) or color images are used as a source.

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.

The Use of Iterative Linear-Equation Solvers in Codes for Large Systems of Stiff IVPs (Initial-Value Problems) for ODEs (Ordinary Differential Equations).

DTIC Science & Technology

1984-04-01

numerical solution, of sstem ot stiff Wh-f Cr ODs. Fro- qontl. a substantial portia of the total computationskwok and cooap required! to solve stiff...exep, possl- bly, foreciadalms of problem. That is% a syste of linewat o nonlinear algebrac equa- tion mumt be solved at auk step of the numerical ...onjugate gradient method [431 is a mall-know ezuze, have prove to be particularly -2- efecti for solving the linear stwem that &ise in the numerical

Method for calculating the aerodynamic loading on an oscillating finite wing in subsonic and sonic flow

NASA Technical Reports Server (NTRS)

Runyan, Harry L; Woolston, Donald S

1957-01-01

A method is presented for calculating the loading on a finite wing oscillating in subsonic or sonic flow. The method is applicable to any plan form and may be used for determining the loading on deformed wings. The procedure is approximate and requires numerical integration over the wing surface.

Optimal control of a variable spin speed CMG system for space vehicles. [Control Moment Gyros

NASA Technical Reports Server (NTRS)

Liu, T. C.; Chubb, W. B.; Seltzer, S. M.; Thompson, Z.

1973-01-01

Many future NASA programs require very high accurate pointing stability. These pointing requirements are well beyond anything attempted to date. This paper suggests a control system which has the capability of meeting these requirements. An optimal control law for the suggested system is specified. However, since no direct method of solution is known for this complicated system, a computation technique using successive approximations is used to develop the required solution. The method of calculus of variations is applied for estimating the changes of index of performance as well as those constraints of inequality of state variables and terminal conditions. Thus, an algorithm is obtained by the steepest descent method and/or conjugate gradient method. Numerical examples are given to show the optimal controls.

Numerical Simulation of Transitional, Hypersonic Flows using a Hybrid Particle-Continuum Method

NASA Astrophysics Data System (ADS)

Verhoff, Ashley Marie

Analysis of hypersonic flows requires consideration of multiscale phenomena due to the range of flight regimes encountered, from rarefied conditions in the upper atmosphere to fully continuum flow at low altitudes. At transitional Knudsen numbers there are likely to be localized regions of strong thermodynamic nonequilibrium effects that invalidate the continuum assumptions of the Navier-Stokes equations. Accurate simulation of these regions, which include shock waves, boundary and shear layers, and low-density wakes, requires a kinetic theory-based approach where no prior assumptions are made regarding the molecular distribution function. Because of the nature of these types of flows, there is much to be gained in terms of both numerical efficiency and physical accuracy by developing hybrid particle-continuum simulation approaches. The focus of the present research effort is the continued development of the Modular Particle-Continuum (MPC) method, where the Navier-Stokes equations are solved numerically using computational fluid dynamics (CFD) techniques in regions of the flow field where continuum assumptions are valid, and the direct simulation Monte Carlo (DSMC) method is used where strong thermodynamic nonequilibrium effects are present. Numerical solutions of transitional, hypersonic flows are thus obtained with increased physical accuracy relative to CFD alone, and improved numerical efficiency is achieved in comparison to DSMC alone because this more computationally expensive method is restricted to those regions of the flow field where it is necessary to maintain physical accuracy. In this dissertation, a comprehensive assessment of the physical accuracy of the MPC method is performed, leading to the implementation of a non-vacuum supersonic outflow boundary condition in particle domains, and more consistent initialization of DSMC simulator particles along hybrid interfaces. The relative errors between MPC and full DSMC results are greatly reduced as a direct result of these improvements. Next, a new parameter for detecting rotational nonequilibrium effects is proposed and shown to offer advantages over other continuum breakdown parameters, achieving further accuracy gains. Lastly, the capabilities of the MPC method are extended to accommodate multiple chemical species in rotational nonequilibrium, each of which is allowed to equilibrate independently, enabling application of the MPC method to more realistic atmospheric flows.

A Formal Approach to Requirements-Based Programming

NASA Technical Reports Server (NTRS)

Hinchey, Michael G.; Rash, James L.; Rouff, Christopher A.

2005-01-01

No significant general-purpose method is currently available to mechanically transform system requirements into a provably equivalent model. The widespread use of such a method represents a necessary step toward high-dependability system engineering for numerous application domains. Current tools and methods that start with a formal model of a system and mechanically produce a provably equivalent implementation are valuable but not sufficient. The "gap" unfilled by such tools and methods is that the formal models cannot be proven to be equivalent to the requirements. We offer a method for mechanically transforming requirements into a provably equivalent formal model that can be used as the basis for code generation and other transformations. This method is unique in offering full mathematical tractability while using notations and techniques that are well known and well trusted. Finally, we describe further application areas we are investigating for use of the approach.

Reinforcement learning for resource allocation in LEO satellite networks.

PubMed

Usaha, Wipawee; Barria, Javier A

2007-06-01

In this paper, we develop and assess online decision-making algorithms for call admission and routing for low Earth orbit (LEO) satellite networks. It has been shown in a recent paper that, in a LEO satellite system, a semi-Markov decision process formulation of the call admission and routing problem can achieve better performance in terms of an average revenue function than existing routing methods. However, the conventional dynamic programming (DP) numerical solution becomes prohibited as the problem size increases. In this paper, two solution methods based on reinforcement learning (RL) are proposed in order to circumvent the computational burden of DP. The first method is based on an actor-critic method with temporal-difference (TD) learning. The second method is based on a critic-only method, called optimistic TD learning. The algorithms enhance performance in terms of requirements in storage, computational complexity and computational time, and in terms of an overall long-term average revenue function that penalizes blocked calls. Numerical studies are carried out, and the results obtained show that the RL framework can achieve up to 56% higher average revenue over existing routing methods used in LEO satellite networks with reasonable storage and computational requirements.

Designing Adaptive Low Dissipative High Order Schemes

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjoegreen, B.; Parks, John W. (Technical Monitor)

2002-01-01

Proper control of the numerical dissipation/filter to accurately resolve all relevant multiscales of complex flow problems while still maintaining nonlinear stability and efficiency for long-time numerical integrations poses a great challenge to the design of numerical methods. The required type and amount of numerical dissipation/filter are not only physical problem dependent, but also vary from one flow region to another. This is particularly true for unsteady high-speed shock/shear/boundary-layer/turbulence/acoustics interactions and/or combustion problems since the dynamics of the nonlinear effect of these flows are not well-understood. Even with extensive grid refinement, it is of paramount importance to have proper control on the type and amount of numerical dissipation/filter in regions where it is needed.

USING CFD TO ANALYZE NUCLEAR SYSTEMS BEHAVIOR: DEFINING THE VALIDATION REQUIREMENTS

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

Richard Schultz

2012-09-01

A recommended protocol to formulate numeric tool specifications and validation needs in concert with practices accepted by regulatory agencies for advanced reactors is described. The protocol is based on the plant type and perceived transient and accident envelopes that translates to boundary conditions for a process that gives the: (a) key phenomena and figures-of-merit which must be analyzed to ensure that the advanced plant can be licensed, (b) specification of the numeric tool capabilities necessary to perform the required analyses—including bounding calculational uncertainties, and (c) specification of the validation matrices and experiments--including the desired validation data. The result of applyingmore » the process enables a complete program to be defined, including costs, for creating and benchmarking transient and accident analysis methods for advanced reactors. By following a process that is in concert with regulatory agency licensing requirements from the start to finish, based on historical acceptance of past licensing submittals, the methods derived and validated have a high probability of regulatory agency acceptance.« less

Explicit formulation of second and third order optical nonlinearity in the FDTD framework

NASA Astrophysics Data System (ADS)

Varin, Charles; Emms, Rhys; Bart, Graeme; Fennel, Thomas; Brabec, Thomas

2018-01-01

The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell's equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires solving iteratively an implicit form of Maxwell's equations over the entire numerical space and at each time step. Reaching numerical convergence demands significant computational resources and practical implementation often requires major modifications to the core FDTD engine. In this paper, we present an explicit method to include second and third order optical nonlinearity in the FDTD framework based on a nonlinear generalization of the Lorentz dispersion model. A formal derivation of the nonlinear Lorentz dispersion equation is equally provided, starting from the quantum mechanical equations describing nonlinear optics in the two-level approximation. With the proposed approach, numerical integration of optical nonlinearity and dispersion in FDTD is intuitive, transparent, and fully explicit. A strong-field formulation is also proposed, which opens an interesting avenue for FDTD-based modelling of the extreme nonlinear optics phenomena involved in laser filamentation and femtosecond micromachining of dielectrics.

Implicit LES using adaptive filtering

NASA Astrophysics Data System (ADS)

Sun, Guangrui; Domaradzki, Julian A.

2018-04-01

In implicit large eddy simulations (ILES) numerical dissipation prevents buildup of small scale energy in a manner similar to the explicit subgrid scale (SGS) models. If spectral methods are used the numerical dissipation is negligible but it can be introduced by applying a low-pass filter in the physical space, resulting in an effective ILES. In the present work we provide a comprehensive analysis of the numerical dissipation produced by different filtering operations in a turbulent channel flow simulated using a non-dissipative, pseudo-spectral Navier-Stokes solver. The amount of numerical dissipation imparted by filtering can be easily adjusted by changing how often a filter is applied. We show that when the additional numerical dissipation is close to the subgrid-scale (SGS) dissipation of an explicit LES the overall accuracy of ILES is also comparable, indicating that periodic filtering can replace explicit SGS models. A new method is proposed, which does not require any prior knowledge of a flow, to determine the filtering period adaptively. Once an optimal filtering period is found, the accuracy of ILES is significantly improved at low implementation complexity and computational cost. The method is general, performing well for different Reynolds numbers, grid resolutions, and filter shapes.

Faster methods for estimating arc centre position during VAR and results from Ti-6Al-4V and INCONEL 718 alloys

NASA Astrophysics Data System (ADS)

Nair, B. G.; Winter, N.; Daniel, B.; Ward, R. M.

2016-07-01

Direct measurement of the flow of electric current during VAR is extremely difficult due to the aggressive environment as the arc process itself controls the distribution of current. In previous studies the technique of “magnetic source tomography” was presented; this was shown to be effective but it used a computationally intensive iterative method to analyse the distribution of arc centre position. In this paper we present faster computational methods requiring less numerical optimisation to determine the centre position of a single distributed arc both numerically and experimentally. Numerical validation of the algorithms were done on models and experimental validation on measurements based on titanium and nickel alloys (Ti6Al4V and INCONEL 718). The results are used to comment on the effects of process parameters on arc behaviour during VAR.

On the application of the lattice Boltzmann method to the investigation of glottal flow

PubMed Central

Kucinschi, Bogdan R.; Afjeh, Abdollah A.; Scherer, Ronald C.

2008-01-01

The production of voice is directly related to the vibration of the vocal folds, which is generated by the interaction between the glottal flow and the tissue of the vocal folds. In the current study, the aerodynamics of the symmetric glottis is investigated numerically for a number of static configurations. The numerical investigation is based on the lattice Boltzmann method (LBM), which is an alternative approach within computational fluid dynamics. Compared to the traditional Navier–Stokes computational fluid dynamics methods, the LBM is relatively easy to implement and can deal with complex geometries without requiring a dedicated grid generator. The multiple relaxation time model was used to improve the numerical stability. The results obtained with LBM were compared to the results provided by a traditional Navier–Stokes solver and experimental data. It was shown that LBM results are satisfactory for all the investigated cases. PMID:18646995

Markov chain sampling of the O(n) loop models on the infinite plane

NASA Astrophysics Data System (ADS)

Herdeiro, Victor

2017-07-01

A numerical method was recently proposed in Herdeiro and Doyon [Phys. Rev. E 94, 043322 (2016), 10.1103/PhysRevE.94.043322] showing a precise sampling of the infinite plane two-dimensional critical Ising model for finite lattice subsections. The present note extends the method to a larger class of models, namely the O(n) loop gas models for n ∈(1 ,2 ] . We argue that even though the Gibbs measure is nonlocal, it is factorizable on finite subsections when sufficient information on the loops touching the boundaries is stored. Our results attempt to show that provided an efficient Markov chain mixing algorithm and an improved discrete lattice dilation procedure the planar limit of the O(n) models can be numerically studied with efficiency similar to the Ising case. This confirms that scale invariance is the only requirement for the present numerical method to work.

Method for assigning sites to projected generic nuclear power plants

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

Holter, G.M.; Purcell, W.L.; Shutz, M.E.

1986-07-01

Pacific Northwest Laboratory developed a method for forecasting potential locations and startup sequences of nuclear power plants that will be required in the future but have not yet been specifically identified by electric utilities. Use of the method results in numerical ratings for potential nuclear power plant sites located in each of the 10 federal energy regions. The rating for each potential site is obtained from numerical factors assigned to each of 5 primary siting characteristics: (1) cooling water availability, (2) site land area, (3) power transmission land area, (4) proximity to metropolitan areas, and (5) utility plans for themore » site. The sequence of plant startups in each federal energy region is obtained by use of the numerical ratings and the forecasts of generic nuclear power plant startups obtained from the EIA Middle Case electricity forecast. Sites are assigned to generic plants in chronological order according to startup date.« less

Reducing microwave absorption with fast frequency modulation.

PubMed

Qin, Juehang; Hubler, A

2017-05-01

We study the response of a two-level quantum system to a chirp signal, using both numerical and analytical methods. The numerical method is based on numerical solutions of the Schrödinger solution of the two-level system, while the analytical method is based on an approximate solution of the same equations. We find that when two-level systems are perturbed by a chirp signal, the peak population of the initially unpopulated state exhibits a high sensitivity to frequency modulation rate. We also find that the aforementioned sensitivity depends on the strength of the forcing, and weaker forcings result in a higher sensitivity, where the frequency modulation rate required to produce the same reduction in peak population would be lower. We discuss potential applications of this result in the field of microwave power transmission, as it shows applying fast frequency modulation to transmitted microwaves used for power transmission could decrease unintended absorption of microwaves by organic tissue.

40 CFR 35.937-4 - Solicitation and evaluation of proposals.

Code of Federal Regulations, 2010 CFR

2010-07-01

... relative importance attached to each criterion (a numerical weighted formula need not be utilized). (c) All... subpart. The grantee shall also evaluate the candidate's proposed method to accomplish the work required...

Calculation of Radar Probability of Detection in K-Distributed Sea Clutter and Noise

DTIC Science & Technology

2011-04-01

Laguerre polynomials are generated from a recurrence relation, and the nodes and weights are calculated from the eigenvalues and eigenvectors of a...B.P. Flannery, Numerical Recipes in Fortran, Second Edition, Cambridge University Press (1992). 12. W. Gautschi, Orthogonal Polynomials (in Matlab...the integration, with the nodes and weights calculated using matrix methods, so that a general purpose numerical integration routine is not required

Algorithms for the Fractional Calculus: A Selection of Numerical Methods

NASA Technical Reports Server (NTRS)

Diethelm, K.; Ford, N. J.; Freed, A. D.; Luchko, Yu.

2003-01-01

Many recently developed models in areas like viscoelasticity, electrochemistry, diffusion processes, etc. are formulated in terms of derivatives (and integrals) of fractional (non-integer) order. In this paper we present a collection of numerical algorithms for the solution of the various problems arising in this context. We believe that this will give the engineer the necessary tools required to work with fractional models in an efficient way.

Using Formal Methods to Assist in the Requirements Analysis of the Space Shuttle GPS Change Request

NASA Technical Reports Server (NTRS)

DiVito, Ben L.; Roberts, Larry W.

1996-01-01

We describe a recent NASA-sponsored pilot project intended to gauge the effectiveness of using formal methods in Space Shuttle software requirements analysis. Several Change Requests (CR's) were selected as promising targets to demonstrate the utility of formal methods in this application domain. A CR to add new navigation capabilities to the Shuttle, based on Global Positioning System (GPS) technology, is the focus of this report. Carried out in parallel with the Shuttle program's conventional requirements analysis process was a limited form of analysis based on formalized requirements. Portions of the GPS CR were modeled using the language of SRI's Prototype Verification System (PVS). During the formal methods-based analysis, numerous requirements issues were discovered and submitted as official issues through the normal requirements inspection process. Shuttle analysts felt that many of these issues were uncovered earlier than would have occurred with conventional methods. We present a summary of these encouraging results and conclusions we have drawn from the pilot project.

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.

Minimizing Higgs potentials via numerical polynomial homotopy continuation

NASA Astrophysics Data System (ADS)

Maniatis, M.; Mehta, D.

2012-08-01

The study of models with extended Higgs sectors requires to minimize the corresponding Higgs potentials, which is in general very difficult. Here, we apply a recently developed method, called numerical polynomial homotopy continuation (NPHC), which guarantees to find all the stationary points of the Higgs potentials with polynomial-like non-linearity. The detection of all stationary points reveals the structure of the potential with maxima, metastable minima, saddle points besides the global minimum. We apply the NPHC method to the most general Higgs potential having two complex Higgs-boson doublets and up to five real Higgs-boson singlets. Moreover the method is applicable to even more involved potentials. Hence the NPHC method allows to go far beyond the limits of the Gröbner basis approach.

Fast non-overlapping Schwarz domain decomposition methods for solving the neutron diffusion equation

NASA Astrophysics Data System (ADS)

Jamelot, Erell; Ciarlet, Patrick

2013-05-01

Studying numerically the steady state of a nuclear core reactor is expensive, in terms of memory storage and computational time. In order to address both requirements, one can use a domain decomposition method, implemented on a parallel computer. We present here such a method for the mixed neutron diffusion equations, discretized with Raviart-Thomas-Nédélec finite elements. This method is based on the Schwarz iterative algorithm with Robin interface conditions to handle communications. We analyse this method from the continuous point of view to the discrete point of view, and we give some numerical results in a realistic highly heterogeneous 3D configuration. Computations are carried out with the MINOS solver of the APOLLO3® neutronics code. APOLLO3 is a registered trademark in France.

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

Shadid, John Nicolas; Fish, Jacob; Waisman, Haim

Two heuristic strategies intended to enhance the performance of the generalized global basis (GGB) method [H. Waisman, J. Fish, R.S. Tuminaro, J. Shadid, The Generalized Global Basis (GGB) method, International Journal for Numerical Methods in Engineering 61(8), 1243-1269] applied to nonlinear systems are presented. The standard GGB accelerates a multigrid scheme by an additional coarse grid correction that filters out slowly converging modes. This correction requires a potentially costly eigen calculation. This paper considers reusing previously computed eigenspace information. The GGB? scheme enriches the prolongation operator with new eigenvectors while the modified method (MGGB) selectively reuses the same prolongation. Bothmore » methods use the criteria of principal angles between subspaces spanned between the previous and current prolongation operators. Numerical examples clearly indicate significant time savings in particular for the MGGB scheme.« less

Dynamic analysis of ultrasonically levitated droplet with moving particle semi-implicit and distributed point source method

NASA Astrophysics Data System (ADS)

Wada, Yuji; Yuge, Kohei; Nakamura, Ryohei; Tanaka, Hiroki; Nakamura, Kentaro

2015-07-01

Numerical analysis of an ultrasonically levitated droplet with a free surface boundary is discussed. The droplet is known to change its shape from sphere to spheroid when it is suspended in a standing wave owing to the acoustic radiation force. However, few studies on numerical simulation have been reported in association with this phenomenon including fluid dynamics inside the droplet. In this paper, coupled analysis using the distributed point source method (DPSM) and the moving particle semi-implicit (MPS) method, both of which do not require grids or meshes to handle the moving boundary with ease, is suggested. A droplet levitated in a plane standing wave field between a piston-vibrating ultrasonic transducer and a reflector is simulated with the DPSM-MPS coupled method. The dynamic change in the spheroidal shape of the droplet is successfully reproduced numerically, and the gravitational center and the change in the spheroidal aspect ratio are discussed and compared with the previous literature.

Computer numeric control generation of toric surfaces

NASA Astrophysics Data System (ADS)

Bradley, Norman D.; Ball, Gary A.; Keller, John R.

1994-05-01

Until recently, the manufacture of toric ophthalmic lenses relied largely upon expensive, manual techniques for generation and polishing. Recent gains in computer numeric control (CNC) technology and tooling enable lens designers to employ single- point diamond, fly-cutting methods in the production of torics. Fly-cutting methods continue to improve, significantly expanding lens design possibilities while lowering production costs. Advantages of CNC fly cutting include precise control of surface geometry, rapid production with high throughput, and high-quality lens surface finishes requiring minimal polishing. As accessibility and affordability increase within the ophthalmic market, torics promise to dramatically expand lens design choices available to consumers.

Computation of type curves for flow to partially penetrating wells in water-table aquifers

USGS Publications Warehouse

Moench, Allen F.

1993-01-01

Evaluation of Neuman's analytical solution for flow to a well in a homogeneous, anisotropic, water-table aquifer commonly requires large amounts of computation time and can produce inaccurate results for selected combinations of parameters. Large computation times occur because the integrand of a semi-infinite integral involves the summation of an infinite series. Each term of the series requires evaluation of the roots of equations, and the series itself is sometimes slowly convergent. Inaccuracies can result from lack of computer precision or from the use of improper methods of numerical integration. In this paper it is proposed to use a method of numerical inversion of the Laplace transform solution, provided by Neuman, to overcome these difficulties. The solution in Laplace space is simpler in form than the real-time solution; that is, the integrand of the semi-infinite integral does not involve an infinite series or the need to evaluate roots of equations. Because the integrand is evaluated rapidly, advanced methods of numerical integration can be used to improve accuracy with an overall reduction in computation time. The proposed method of computing type curves, for which a partially documented computer program (WTAQ1) was written, was found to reduce computation time by factors of 2 to 20 over the time needed to evaluate the closed-form, real-time solution.

Quantifying induced effects of subsurface renewable energy storage

NASA Astrophysics Data System (ADS)

Bauer, Sebastian; Beyer, Christof; Pfeiffer, Tilmann; Boockmeyer, Anke; Popp, Steffi; Delfs, Jens-Olaf; Wang, Bo; Li, Dedong; Dethlefsen, Frank; Dahmke, Andreas

2015-04-01

New methods and technologies for energy storage are required for the transition to renewable energy sources. Subsurface energy storage systems such as salt caverns or porous formations offer the possibility of hosting large amounts of energy or substance. When employing these systems, an adequate system and process understanding is required in order to assess the feasibility of the individual storage option at the respective site and to predict the complex and interacting effects induced. This understanding is the basis for assessing the potential as well as the risks connected with a sustainable usage of these storage options, especially when considering possible mutual influences. For achieving this aim, in this work synthetic scenarios for the use of the geological underground as an energy storage system are developed and parameterized. The scenarios are designed to represent typical conditions in North Germany. The types of subsurface use investigated here include gas storage and heat storage in porous formations. The scenarios are numerically simulated and interpreted with regard to risk analysis and effect forecasting. For this, the numerical simulators Eclipse and OpenGeoSys are used. The latter is enhanced to include the required coupled hydraulic, thermal, geomechanical and geochemical processes. Using the simulated and interpreted scenarios, the induced effects are quantified individually and monitoring concepts for observing these effects are derived. This presentation will detail the general investigation concept used and analyze the parameter availability for this type of model applications. Then the process implementation and numerical methods required and applied for simulating the induced effects of subsurface storage are detailed and explained. Application examples show the developed methods and quantify induced effects and storage sizes for the typical settings parameterized. This work is part of the ANGUS+ project, funded by the German Ministry of Education and Research (BMBF).

An efficient fully-implicit multislope MUSCL method for multiphase flow with gravity in discrete fractured media

NASA Astrophysics Data System (ADS)

Jiang, Jiamin; Younis, Rami M.

2017-06-01

The first-order methods commonly employed in reservoir simulation for computing the convective fluxes introduce excessive numerical diffusion leading to severe smoothing of displacement fronts. We present a fully-implicit cell-centered finite-volume (CCFV) framework that can achieve second-order spatial accuracy on smooth solutions, while at the same time maintain robustness and nonlinear convergence performance. A novel multislope MUSCL method is proposed to construct the required values at edge centroids in a straightforward and effective way by taking advantage of the triangular mesh geometry. In contrast to the monoslope methods in which a unique limited gradient is used, the multislope concept constructs specific scalar slopes for the interpolations on each edge of a given element. Through the edge centroids, the numerical diffusion caused by mesh skewness is reduced, and optimal second order accuracy can be achieved. Moreover, an improved smooth flux-limiter is introduced to ensure monotonicity on non-uniform meshes. The flux-limiter provides high accuracy without degrading nonlinear convergence performance. The CCFV framework is adapted to accommodate a lower-dimensional discrete fracture-matrix (DFM) model. Several numerical tests with discrete fractured system are carried out to demonstrate the efficiency and robustness of the numerical model.

Numerical experiments with a symmetric high-resolution shock-capturing scheme

NASA Technical Reports Server (NTRS)

Yee, H. C.

1986-01-01

Characteristic-based explicit and implicit total variation diminishing (TVD) schemes for the two-dimensional compressible Euler equations have recently been developed. This is a generalization of recent work of Roe and Davis to a wider class of symmetric (non-upwind) TVD schemes other than Lax-Wendroff. The Roe and Davis schemes can be viewed as a subset of the class of explicit methods. The main properties of the present class of schemes are that they can be implicit, and, when steady-state calculations are sought, the numerical solution is independent of the time step. In a recent paper, a comparison of a linearized form of the present implicit symmetric TVD scheme with an implicit upwind TVD scheme originally developed by Harten and modified by Yee was given. Results favored the symmetric method. It was found that the latter is just as accurate as the upwind method while requiring less computational effort. Currently, more numerical experiments are being conducted on time-accurate calculations and on the effect of grid topology, numerical boundary condition procedures, and different flow conditions on the behavior of the method for steady-state applications. The purpose here is to report experiences with this type of scheme and give guidelines for its use.

A new numerical approach for uniquely solvable exterior Riemann-Hilbert problem on region with corners

NASA Astrophysics Data System (ADS)

Zamzamir, Zamzana; Murid, Ali H. M.; Ismail, Munira

2014-06-01

Numerical solution for uniquely solvable exterior Riemann-Hilbert problem on region with corners at offcorner points has been explored by discretizing the related integral equation using Picard iteration method without any modifications to the left-hand side (LHS) and right-hand side (RHS) of the integral equation. Numerical errors for all iterations are converge to the required solution. However, for certain problems, it gives lower accuracy. Hence, this paper presents a new numerical approach for the problem by treating the generalized Neumann kernel at LHS and the function at RHS of the integral equation. Due to the existence of the corner points, Gaussian quadrature is employed which avoids the corner points during numerical integration. Numerical example on a test region is presented to demonstrate the effectiveness of this formulation.

Evaluation of ground-penetrating radar to detect free-phase hydrocarbons in fractured rocks - Results of numerical modeling and physical experiments

USGS Publications Warehouse

Lane, J.W.; Buursink, M.L.; Haeni, F.P.; Versteeg, R.J.

2000-01-01

The suitability of common-offset ground-penetrating radar (GPR) to detect free-phase hydrocarbons in bedrock fractures was evaluated using numerical modeling and physical experiments. The results of one- and two-dimensional numerical modeling at 100 megahertz indicate that GPR reflection amplitudes are relatively insensitive to fracture apertures ranging from 1 to 4 mm. The numerical modeling and physical experiments indicate that differences in the fluids that fill fractures significantly affect the amplitude and the polarity of electromagnetic waves reflected by subhorizontal fractures. Air-filled and hydrocarbon-filled fractures generate low-amplitude reflections that are in-phase with the transmitted pulse. Water-filled fractures create reflections with greater amplitude and opposite polarity than those reflections created by air-filled or hydrocarbon-filled fractures. The results from the numerical modeling and physical experiments demonstrate it is possible to distinguish water-filled fracture reflections from air- or hydrocarbon-filled fracture reflections, nevertheless subsurface heterogeneity, antenna coupling changes, and other sources of noise will likely make it difficult to observe these changes in GPR field data. This indicates that the routine application of common-offset GPR reflection methods for detection of hydrocarbon-filled fractures will be problematic. Ideal cases will require appropriately processed, high-quality GPR data, ground-truth information, and detailed knowledge of subsurface physical properties. Conversely, the sensitivity of GPR methods to changes in subsurface physical properties as demonstrated by the numerical and experimental results suggests the potential of using GPR methods as a monitoring tool. GPR methods may be suited for monitoring pumping and tracer tests, changes in site hydrologic conditions, and remediation activities.The suitability of common-offset ground-penetrating radar (GPR) to detect free-phase hydrocarbons in bedrock fractures was evaluated using numerical modeling and physical experiments. The results of one- and two-dimensional numerical modeling at 100 megahertz indicate that GPR reflection amplitudes are relatively insensitive to fracture apertures ranging from 1 to 4 mm. The numerical modeling and physical experiments indicate that differences in the fluids that fill fractures significantly affect the amplitude and the polarity of electromagnetic waves reflected by subhorizontal fractures. Air-filled and hydrocarbon-filled fractures generate low-amplitude reflections that are in-phase with the transmitted pulse. Water-filled fractures create reflections with greater amplitude and opposite polarity than those reflections created by air-filled or hydrocarbon-filled fractures. The results from the numerical modeling and physical experiments demonstrate it is possible to distinguish water-filled fracture reflections from air- or hydrocarbon-filled fracture reflections, nevertheless subsurface heterogeneity, antenna coupling changes, and other sources of noise will likely make it difficult to observe these changes in GPR field data. This indicates that the routine application of common-offset GPR reflection methods for detection of hydrocarbon-filled fractures will be problematic. Ideal cases will require appropriately processed, high-quality GPR data, ground-truth information, and detailed knowledge of subsurface physical properties. Conversely, the sensitivity of GPR methods to changes in subsurface physical properties as demonstrated by the numerical and experimental results suggests the potential of using GPR methods as a monitoring tool. GPR methods may be suited for monitoring pumping and tracer tests, changes in site hydrologic conditions, and remediation activities.

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.

Long-Range Educational Policy Planning and the Demand for Educated Manpower in Times of Uncertainty.

ERIC Educational Resources Information Center

Bakke, E. K.

1984-01-01

There is no good method of regulating the educational system based on specific, numerical measurements of labor requirements, and it will be important to integrate uncertainty into future forecasts. Adjustments in demand and supply of educated labor in Norway require a decentralized authority structure providing incentives for institutions and the…

Plasma characteristics in the discharge region of a 20 A emission current hollow cathode

NASA Astrophysics Data System (ADS)

Mingming, SUN; Tianping, ZHANG; Xiaodong, WEN; Weilong, GUO; Jiayao, SONG

2018-02-01

Numerical calculation and fluid simulation methods were used to obtain the plasma characteristics in the discharge region of the LIPS-300 ion thruster’s 20 A emission current hollow cathode and to verify the structural design of the emitter. The results of the two methods indicated that the highest plasma density and electron temperature, which improved significantly in the orifice region, were located in the discharge region of the hollow cathode. The magnitude of plasma density was about 1021 m-3 in the emitter and orifice regions, as obtained by numerical calculations, but decreased exponentially in the plume region with the distance from the orifice exit. Meanwhile, compared to the emitter region, the electron temperature and current improved by about 36% in the orifice region. The hollow cathode performance test results were in good agreement with the numerical calculation results, which proved that that the structural design of the emitter and the orifice met the requirements of a 20 A emission current. The numerical calculation method can be used to estimate plasma characteristics in the preliminary design stage of hollow cathodes.

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.

Fully implicit moving mesh adaptive algorithm

NASA Astrophysics Data System (ADS)

Chacon, Luis

2005-10-01

In many problems of interest, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former is best dealt with with fully implicit methods, which are able to step over fast frequencies to resolve the dynamical time scale of interest. The latter requires grid adaptivity for efficiency. Moving-mesh grid adaptive methods are attractive because they can be designed to minimize the numerical error for a given resolution. However, the required grid governing equations are typically very nonlinear and stiff, and of considerably difficult numerical treatment. Not surprisingly, fully coupled, implicit approaches where the grid and the physics equations are solved simultaneously are rare in the literature, and circumscribed to 1D geometries. In this study, we present a fully implicit algorithm for moving mesh methods that is feasible for multidimensional geometries. A crucial element is the development of an effective multilevel treatment of the grid equation.ootnotetextL. Chac'on, G. Lapenta, A fully implicit, nonlinear adaptive grid strategy, J. Comput. Phys., accepted (2005) We will show that such an approach is competitive vs. uniform grids both from the accuracy (due to adaptivity) and the efficiency standpoints. Results for a variety of models 1D and 2D geometries, including nonlinear diffusion, radiation-diffusion, Burgers equation, and gas dynamics will be presented.

Hybrid matrix method for stable numerical analysis of the propagation of Dirac electrons in gapless bilayer graphene superlattices

NASA Astrophysics Data System (ADS)

Briones-Torres, J. A.; Pernas-Salomón, R.; Pérez-Álvarez, R.; Rodríguez-Vargas, I.

2016-05-01

Gapless bilayer graphene (GBG), like monolayer graphene, is a material system with unique properties, such as anti-Klein tunneling and intrinsic Fano resonances. These properties rely on the gapless parabolic dispersion relation and the chiral nature of bilayer graphene electrons. In addition, propagating and evanescent electron states coexist inherently in this material, giving rise to these exotic properties. In this sense, bilayer graphene is unique, since in most material systems in which Fano resonance phenomena are manifested an external source that provides extended states is required. However, from a numerical standpoint, the presence of evanescent-divergent states in the eigenfunctions linear superposition representing the Dirac spinors, leads to a numerical degradation (the so called Ωd problem) in the practical applications of the standard Coefficient Transfer Matrix (K) method used to study charge transport properties in Bilayer Graphene based multi-barrier systems. We present here a straightforward procedure based in the hybrid compliance-stiffness matrix method (H) that can overcome this numerical degradation. Our results show that in contrast to standard matrix method, the proposed H method is suitable to study the transmission and transport properties of electrons in GBG superlattice since it remains numerically stable regardless the size of the superlattice and the range of values taken by the input parameters: the energy and angle of the incident electrons, the barrier height and the thickness and number of barriers. We show that the matrix determinant can be used as a test of the numerical accuracy in real calculations.

Requirements to Design to Code: Towards a Fully Formal Approach to Automatic Code Generation

NASA Technical Reports Server (NTRS)

Hinchey, Michael G.; Rash, James L.; Rouff, Christopher A.

2004-01-01

A general-purpose method to mechanically transform system requirements into a provably equivalent model has yet to appear. Such a method represents a necessary step toward high-dependability system engineering for numerous possible application domains, including sensor networks and autonomous systems. Currently available tools and methods that start with a formal model of a system and mechanically produce a provably equivalent implementation are valuable but not sufficient. The gap that current tools and methods leave unfilled is that their formal models cannot be proven to be equivalent to the system requirements as originated by the customer. For the classes of systems whose behavior can be described as a finite (but significant) set of scenarios, we offer a method for mechanically transforming requirements (expressed in restricted natural language, or in other appropriate graphical notations) into a provably equivalent formal model that can be used as the basis for code generation and other transformations.

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.

Toward Scientific Numerical Modeling

NASA Technical Reports Server (NTRS)

Kleb, Bil

2007-01-01

Ultimately, scientific numerical models need quantified output uncertainties so that modeling can evolve to better match reality. Documenting model input uncertainties and verifying that numerical models are translated into code correctly, however, are necessary first steps toward that goal. Without known input parameter uncertainties, model sensitivities are all one can determine, and without code verification, output uncertainties are simply not reliable. To address these two shortcomings, two proposals are offered: (1) an unobtrusive mechanism to document input parameter uncertainties in situ and (2) an adaptation of the Scientific Method to numerical model development and deployment. Because these two steps require changes in the computational simulation community to bear fruit, they are presented in terms of the Beckhard-Harris-Gleicher change model.

Numerical simulation of axisymmetric turbulent flow in combustors and diffusors. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Yung, Chain Nan

1988-01-01

A method for predicting turbulent flow in combustors and diffusers is developed. The Navier-Stokes equations, incorporating a turbulence kappa-epsilon model equation, were solved in a nonorthogonal curvilinear coordinate system. The solution applied the finite volume method to discretize the differential equations and utilized the SIMPLE algorithm iteratively to solve the differenced equations. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass, momentum and energy fluxes. The numerical accuracy was assessed using different finite differencing methods, i.e., hybrid, quadratic upwind and skew upwind, to represent the convection terms. Flows in different geometries of combustors and diffusers were simulated and results compared with experimental data and good agreement was obtained.

Triangular dislocation: an analytical, artefact-free solution

NASA Astrophysics Data System (ADS)

Nikkhoo, Mehdi; Walter, Thomas R.

2015-05-01

Displacements and stress-field changes associated with earthquakes, volcanoes, landslides and human activity are often simulated using numerical models in an attempt to understand the underlying processes and their governing physics. The application of elastic dislocation theory to these problems, however, may be biased because of numerical instabilities in the calculations. Here, we present a new method that is free of artefact singularities and numerical instabilities in analytical solutions for triangular dislocations (TDs) in both full-space and half-space. We apply the method to both the displacement and the stress fields. The entire 3-D Euclidean space {R}3 is divided into two complementary subspaces, in the sense that in each one, a particular analytical formulation fulfils the requirements for the ideal, artefact-free solution for a TD. The primary advantage of the presented method is that the development of our solutions involves neither numerical approximations nor series expansion methods. As a result, the final outputs are independent of the scale of the input parameters, including the size and position of the dislocation as well as its corresponding slip vector components. Our solutions are therefore well suited for application at various scales in geoscience, physics and engineering. We validate the solutions through comparison to other well-known analytical methods and provide the MATLAB codes.

Forward-facing cavity and opposing jet combined thermal protection system

NASA Astrophysics Data System (ADS)

Lu, H. B.; Liu, W. Q.

2012-12-01

This paper focuses on the design of a forward-facing cavity and opposing jet combined configuration for thermal protection system (TPS) of hypersonic vehicles. The cooling efficiency of the combined TPS was investigated numerically, and the numerical method was validated by the related experiment in the open literature. The flow field parameters, aerodynamic force, and surface heat flux distribution were obtained. The detailed numerical results show that this kind of combined TPS has an excellent impact on cooling the nose-tip, and it is suitable for the thermal protection of hypersonic vehicles which require long-range and time to cruise.

Application of up-sampling and resolution scaling to Fresnel reconstruction of digital holograms.

PubMed

Williams, Logan A; Nehmetallah, Georges; Aylo, Rola; Banerjee, Partha P

2015-02-20

Fresnel transform implementation methods using numerical preprocessing techniques are investigated in this paper. First, it is shown that up-sampling dramatically reduces the minimum reconstruction distance requirements and allows maximal signal recovery by eliminating aliasing artifacts which typically occur at distances much less than the Rayleigh range of the object. Second, zero-padding is employed to arbitrarily scale numerical resolution for the purpose of resolution matching multiple holograms, where each hologram is recorded using dissimilar geometric or illumination parameters. Such preprocessing yields numerical resolution scaling at any distance. Both techniques are extensively illustrated using experimental results.

Hints for an extension of the early exercise premium formula for American options

NASA Astrophysics Data System (ADS)

Bermin, Hans-Peter; Kohatsu-Higa, Arturo; Perelló, Josep

2005-09-01

There exists a non-closed formula for the American put option price and non-trivial computations are required to solve it. Strong efforts have been made to propose efficient numerical techniques but few have strong mathematical reasoning to ascertain why they work well. We present an extension of the American put price aiming to catch weaknesses of the numerical methods based on their non-fulfillment of the smooth pasting condition.

Using SpF to Achieve Petascale for Legacy Pseudospectral Applications

NASA Technical Reports Server (NTRS)

Clune, Thomas L.; Jiang, Weiyuan

2014-01-01

Pseudospectral (PS) methods possess a number of characteristics (e.g., efficiency, accuracy, natural boundary conditions) that are extremely desirable for dynamo models. Unfortunately, dynamo models based upon PS methods face a number of daunting challenges, which include exposing additional parallelism, leveraging hardware accelerators, exploiting hybrid parallelism, and improving the scalability of global memory transposes. Although these issues are a concern for most models, solutions for PS methods tend to require far more pervasive changes to underlying data and control structures. Further, improvements in performance in one model are difficult to transfer to other models, resulting in significant duplication of effort across the research community. We have developed an extensible software framework for pseudospectral methods called SpF that is intended to enable extreme scalability and optimal performance. Highlevel abstractions provided by SpF unburden applications of the responsibility of managing domain decomposition and load balance while reducing the changes in code required to adapt to new computing architectures. The key design concept in SpF is that each phase of the numerical calculation is partitioned into disjoint numerical kernels that can be performed entirely inprocessor. The granularity of domain decomposition provided by SpF is only constrained by the datalocality requirements of these kernels. SpF builds on top of optimized vendor libraries for common numerical operations such as transforms, matrix solvers, etc., but can also be configured to use open source alternatives for portability. SpF includes several alternative schemes for global data redistribution and is expected to serve as an ideal testbed for further research into optimal approaches for different network architectures. In this presentation, we will describe our experience in porting legacy pseudospectral models, MoSST and DYNAMO, to use SpF as well as present preliminary performance results provided by the improved scalability.

A New Runge-Kutta Discontinuous Galerkin Method with Conservation Constraint to Improve CFL Condition for Solving Conservation Laws

PubMed Central

Xu, Zhiliang; Chen, Xu-Yan; Liu, Yingjie

2014-01-01

We present a new formulation of the Runge-Kutta discontinuous Galerkin (RKDG) method [9, 8, 7, 6] for solving conservation Laws with increased CFL numbers. The new formulation requires the computed RKDG solution in a cell to satisfy additional conservation constraint in adjacent cells and does not increase the complexity or change the compactness of the RKDG method. Numerical computations for solving one-dimensional and two-dimensional scalar and systems of nonlinear hyperbolic conservation laws are performed with approximate solutions represented by piecewise quadratic and cubic polynomials, respectively. The hierarchical reconstruction [17, 33] is applied as a limiter to eliminate spurious oscillations in discontinuous solutions. From both numerical experiments and the analytic estimate of the CFL number of the newly formulated method, we find that: 1) this new formulation improves the CFL number over the original RKDG formulation by at least three times or more and thus reduces the overall computational cost; and 2) the new formulation essentially does not compromise the resolution of the numerical solutions of shock wave problems compared with ones computed by the RKDG method. PMID:25414520

Predicting the probability of slip in gait: methodology and distribution study.

PubMed

Gragg, Jared; Yang, James

2016-01-01

The likelihood of a slip is related to the available and required friction for a certain activity, here gait. Classical slip and fall analysis presumed that a walking surface was safe if the difference between the mean available and required friction coefficients exceeded a certain threshold. Previous research was dedicated to reformulating the classical slip and fall theory to include the stochastic variation of the available and required friction when predicting the probability of slip in gait. However, when predicting the probability of a slip, previous researchers have either ignored the variation in the required friction or assumed the available and required friction to be normally distributed. Also, there are no published results that actually give the probability of slip for various combinations of required and available frictions. This study proposes a modification to the equation for predicting the probability of slip, reducing the previous equation from a double-integral to a more convenient single-integral form. Also, a simple numerical integration technique is provided to predict the probability of slip in gait: the trapezoidal method. The effect of the random variable distributions on the probability of slip is also studied. It is shown that both the required and available friction distributions cannot automatically be assumed as being normally distributed. The proposed methods allow for any combination of distributions for the available and required friction, and numerical results are compared to analytical solutions for an error analysis. The trapezoidal method is shown to be highly accurate and efficient. The probability of slip is also shown to be sensitive to the input distributions of the required and available friction. Lastly, a critical value for the probability of slip is proposed based on the number of steps taken by an average person in a single day.

Numerical investigation of a modified family of centered schemes applied to multiphase equations with nonconservative sources

NASA Astrophysics Data System (ADS)

Crochet, M. W.; Gonthier, K. A.

2013-12-01

Systems of hyperbolic partial differential equations are frequently used to model the flow of multiphase mixtures. These equations often contain sources, referred to as nozzling terms, that cannot be posed in divergence form, and have proven to be particularly challenging in the development of finite-volume methods. Upwind schemes have recently shown promise in properly resolving the steady wave solution of the associated multiphase Riemann problem. However, these methods require a full characteristic decomposition of the system eigenstructure, which may be either unavailable or computationally expensive. Central schemes, such as the Kurganov-Tadmor (KT) family of methods, require minimal characteristic information, which makes them easily applicable to systems with an arbitrary number of phases. However, the proper implementation of nozzling terms in these schemes has been mathematically ambiguous. The primary objectives of this work are twofold: first, an extension of the KT family of schemes is proposed that formally accounts for the nonconservative nozzling sources. This modification results in a semidiscrete form that retains the simplicity of its predecessor and introduces little additional computational expense. Second, this modified method is applied to multiple, but equivalent, forms of the multiphase equations to perform a numerical study by solving several one-dimensional test problems. Both ideal and Mie-Grüneisen equations of state are used, with the results compared to an analytical solution. This study demonstrates that the magnitudes of the resulting numerical errors are sensitive to the form of the equations considered, and suggests an optimal form to minimize these errors. Finally, a separate modification of the wave propagation speeds used in the KT family is also suggested that can reduce the extent of numerical diffusion in multiphase flows.

A new numerical method for calculating extrema of received power for polarimetric SAR

USGS Publications Warehouse

Zhang, Y.; Zhang, Jiahua; Lu, Z.; Gong, W.

2009-01-01

A numerical method called cross-step iteration is proposed to calculate the maximal/minimal received power for polarized imagery based on a target's Kennaugh matrix. This method is much more efficient than the systematic method, which searches for the extrema of received power by varying the polarization ellipse angles of receiving and transmitting polarizations. It is also more advantageous than the Schuler method, which has been adopted by the PolSARPro package, because the cross-step iteration method requires less computation time and can derive both the maximal and minimal received powers, whereas the Schuler method is designed to work out only the maximal received power. The analytical model of received-power optimization indicates that the first eigenvalue of the Kennaugh matrix is the supremum of the maximal received power. The difference between these two parameters reflects the depolarization effect of the target's backscattering, which might be useful for target discrimination. ?? 2009 IEEE.

Thermal radiation view factor: Methods, accuracy and computer-aided procedures

NASA Technical Reports Server (NTRS)

Kadaba, P. V.

1982-01-01

The computer aided thermal analysis programs which predicts the result of predetermined acceptable temperature range prior to stationing of these orbiting equipment in various attitudes with respect to the Sun and the Earth was examined. Complexity of the surface geometries suggests the use of numerical schemes for the determination of these viewfactors. Basic definitions and standard methods which form the basis for various digital computer methods and various numerical methods are presented. The physical model and the mathematical methods on which a number of available programs are built are summarized. The strength and the weaknesses of the methods employed, the accuracy of the calculations and the time required for computations are evaluated. The situations where accuracies are important for energy calculations are identified and methods to save computational times are proposed. Guide to best use of the available programs at several centers and the future choices for efficient use of digital computers are included in the recommendations.

Climate Prediction for Brazil's Nordeste: Performance of Empirical and Numerical Modeling Methods.

NASA Astrophysics Data System (ADS)

Moura, Antonio Divino; Hastenrath, Stefan

2004-07-01

Comparisons of performance of climate forecast methods require consistency in the predictand and a long common reference period. For Brazil's Nordeste, empirical methods developed at the University of Wisconsin use preseason (October January) rainfall and January indices of the fields of meridional wind component and sea surface temperature (SST) in the tropical Atlantic and the equatorial Pacific as input to stepwise multiple regression and neural networking. These are used to predict the March June rainfall at a network of 27 stations. An experiment at the International Research Institute for Climate Prediction, Columbia University, with a numerical model (ECHAM4.5) used global SST information through February to predict the March June rainfall at three grid points in the Nordeste. The predictands for the empirical and numerical model forecasts are correlated at +0.96, and the period common to the independent portion of record of the empirical prediction and the numerical modeling is 1968 99. Over this period, predicted versus observed rainfall are evaluated in terms of correlation, root-mean-square error, absolute error, and bias. Performance is high for both approaches. Numerical modeling produces a correlation of +0.68, moderate errors, and strong negative bias. For the empirical methods, errors and bias are small, and correlations of +0.73 and +0.82 are reached between predicted and observed rainfall.

Mathematical, Constitutive and Numerical Modelling of Catastrophic Landslides and Related Phenomena

NASA Astrophysics Data System (ADS)

Pastor, M.; Fernández Merodo, J. A.; Herreros, M. I.; Mira, P.; González, E.; Haddad, B.; Quecedo, M.; Tonni, L.; Drempetic, V.

2008-02-01

Mathematical and numerical models are a fundamental tool for predicting the behaviour of geostructures and their interaction with the environment. The term “mathematical model” refers to a mathematical description of the more relevant physical phenomena which take place in the problem being analyzed. It is indeed a wide area including models ranging from the very simple ones for which analytical solutions can be obtained to those more complicated requiring the use of numerical approximations such as the finite element method. During the last decades, mathematical, constitutive and numerical models have been very much improved and today their use is widespread both in industry and in research. One special case is that of fast catastrophic landslides, for which simplified methods are not able to provide accurate solutions in many occasions. Moreover, many finite element codes cannot be applied for propagation of the mobilized mass. The purpose of this work is to present an overview of the different alternative mathematical and numerical models which can be applied to both the initiation and propagation mechanisms of fast catastrophic landslides and other related problems such as waves caused by landslides.

Implicitly solving phase appearance and disappearance problems using two-fluid six-equation model

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-01-25

Phase appearance and disappearance issue presents serious numerical challenges in two-phase flow simulations using the two-fluid six-equation model. Numerical challenges arise from the singular equation system when one phase is absent, as well as from the discontinuity in the solution space when one phase appears or disappears. In this work, a high-resolution spatial discretization scheme on staggered grids and fully implicit methods were applied for the simulation of two-phase flow problems using the two-fluid six-equation model. A Jacobian-free Newton-Krylov (JFNK) method was used to solve the discretized nonlinear problem. An improved numerical treatment was proposed and proved to be effectivemore » to handle the numerical challenges. The treatment scheme is conceptually simple, easy to implement, and does not require explicit truncations on solutions, which is essential to conserve mass and energy. Various types of phase appearance and disappearance problems relevant to thermal-hydraulics analysis have been investigated, including a sedimentation problem, an oscillating manometer problem, a non-condensable gas injection problem, a single-phase flow with heat addition problem and a subcooled flow boiling problem. Successful simulations of these problems demonstrate the capability and robustness of the proposed numerical methods and numerical treatments. As a result, volume fraction of the absent phase can be calculated effectively as zero.« less

Method for thermal and structural evaluation of shallow intense-beam deposition in matter

NASA Astrophysics Data System (ADS)

Pilan Zanoni, André

2018-05-01

The projected range of high-intensity proton and heavy-ion beams at energies below a few tens of MeV/A in matter can be as short as a few micrometers. For the evaluation of temperature and stresses from a shallow beam energy deposition in matter conventional numerical 3D models require minuscule element sizes for acceptable element aspect ratio as well as extremely short time steps for numerical convergence. In order to simulate energy deposition using a manageable number of elements this article presents a method using layered elements. This method is applied to beam stoppers and accidental intense-beam impact onto UHV sector valves. In those cases the thermal results from the new method are congruent to those from conventional solid-element and adiabatic models.

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.

Scattering and radiation analysis of three-dimensional cavity arrays via a hybrid finite element method

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.

1992-01-01

A hybrid numerical technique is presented for a characterization of the scattering and radiation properties of three-dimensional cavity arrays recessed in a ground plane. The technique combines the finite element and boundary integral methods and invokes Floquet's representation to formulate a system of equations for the fields at the apertures and those inside the cavities. The system is solved via the conjugate gradient method in conjunction with the Fast Fourier Transform (FFT) thus achieving an O(N) storage requirement. By virtue of the finite element method, the proposed technique is applicable to periodic arrays comprised of cavities having arbitrary shape and filled with inhomogeneous dielectrics. Several numerical results are presented, along with new measured data, which demonstrate the validity, efficiency, and capability of the technique.

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.

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.

Confessions of a robot lobotomist

NASA Technical Reports Server (NTRS)

Gottshall, R. Marc

1994-01-01

Since its inception, numerically controlled (NC) machining methods have been used throughout the aerospace industry to mill, drill, and turn complex shapes by sequentially stepping through motion programs. However, the recent demand for more precision, faster feeds, exotic sensors, and branching execution have existing computer numerical control (CNC) and distributed numerical control (DNC) systems running at maximum controller capacity. Typical disadvantages of current CNC's include fixed memory capacities, limited communication ports, and the use of multiple control languages. The need to tailor CNC's to meet specific applications, whether it be expanded memory, additional communications, or integrated vision, often requires replacing the original controller supplied with the commercial machine tool with a more powerful and capable system. This paper briefly describes the process and equipment requirements for new controllers and their evolutionary implementation in an aerospace environment. The process of controller retrofit with currently available machines is examined, along with several case studies and their computational and architectural implications.

Numerical modeling of heat transfer and pasteurizing value during thermal processing of intact egg.

PubMed

Abbasnezhad, Behzad; Hamdami, Nasser; Monteau, Jean-Yves; Vatankhah, Hamed

2016-01-01

Thermal Pasteurization of Eggs, as a widely used nutritive food, has been simulated. A three-dimensional numerical model, computational fluid dynamics codes of heat transfer equations using heat natural convection, and conduction mechanisms, based on finite element method, was developed to study the effect of air cell size and eggshell thickness. The model, confirmed by comparing experimental and numerical results, was able to predict the temperature profiles, the slowest heating zone, and the required heating time during pasteurization of intact eggs. The results showed that the air cell acted as a heat insulator. Increasing the air cell volume resulted in decreasing of the heat transfer rate, and the increasing the required time of pasteurization (up to 14%). The findings show that the effect on thermal pasteurization of the eggshell thickness was not considerable in comparison to the air cell volume.

Requirements for sustainable schistosomiasis control.

PubMed

Traoré, M

1996-01-01

In Mali the increased transmission of schistosomiasis following the construction of numerous reservoirs and irrigation schemes, together with experience gained in tackling the disease, have led to a major effort to train personnel in control methods, to achieve decentralized delivery and management, and to foster self-reliance in this field. The author outlines the essential components of a sound national control programme requiring long-term commitment.

Numerical Nuclear Second Derivatives on a Computing Grid: Enabling and Accelerating Frequency Calculations on Complex Molecular Systems.

PubMed

Yang, Tzuhsiung; Berry, John F

2018-06-04

The computation of nuclear second derivatives of energy, or the nuclear Hessian, is an essential routine in quantum chemical investigations of ground and transition states, thermodynamic calculations, and molecular vibrations. Analytic nuclear Hessian computations require the resolution of costly coupled-perturbed self-consistent field (CP-SCF) equations, while numerical differentiation of analytic first derivatives has an unfavorable 6 N ( N = number of atoms) prefactor. Herein, we present a new method in which grid computing is used to accelerate and/or enable the evaluation of the nuclear Hessian via numerical differentiation: NUMFREQ@Grid. Nuclear Hessians were successfully evaluated by NUMFREQ@Grid at the DFT level as well as using RIJCOSX-ZORA-MP2 or RIJCOSX-ZORA-B2PLYP for a set of linear polyacenes with systematically increasing size. For the larger members of this group, NUMFREQ@Grid was found to outperform the wall clock time of analytic Hessian evaluation; at the MP2 or B2LYP levels, these Hessians cannot even be evaluated analytically. We also evaluated a 156-atom catalytically relevant open-shell transition metal complex and found that NUMFREQ@Grid is faster (7.7 times shorter wall clock time) and less demanding (4.4 times less memory requirement) than an analytic Hessian. Capitalizing on the capabilities of parallel grid computing, NUMFREQ@Grid can outperform analytic methods in terms of wall time, memory requirements, and treatable system size. The NUMFREQ@Grid method presented herein demonstrates how grid computing can be used to facilitate embarrassingly parallel computational procedures and is a pioneer for future implementations.

Marker-based reconstruction of the kinematics of a chain of segments: a new method that incorporates joint kinematic constraints.

PubMed

Klous, Miriam; Klous, Sander

2010-07-01

The aim of skin-marker-based motion analysis is to reconstruct the motion of a kinematical model from noisy measured motion of skin markers. Existing kinematic models for reconstruction of chains of segments can be divided into two categories: analytical methods that do not take joint constraints into account and numerical global optimization methods that do take joint constraints into account but require numerical optimization of a large number of degrees of freedom, especially when the number of segments increases. In this study, a new and largely analytical method for a chain of rigid bodies is presented, interconnected in spherical joints (chain-method). In this method, the number of generalized coordinates to be determined through numerical optimization is three, irrespective of the number of segments. This new method is compared with the analytical method of Veldpaus et al. [1988, "A Least-Squares Algorithm for the Equiform Transformation From Spatial Marker Co-Ordinates," J. Biomech., 21, pp. 45-54] (Veldpaus-method, a method of the first category) and the numerical global optimization method of Lu and O'Connor [1999, "Bone Position Estimation From Skin-Marker Co-Ordinates Using Global Optimization With Joint Constraints," J. Biomech., 32, pp. 129-134] (Lu-method, a method of the second category) regarding the effects of continuous noise simulating skin movement artifacts and regarding systematic errors in joint constraints. The study is based on simulated data to allow a comparison of the results of the different algorithms with true (noise- and error-free) marker locations. Results indicate a clear trend that accuracy for the chain-method is higher than the Veldpaus-method and similar to the Lu-method. Because large parts of the equations in the chain-method can be solved analytically, the speed of convergence in this method is substantially higher than in the Lu-method. With only three segments, the average number of required iterations with the chain-method is 3.0+/-0.2 times lower than with the Lu-method when skin movement artifacts are simulated by applying a continuous noise model. When simulating systematic errors in joint constraints, the number of iterations for the chain-method was almost a factor 5 lower than the number of iterations for the Lu-method. However, the Lu-method performs slightly better than the chain-method. The RMSD value between the reconstructed and actual marker positions is approximately 57% of the systematic error on the joint center positions for the Lu-method compared with 59% for the chain-method.

Force-controlled absorption in a fully-nonlinear numerical wave tank

NASA Astrophysics Data System (ADS)

Spinneken, Johannes; Christou, Marios; Swan, Chris

2014-09-01

An active control methodology for the absorption of water waves in a numerical wave tank is introduced. This methodology is based upon a force-feedback technique which has previously been shown to be very effective in physical wave tanks. Unlike other methods, an a-priori knowledge of the wave conditions in the tank is not required; the absorption controller being designed to automatically respond to a wide range of wave conditions. In comparison to numerical sponge layers, effective wave absorption is achieved on the boundary, thereby minimising the spatial extent of the numerical wave tank. In contrast to the imposition of radiation conditions, the scheme is inherently capable of absorbing irregular waves. Most importantly, simultaneous generation and absorption can be achieved. This is an important advance when considering inclusion of reflective bodies within the numerical wave tank. In designing the absorption controller, an infinite impulse response filter is adopted, thereby eliminating the problem of non-causality in the controller optimisation. Two alternative controllers are considered, both implemented in a fully-nonlinear wave tank based on a multiple-flux boundary element scheme. To simplify the problem under consideration, the present analysis is limited to water waves propagating in a two-dimensional domain. The paper presents an extensive numerical validation which demonstrates the success of the method for a wide range of wave conditions including regular, focused and random waves. The numerical investigation also highlights some of the limitations of the method, particularly in simultaneously generating and absorbing large amplitude or highly-nonlinear waves. The findings of the present numerical study are directly applicable to related fields where optimum absorption is sought; these include physical wavemaking, wave power absorption and a wide range of numerical wave tank schemes.

Simulations of nearly extremal binary black holes

NASA Astrophysics Data System (ADS)

Giesler, Matthew; Scheel, Mark; Hemberger, Daniel; Lovelace, Geoffrey; Kuper, Kevin; Boyle, Michael; Szilagyi, Bela; Kidder, Lawrence; SXS Collaboration

2015-04-01

Astrophysical black holes could have nearly extremal spins; therefore, nearly extremal black holes could be among the binaries that current and future gravitational-wave observatories will detect. Predicting the gravitational waves emitted by merging black holes requires numerical-relativity simulations, but these simulations are especially challenging when one or both holes have mass m and spin S exceeding the Bowen-York limit of S /m2 = 0 . 93 . Using improved methods we simulate an unequal-mass, precessing binary black hole coalescence, where the larger black hole has S /m2 = 0 . 99 . We also use these methods to simulate a nearly extremal non-precessing binary black hole coalescence, where both black holes have S /m2 = 0 . 994 , nearly reaching the Novikov-Thorne upper bound for holes spun up by thin accretion disks. We demonstrate numerical convergence and estimate the numerical errors of the waveforms; we compare numerical waveforms from our simulations with post-Newtonian and effective-one-body waveforms; and we compare the evolution of the black-hole masses and spins with analytic predictions.

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.

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 calculation procedure for viscous flow in turbomachines, volume 3. [computer programs

NASA Technical Reports Server (NTRS)

Khalil, I.; Sheoran, Y.; Tabakoff, W.

1980-01-01

A method for analyzing the nonadiabatic viscous flow through turbomachine blade passages was developed. The field analysis is based upon the numerical integration of the full incompressible Navier-Stokes equations, together with the energy equation on the blade-to-blade surface. A FORTRAN IV computer program was written based on this method. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system. The flow may be axial, radial or mixed and there may be a change in stream channel thickness in the through-flow direction. The inputs required for two FORTRAN IV programs are presented. The first program considers laminar flows and the second can handle turbulent flows. Numerical examples are included to illustrate the use of the program, and to show the results that are obtained.

Numerical modeling for the retrofit of the hydraulic cooling subsystems in operating power plant

NASA Astrophysics Data System (ADS)

AlSaqoor, S.; Alahmer, A.; Al Quran, F.; Andruszkiewicz, A.; Kubas, K.; Regucki, P.; Wędrychowicz, W.

2017-08-01

This paper presents the possibility of using the numerical methods to analyze the work of hydraulic systems on the example of a cooling system of a power boiler auxiliary devices. The variety of conditions at which hydraulic system that operated in specific engineering subsystems requires an individualized approach to the model solutions that have been developed for these systems modernizing. A mathematical model of a series-parallel propagation for the cooling water was derived and iterative methods were used to solve the system of nonlinear equations. The results of numerical calculations made it possible to analyze different variants of a modernization of the studied system and to indicate its critical elements. An economic analysis of different options allows an investor to choose an optimal variant of a reconstruction of the installation.

The arbitrary order mixed mimetic finite difference method for the diffusion equation

DOE PAGES

Gyrya, Vitaliy; Lipnikov, Konstantin; Manzini, Gianmarco

2016-05-01

Here, we propose an arbitrary-order accurate mimetic finite difference (MFD) method for the approximation of diffusion problems in mixed form on unstructured polygonal and polyhedral meshes. As usual in the mimetic numerical technology, the method satisfies local consistency and stability conditions, which determines the accuracy and the well-posedness of the resulting approximation. The method also requires the definition of a high-order discrete divergence operator that is the discrete analog of the divergence operator and is acting on the degrees of freedom. The new family of mimetic methods is proved theoretically to be convergent and optimal error estimates for flux andmore » scalar variable are derived from the convergence analysis. A numerical experiment confirms the high-order accuracy of the method in solving diffusion problems with variable diffusion tensor. It is worth mentioning that the approximation of the scalar variable presents a superconvergence effect.« less

A Numerical Optimization Approach for Tuning Fuzzy Logic Controllers

NASA Technical Reports Server (NTRS)

Woodard, Stanley E.; Garg, Devendra P.

1998-01-01

This paper develops a method to tune fuzzy controllers using numerical optimization. The main attribute of this approach is that it allows fuzzy logic controllers to be tuned to achieve global performance requirements. Furthermore, this approach allows design constraints to be implemented during the tuning process. The method tunes the controller by parameterizing the membership functions for error, change-in-error and control output. The resulting parameters form a design vector which is iteratively changed to minimize an objective function. The minimal objective function results in an optimal performance of the system. A spacecraft mounted science instrument line-of-sight pointing control is used to demonstrate results.

Computationally efficient method for Fourier transform of highly chirped pulses for laser and parametric amplifier modeling.

PubMed

Andrianov, Alexey; Szabo, Aron; Sergeev, Alexander; Kim, Arkady; Chvykov, Vladimir; Kalashnikov, Mikhail

2016-11-14

We developed an improved approach to calculate the Fourier transform of signals with arbitrary large quadratic phase which can be efficiently implemented in numerical simulations utilizing Fast Fourier transform. The proposed algorithm significantly reduces the computational cost of Fourier transform of a highly chirped and stretched pulse by splitting it into two separate transforms of almost transform limited pulses, thereby reducing the required grid size roughly by a factor of the pulse stretching. The application of our improved Fourier transform algorithm in the split-step method for numerical modeling of CPA and OPCPA shows excellent agreement with standard algorithms.

Numerical Calculation of Non-uniform Magnetization Using Experimental Magnetic Field Data

NASA Astrophysics Data System (ADS)

Jhun, Bukyoung; Jhun, Youngseok; Kim, Seung-wook; Han, JungHyun

2018-05-01

A relation between the distance from the surface of a magnet and the number of cells required for a numerical calculation in order to secure the error below a certain threshold is derived. We also developed a method to obtain the magnetization at each part of the magnet from the experimentally measured magnetic field. This method is applied to three magnets with distinct patterns on magnetic-field-viewing film. Each magnet showed a unique pattern of magnetization. We found that the magnet that shows symmetric magnetization on the magnetic-field-viewing film is not uniformly magnetized. This method can be useful comparing the magnetization between magnets that yield typical magnetic field and those that yield atypical magnetic field.

Power Series Solution to the Pendulum Equation

ERIC Educational Resources Information Center

Benacka, Jan

2009-01-01

This note gives a power series solution to the pendulum equation that enables to investigate the system in an analytical way only, i.e. to avoid numeric methods. A method of determining the number of the terms for getting a required relative error is presented that uses bigger and lesser geometric series. The solution is suitable for modelling the…

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.

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…

LAYER DEPENDENT ADVECTION IN CMAQ

EPA Science Inventory

The advection methods used in CMAQ require that the Courant-Friedrichs-Lewy (CFL) condition be satisfied for numerical stability and accuracy. In CMAQ prior to version 4.3, the ADVSTEP algorithm established CFL-safe synchronization and advection timesteps that were uniform throu...

The numerical simulation of heat transfer during a hybrid laser-MIG welding using equivalent heat source approach

NASA Astrophysics Data System (ADS)

Bendaoud, Issam; Matteï, Simone; Cicala, Eugen; Tomashchuk, Iryna; Andrzejewski, Henri; Sallamand, Pierre; Mathieu, Alexandre; Bouchaud, Fréderic

2014-03-01

The present study is dedicated to the numerical simulation of an industrial case of hybrid laser-MIG welding of high thickness duplex steel UR2507Cu with Y-shaped chamfer geometry. It consists in simulation of heat transfer phenomena using heat equivalent source approach and implementing in finite element software COMSOL Multiphysics. A numerical exploratory designs method is used to identify the heat sources parameters in order to obtain a minimal required difference between the numerical results and the experiment which are the shape of the welded zone and the temperature evolution in different locations. The obtained results were found in good correspondence with experiment, both for melted zone shape and thermal history.

Method for simulating discontinuous physical systems

DOEpatents

Baty, Roy S.; Vaughn, Mark R.

2001-01-01

The mathematical foundations of conventional numerical simulation of physical systems provide no consistent description of the behavior of such systems when subjected to discontinuous physical influences. As a result, the numerical simulation of such problems requires ad hoc encoding of specific experimental results in order to address the behavior of such discontinuous physical systems. In the present invention, these foundations are replaced by a new combination of generalized function theory and nonstandard analysis. The result is a class of new approaches to the numerical simulation of physical systems which allows the accurate and well-behaved simulation of discontinuous and other difficult physical systems, as well as simpler physical systems. Applications of this new class of numerical simulation techniques to process control, robotics, and apparatus design are outlined.

Classical nucleation theory in the phase-field crystal model

NASA Astrophysics Data System (ADS)

Jreidini, Paul; Kocher, Gabriel; Provatas, Nikolas

2018-04-01

A full understanding of polycrystalline materials requires studying the process of nucleation, a thermally activated phase transition that typically occurs at atomistic scales. The numerical modeling of this process is problematic for traditional numerical techniques: commonly used phase-field methods' resolution does not extend to the atomic scales at which nucleation takes places, while atomistic methods such as molecular dynamics are incapable of scaling to the mesoscale regime where late-stage growth and structure formation takes place following earlier nucleation. Consequently, it is of interest to examine nucleation in the more recently proposed phase-field crystal (PFC) model, which attempts to bridge the atomic and mesoscale regimes in microstructure simulations. In this work, we numerically calculate homogeneous liquid-to-solid nucleation rates and incubation times in the simplest version of the PFC model, for various parameter choices. We show that the model naturally exhibits qualitative agreement with the predictions of classical nucleation theory (CNT) despite a lack of some explicit atomistic features presumed in CNT. We also examine the early appearance of lattice structure in nucleating grains, finding disagreement with some basic assumptions of CNT. We then argue that a quantitatively correct nucleation theory for the PFC model would require extending CNT to a multivariable theory.

Classical nucleation theory in the phase-field crystal model.

PubMed

Jreidini, Paul; Kocher, Gabriel; Provatas, Nikolas

2018-04-01

A full understanding of polycrystalline materials requires studying the process of nucleation, a thermally activated phase transition that typically occurs at atomistic scales. The numerical modeling of this process is problematic for traditional numerical techniques: commonly used phase-field methods' resolution does not extend to the atomic scales at which nucleation takes places, while atomistic methods such as molecular dynamics are incapable of scaling to the mesoscale regime where late-stage growth and structure formation takes place following earlier nucleation. Consequently, it is of interest to examine nucleation in the more recently proposed phase-field crystal (PFC) model, which attempts to bridge the atomic and mesoscale regimes in microstructure simulations. In this work, we numerically calculate homogeneous liquid-to-solid nucleation rates and incubation times in the simplest version of the PFC model, for various parameter choices. We show that the model naturally exhibits qualitative agreement with the predictions of classical nucleation theory (CNT) despite a lack of some explicit atomistic features presumed in CNT. We also examine the early appearance of lattice structure in nucleating grains, finding disagreement with some basic assumptions of CNT. We then argue that a quantitatively correct nucleation theory for the PFC model would require extending CNT to a multivariable theory.

Runge-Kutta Methods for Linear Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

Zingg, David W.; Chisholm, Todd T.

1997-01-01

Three new Runge-Kutta methods are presented for numerical integration of systems of linear inhomogeneous ordinary differential equations (ODES) with constant coefficients. Such ODEs arise in the numerical solution of the partial differential equations governing linear wave phenomena. The restriction to linear ODEs with constant coefficients reduces the number of conditions which the coefficients of the Runge-Kutta method must satisfy. This freedom is used to develop methods which are more efficient than conventional Runge-Kutta methods. A fourth-order method is presented which uses only two memory locations per dependent variable, while the classical fourth-order Runge-Kutta method uses three. This method is an excellent choice for simulations of linear wave phenomena if memory is a primary concern. In addition, fifth- and sixth-order methods are presented which require five and six stages, respectively, one fewer than their conventional counterparts, and are therefore more efficient. These methods are an excellent option for use with high-order spatial discretizations.

A semantic framework to protect the privacy of electronic health records with non-numerical attributes.

PubMed

Martínez, Sergio; Sánchez, David; Valls, Aida

2013-04-01

Structured patient data like Electronic Health Records (EHRs) are a valuable source for clinical research. However, the sensitive nature of such information requires some anonymisation procedure to be applied before releasing the data to third parties. Several studies have shown that the removal of identifying attributes, like the Social Security Number, is not enough to obtain an anonymous data file, since unique combinations of other attributes as for example, rare diagnoses and personalised treatments, may lead to patient's identity disclosure. To tackle this problem, Statistical Disclosure Control (SDC) methods have been proposed to mask sensitive attributes while preserving, up to a certain degree, the utility of anonymised data. Most of these methods focus on continuous-scale numerical data. Considering that part of the clinical data found in EHRs is expressed with non-numerical attributes as for example, diagnoses, symptoms, procedures, etc., their application to EHRs produces far from optimal results. In this paper, we propose a general framework to enable the accurate application of SDC methods to non-numerical clinical data, with a focus on the preservation of semantics. To do so, we exploit structured medical knowledge bases like SNOMED CT to propose semantically-grounded operators to compare, aggregate and sort non-numerical terms. Our framework has been applied to several well-known SDC methods and evaluated using a real clinical dataset with non-numerical attributes. Results show that the exploitation of medical semantics produces anonymised datasets that better preserve the utility of EHRs. Copyright © 2012 Elsevier Inc. All rights reserved.

A parallel direct-forcing fictitious domain method for simulating microswimmers

NASA Astrophysics Data System (ADS)

Gao, Tong; Lin, Zhaowu

2017-11-01

We present a 3D parallel direct-forcing fictitious domain method for simulating swimming micro-organisms at small Reynolds numbers. We treat the motile micro-swimmers as spherical rigid particles using the ``Squirmer'' model. The particle dynamics are solved on the moving Larangian meshes that overlay upon a fixed Eulerian mesh for solving the fluid motion, and the momentum exchange between the two phases is resolved by distributing pseudo body-forces over the particle interior regions which constrain the background fictitious fluids to follow the particle movement. While the solid and fluid subproblems are solved separately, no inner-iterations are required to enforce numerical convergence. We demonstrate the accuracy and robustness of the method by comparing our results with the existing analytical and numerical studies for various cases of single particle dynamics and particle-particle interactions. We also perform a series of numerical explorations to obtain statistical and rheological measurements to characterize the dynamics and structures of Squirmer suspensions. NSF DMS 1619960.

Numerical Study on Focusing of Ultrasounds in Microbubble-enhanced HIFU

NASA Astrophysics Data System (ADS)

Matsumoto, Yoichiro; Okita, Kohei; Takagi, Shu

2011-11-01

The injection of microbubbles into the target tissue enhances tissue heating in High-Intensity Focused Ultrasound therapy, via inertial cavitation. The control of the inertial cavitation is required to achieve the efficient tissue ablation. Microbubbles between a transducer and a target disturb the ultrasound propagation depending on the conditions. A method to clear such microbubbles has been proposed by Kajiyama et al. [Physics Procedia 3 (2010) 305-314]. In the method, the irradiation of intense ultrasounds with a burst waveform fragmentize microbubbles in the pathways before the irradiation of ultrasounds for tissue heating. The vitro experiment using a gel containing microbubbles has showed that the method enables to heat the target correctly by controlling the microbubble distribution. Following the experiment, we simulate the focusing of ultrasounds through a mixture containing microbubbles with considering the size and number density distributions in space. The numerical simulation shows that the movement of the heating region from the transducer side to the target by controlling the microbubble distributions. The numerical results elucidate well the experimental ones.

A numerical scheme based on radial basis function finite difference (RBF-FD) technique for solving the high-dimensional nonlinear Schrödinger equations using an explicit time discretization: Runge-Kutta method

NASA Astrophysics Data System (ADS)

Dehghan, Mehdi; Mohammadi, Vahid

2017-08-01

In this research, we investigate the numerical solution of nonlinear Schrödinger equations in two and three dimensions. The numerical meshless method which will be used here is RBF-FD technique. The main advantage of this method is the approximation of the required derivatives based on finite difference technique at each local-support domain as Ωi. At each Ωi, we require to solve a small linear system of algebraic equations with a conditionally positive definite matrix of order 1 (interpolation matrix). This scheme is efficient and its computational cost is same as the moving least squares (MLS) approximation. A challengeable issue is choosing suitable shape parameter for interpolation matrix in this way. In order to overcome this matter, an algorithm which was established by Sarra (2012), will be applied. This algorithm computes the condition number of the local interpolation matrix using the singular value decomposition (SVD) for obtaining the smallest and largest singular values of that matrix. Moreover, an explicit method based on Runge-Kutta formula of fourth-order accuracy will be applied for approximating the time variable. It also decreases the computational costs at each time step since we will not solve a nonlinear system. On the other hand, to compare RBF-FD method with another meshless technique, the moving kriging least squares (MKLS) approximation is considered for the studied model. Our results demonstrate the ability of the present approach for solving the applicable model which is investigated in the current research work.

A fast algorithm for forward-modeling of gravitational fields in spherical coordinates with 3D Gauss-Legendre quadrature

NASA Astrophysics Data System (ADS)

Zhao, G.; Liu, J.; Chen, B.; Guo, R.; Chen, L.

2017-12-01

Forward modeling of gravitational fields at large-scale requires to consider the curvature of the Earth and to evaluate the Newton's volume integral in spherical coordinates. To acquire fast and accurate gravitational effects for subsurface structures, subsurface mass distribution is usually discretized into small spherical prisms (called tesseroids). The gravity fields of tesseroids are generally calculated numerically. One of the commonly used numerical methods is the 3D Gauss-Legendre quadrature (GLQ). However, the traditional GLQ integration suffers from low computational efficiency and relatively poor accuracy when the observation surface is close to the source region. We developed a fast and high accuracy 3D GLQ integration based on the equivalence of kernel matrix, adaptive discretization and parallelization using OpenMP. The equivalence of kernel matrix strategy increases efficiency and reduces memory consumption by calculating and storing the same matrix elements in each kernel matrix just one time. In this method, the adaptive discretization strategy is used to improve the accuracy. The numerical investigations show that the executing time of the proposed method is reduced by two orders of magnitude compared with the traditional method that without these optimized strategies. High accuracy results can also be guaranteed no matter how close the computation points to the source region. In addition, the algorithm dramatically reduces the memory requirement by N times compared with the traditional method, where N is the number of discretization of the source region in the longitudinal direction. It makes the large-scale gravity forward modeling and inversion with a fine discretization possible.

Analysis of ultrasonically rotating droplet using moving particle semi-implicit and distributed point source methods

NASA Astrophysics Data System (ADS)

Wada, Yuji; Yuge, Kohei; Tanaka, Hiroki; Nakamura, Kentaro

2016-07-01

Numerical analysis of the rotation of an ultrasonically levitated droplet with a free surface boundary is discussed. The ultrasonically levitated droplet is often reported to rotate owing to the surface tangential component of acoustic radiation force. To observe the torque from an acoustic wave and clarify the mechanism underlying the phenomena, it is effective to take advantage of numerical simulation using the distributed point source method (DPSM) and moving particle semi-implicit (MPS) method, both of which do not require a calculation grid or mesh. In this paper, the numerical treatment of the viscoacoustic torque, which emerges from the viscous boundary layer and governs the acoustical droplet rotation, is discussed. The Reynolds stress traction force is calculated from the DPSM result using the idea of effective normal particle velocity through the boundary layer and input to the MPS surface particles. A droplet levitated in an acoustic chamber is simulated using the proposed calculation method. The droplet is vertically supported by a plane standing wave from an ultrasonic driver and subjected to a rotating sound field excited by two acoustic sources on the side wall with different phases. The rotation of the droplet is successfully reproduced numerically and its acceleration is discussed and compared with those in the literature.

A conservative fully implicit algorithm for predicting slug flows

NASA Astrophysics Data System (ADS)

Krasnopolsky, Boris I.; Lukyanov, Alexander A.

2018-02-01

An accurate and predictive modelling of slug flows is required by many industries (e.g., oil and gas, nuclear engineering, chemical engineering) to prevent undesired events potentially leading to serious environmental accidents. For example, the hydrodynamic and terrain-induced slugging leads to unwanted unsteady flow conditions. This demands the development of fast and robust numerical techniques for predicting slug flows. The presented in this paper study proposes a multi-fluid model and its implementation method accounting for phase appearance and disappearance. The numerical modelling of phase appearance and disappearance presents a complex numerical challenge for all multi-component and multi-fluid models. Numerical challenges arise from the singular systems of equations when some phases are absent and from the solution discontinuity when some phases appear or disappear. This paper provides a flexible and robust solution to these issues. A fully implicit formulation described in this work enables to efficiently solve governing fluid flow equations. The proposed numerical method provides a modelling capability of phase appearance and disappearance processes, which is based on switching procedure between various sets of governing equations. These sets of equations are constructed using information about the number of phases present in the computational domain. The proposed scheme does not require an explicit truncation of solutions leading to a conservative scheme for mass and linear momentum. A transient two-fluid model is used to verify and validate the proposed algorithm for conditions of hydrodynamic and terrain-induced slug flow regimes. The developed modelling capabilities allow to predict all the major features of the experimental data, and are in a good quantitative agreement with them.

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.

Development and Application of a Numerical Framework for Improving Building Foundation Heat Transfer Calculations

NASA Astrophysics Data System (ADS)

Kruis, Nathanael J. F.

Heat transfer from building foundations varies significantly in all three spatial dimensions and has important dynamic effects at all timescales, from one hour to several years. With the additional consideration of moisture transport, ground freezing, evapotranspiration, and other physical phenomena, the estimation of foundation heat transfer becomes increasingly sophisticated and computationally intensive to the point where accuracy must be compromised for reasonable computation time. The tools currently available to calculate foundation heat transfer are often either too limited in their capabilities to draw meaningful conclusions or too sophisticated to use in common practices. This work presents Kiva, a new foundation heat transfer computational framework. Kiva provides a flexible environment for testing different numerical schemes, initialization methods, spatial and temporal discretizations, and geometric approximations. Comparisons within this framework provide insight into the balance of computation speed and accuracy relative to highly detailed reference solutions. The accuracy and computational performance of six finite difference numerical schemes are verified against established IEA BESTEST test cases for slab-on-grade heat conduction. Of the schemes tested, the Alternating Direction Implicit (ADI) scheme demonstrates the best balance between accuracy, performance, and numerical stability. Kiva features four approaches of initializing soil temperatures for an annual simulation. A new accelerated initialization approach is shown to significantly reduce the required years of presimulation. Methods of approximating three-dimensional heat transfer within a representative two-dimensional context further improve computational performance. A new approximation called the boundary layer adjustment method is shown to improve accuracy over other established methods with a negligible increase in computation time. This method accounts for the reduced heat transfer from concave foundation shapes, which has not been adequately addressed to date. Within the Kiva framework, three-dimensional heat transfer that can require several days to simulate is approximated in two-dimensions in a matter of seconds while maintaining a mean absolute deviation within 3%.

Estimating net rainfall, evaporation and water storage of a bare soil from sequential L-band emissivities

NASA Technical Reports Server (NTRS)

Stroosnijder, L.; Lascano, R. J.; Newton, R. W.; Vanbavel, C. H. M.

1984-01-01

A general method to use a time series of L-band emissivities as an input to a hydrological model for continuously monitoring the net rainfall and evaporation as well as the water content over the entire soil profile is proposed. The model requires a sufficiently accurate and general relation between soil emissivity and surface moisture content. A model which requires the soil hydraulic properties as an additional input, but does not need any weather data was developed. The method is shown to be numerically consistent.

Optimization methods and silicon solar cell numerical models

NASA Technical Reports Server (NTRS)

Girardini, K.

1986-01-01

The goal of this project is the development of an optimization algorithm for use with a solar cell model. It is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junctions depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm has been developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAPID). SCAPID uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the operation of a solar cell. A major obstacle is that the numerical methods used in SCAPID require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the value associated with the maximum efficiency. This problem has been 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. Adapting SCAPID so that it could be called iteratively by the optimization code provided another means of reducing the cpu time required to complete an optimization. Instead of calculating the entire I-V curve, as is usually done in SCAPID, only the efficiency is calculated (maximum power voltage and current) and the solution from previous calculations is used to initiate the next solution.

Fully implicit moving mesh adaptive algorithm

NASA Astrophysics Data System (ADS)

Serazio, C.; Chacon, L.; Lapenta, G.

2006-10-01

In many problems of interest, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former is best dealt with with fully implicit methods, which are able to step over fast frequencies to resolve the dynamical time scale of interest. The latter requires grid adaptivity for efficiency. Moving-mesh grid adaptive methods are attractive because they can be designed to minimize the numerical error for a given resolution. However, the required grid governing equations are typically very nonlinear and stiff, and of considerably difficult numerical treatment. Not surprisingly, fully coupled, implicit approaches where the grid and the physics equations are solved simultaneously are rare in the literature, and circumscribed to 1D geometries. In this study, we present a fully implicit algorithm for moving mesh methods that is feasible for multidimensional geometries. Crucial elements are the development of an effective multilevel treatment of the grid equation, and a robust, rigorous error estimator. For the latter, we explore the effectiveness of a coarse grid correction error estimator, which faithfully reproduces spatial truncation errors for conservative equations. We will show that the moving mesh approach is competitive vs. uniform grids both in accuracy (due to adaptivity) and efficiency. Results for a variety of models 1D and 2D geometries will be presented. L. Chac'on, G. Lapenta, J. Comput. Phys., 212 (2), 703 (2006) G. Lapenta, L. Chac'on, J. Comput. Phys., accepted (2006)

A Galleria Boundary Element Method for two-dimensional nonlinear magnetostatics

NASA Astrophysics Data System (ADS)

Brovont, Aaron D.

The Boundary Element Method (BEM) is a numerical technique for solving partial differential equations that is used broadly among the engineering disciplines. The main advantage of this method is that one needs only to mesh the boundary of a solution domain. A key drawback is the myriad of integrals that must be evaluated to populate the full system matrix. To this day these integrals have been evaluated using numerical quadrature. In this research, a Galerkin formulation of the BEM is derived and implemented to solve two-dimensional magnetostatic problems with a focus on accurate, rapid computation. To this end, exact, closed-form solutions have been derived for all the integrals comprising the system matrix as well as those required to compute fields in post-processing; the need for numerical integration has been eliminated. It is shown that calculation of the system matrix elements using analytical solutions is 15-20 times faster than with numerical integration of similar accuracy. Furthermore, through the example analysis of a c-core inductor, it is demonstrated that the present BEM formulation is a competitive alternative to the Finite Element Method (FEM) for linear magnetostatic analysis. Finally, the BEM formulation is extended to analyze nonlinear magnetostatic problems via the Dual Reciprocity Method (DRBEM). It is shown that a coarse, meshless analysis using the DRBEM is able to achieve RMS error of 3-6% compared to a commercial FEM package in lightly saturated conditions.

A fast marching algorithm for the factored eikonal equation

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

Treister, Eran, E-mail: erantreister@gmail.com; Haber, Eldad, E-mail: haber@math.ubc.ca; Department of Mathematics, The University of British Columbia, Vancouver, BC

The eikonal equation is instrumental in many applications in several fields ranging from computer vision to geoscience. This equation can be efficiently solved using the iterative Fast Sweeping (FS) methods and the direct Fast Marching (FM) methods. However, when used for a point source, the original eikonal equation is known to yield inaccurate numerical solutions, because of a singularity at the source. In this case, the factored eikonal equation is often preferred, and is known to yield a more accurate numerical solution. One application that requires the solution of the eikonal equation for point sources is travel time tomography. Thismore » inverse problem may be formulated using the eikonal equation as a forward problem. While this problem has been solved using FS in the past, the more recent choice for applying it involves FM methods because of the efficiency in which sensitivities can be obtained using them. However, while several FS methods are available for solving the factored equation, the FM method is available only for the original eikonal equation. In this paper we develop a Fast Marching algorithm for the factored eikonal equation, using both first and second order finite-difference schemes. Our algorithm follows the same lines as the original FM algorithm and requires the same computational effort. In addition, we show how to obtain sensitivities using this FM method and apply travel time tomography, formulated as an inverse factored eikonal equation. Numerical results in two and three dimensions show that our algorithm solves the factored eikonal equation efficiently, and demonstrate the achieved accuracy for computing the travel time. We also demonstrate a recovery of a 2D and 3D heterogeneous medium by travel time tomography using the eikonal equation for forward modeling and inversion by Gauss–Newton.« less

A Floating Node Method for the Modelling of Discontinuities Within a Finite Element

NASA Technical Reports Server (NTRS)

Pinho, Silvestre T.; Chen, B. Y.; DeCarvalho, Nelson V.; Baiz, P. M.; Tay, T. E.

2013-01-01

This paper focuses on the accurate numerical representation of complex networks of evolving discontinuities in solids, with particular emphasis on cracks. The limitation of the standard finite element method (FEM) in approximating discontinuous solutions has motivated the development of re-meshing, smeared crack models, the eXtended Finite Element Method (XFEM) and the Phantom Node Method (PNM). We propose a new method which has some similarities to the PNM, but crucially: (i) does not introduce an error on the crack geometry when mapping to natural coordinates; (ii) does not require numerical integration over only part of a domain; (iii) can incorporate weak discontinuities and cohesive cracks more readily; (iv) is ideally suited for the representation of multiple and complex networks of (weak, strong and cohesive) discontinuities; (v) leads to the same solution as a finite element mesh where the discontinuity is represented explicitly; and (vi) is conceptually simpler than the PNM.

Parallel scalability and efficiency of vortex particle method for aeroelasticity analysis of bluff bodies

NASA Astrophysics Data System (ADS)

Tolba, Khaled Ibrahim; Morgenthal, Guido

2018-01-01

This paper presents an analysis of the scalability and efficiency of a simulation framework based on the vortex particle method. The code is applied for the numerical aerodynamic analysis of line-like structures. The numerical code runs on multicore CPU and GPU architectures using OpenCL framework. The focus of this paper is the analysis of the parallel efficiency and scalability of the method being applied to an engineering test case, specifically the aeroelastic response of a long-span bridge girder at the construction stage. The target is to assess the optimal configuration and the required computer architecture, such that it becomes feasible to efficiently utilise the method within the computational resources available for a regular engineering office. The simulations and the scalability analysis are performed on a regular gaming type computer.

(N+1)-dimensional fractional reduced differential transform method for fractional order partial differential equations

NASA Astrophysics Data System (ADS)

Arshad, Muhammad; Lu, Dianchen; Wang, Jun

2017-07-01

In this paper, we pursue the general form of the fractional reduced differential transform method (DTM) to (N+1)-dimensional case, so that fractional order partial differential equations (PDEs) can be resolved effectively. The most distinct aspect of this method is that no prescribed assumptions are required, and the huge computational exertion is reduced and round-off errors are also evaded. We utilize the proposed scheme on some initial value problems and approximate numerical solutions of linear and nonlinear time fractional PDEs are obtained, which shows that the method is highly accurate and simple to apply. The proposed technique is thus an influential technique for solving the fractional PDEs and fractional order problems occurring in the field of engineering, physics etc. Numerical results are obtained for verification and demonstration purpose by using Mathematica software.

Time-of-flight PET time calibration using data consistency

NASA Astrophysics Data System (ADS)

Defrise, Michel; Rezaei, Ahmadreza; Nuyts, Johan

2018-05-01

This paper presents new data driven methods for the time of flight (TOF) calibration of positron emission tomography (PET) scanners. These methods are derived from the consistency condition for TOF PET, they can be applied to data measured with an arbitrary tracer distribution and are numerically efficient because they do not require a preliminary image reconstruction from the non-TOF data. Two-dimensional simulations are presented for one of the methods, which only involves the two first moments of the data with respect to the TOF variable. The numerical results show that this method estimates the detector timing offsets with errors that are larger than those obtained via an initial non-TOF reconstruction, but remain smaller than of the TOF resolution and thereby have a limited impact on the quantitative accuracy of the activity image estimated with standard maximum likelihood reconstruction algorithms.

A Parallel Stochastic Framework for Reservoir Characterization and History Matching

DOE PAGES

Thomas, Sunil G.; Klie, Hector M.; Rodriguez, Adolfo A.; ...

2011-01-01

The spatial distribution of parameters that characterize the subsurface is never known to any reasonable level of accuracy required to solve the governing PDEs of multiphase flow or species transport through porous media. This paper presents a numerically cheap, yet efficient, accurate and parallel framework to estimate reservoir parameters, for example, medium permeability, using sensor information from measurements of the solution variables such as phase pressures, phase concentrations, fluxes, and seismic and well log data. Numerical results are presented to demonstrate the method.

Requirements to Design to Code: Towards a Fully Formal Approach to Automatic Code Generation

NASA Technical Reports Server (NTRS)

Hinchey, Michael G.; Rash, James L.; Rouff, Christopher A.

2005-01-01

A general-purpose method to mechanically transform system requirements into a provably equivalent model has yet to appear. Such a method represents a necessary step toward high-dependability system engineering for numerous possible application domains, including distributed software systems, sensor networks, robot operation, complex scripts for spacecraft integration and testing, and autonomous systems. Currently available tools and methods that start with a formal model of a system and mechanically produce a provably equivalent implementation are valuable but not sufficient. The gap that current tools and methods leave unfilled is that their formal models cannot be proven to be equivalent to the system requirements as originated by the customer. For the classes of systems whose behavior can be described as a finite (but significant) set of scenarios, we offer a method for mechanically transforming requirements (expressed in restricted natural language, or in other appropriate graphical notations) into a provably equivalent formal model that can be used as the basis for code generation and other transformations.

Requirements to Design to Code: Towards a Fully Formal Approach to Automatic Code Generation

NASA Technical Reports Server (NTRS)

Hinchey, Michael G.; Rash, James L.; Rouff, Christopher A.

2005-01-01

A general-purpose method to mechanically transform system requirements into a provably equivalent model has yet to appear. Such a method represents a necessary step toward high-dependability system engineering for numerous possible application domains, including distributed software systems, sensor networks, robot operation, complex scripts for spacecraft integration and testing, and autonomous systems. Currently available tools and methods that start with a formal model of a: system and mechanically produce a provably equivalent implementation are valuable but not sufficient. The "gap" that current tools and methods leave unfilled is that their formal models cannot be proven to be equivalent to the system requirements as originated by the customer. For the ciasses of systems whose behavior can be described as a finite (but significant) set of scenarios, we offer a method for mechanically transforming requirements (expressed in restricted natural language, or in other appropriate graphical notations) into a provably equivalent formal model that can be used as the basis for code generation and other transformations.

Lattice Boltzmann model for simulation of magnetohydrodynamics

NASA Technical Reports Server (NTRS)

Chen, Shiyi; Chen, Hudong; Martinez, Daniel; Matthaeus, William

1991-01-01

A numerical method, based on a discrete Boltzmann equation, is presented for solving the equations of magnetohydrodynamics (MHD). The algorithm provides advantages similar to the cellular automaton method in that it is local and easily adapted to parallel computing environments. Because of much lower noise levels and less stringent requirements on lattice size, the method appears to be more competitive with traditional solution methods. Examples show that the model accurately reproduces both linear and nonlinear MHD phenomena.

Immersed boundary-simplified lattice Boltzmann method for incompressible viscous flows

NASA Astrophysics Data System (ADS)

Chen, Z.; Shu, C.; Tan, D.

2018-05-01

An immersed boundary-simplified lattice Boltzmann method is developed in this paper for simulations of two-dimensional incompressible viscous flows with immersed objects. Assisted by the fractional step technique, the problem is resolved in a predictor-corrector scheme. The predictor step solves the flow field without considering immersed objects, and the corrector step imposes the effect of immersed boundaries on the velocity field. Different from the previous immersed boundary-lattice Boltzmann method which adopts the standard lattice Boltzmann method (LBM) as the flow solver in the predictor step, a recently developed simplified lattice Boltzmann method (SLBM) is applied in the present method to evaluate intermediate flow variables. Compared to the standard LBM, SLBM requires lower virtual memories, facilitates the implementation of physical boundary conditions, and shows better numerical stability. The boundary condition-enforced immersed boundary method, which accurately ensures no-slip boundary conditions, is implemented as the boundary solver in the corrector step. Four typical numerical examples are presented to demonstrate the stability, the flexibility, and the accuracy of the present method.

Numerical solution methods for viscoelastic orthotropic materials

NASA Technical Reports Server (NTRS)

Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.

1988-01-01

Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.

A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity

NASA Astrophysics Data System (ADS)

Mercier, Sylvain; Gratton, Serge; Tardieu, Nicolas; Vasseur, Xavier

2017-12-01

Many applications in structural mechanics require the numerical solution of sequences of linear systems typically issued from a finite element discretization of the governing equations on fine meshes. The method of Lagrange multipliers is often used to take into account mechanical constraints. The resulting matrices then exhibit a saddle point structure and the iterative solution of such preconditioned linear systems is considered as challenging. A popular strategy is then to combine preconditioning and deflation to yield an efficient method. We propose an alternative that is applicable to the general case and not only to matrices with a saddle point structure. In this approach, we consider to update an existing algebraic or application-based preconditioner, using specific available information exploiting the knowledge of an approximate invariant subspace or of matrix-vector products. The resulting preconditioner has the form of a limited memory quasi-Newton matrix and requires a small number of linearly independent vectors. Numerical experiments performed on three large-scale applications in elasticity highlight the relevance of the new approach. We show that the proposed method outperforms the deflation method when considering sequences of linear systems with varying matrices.

Towards an Automated Development Methodology for Dependable Systems with Application to Sensor Networks

NASA Technical Reports Server (NTRS)

Hinchey, Michael G.; Rash, James L.; Rouff, Christopher A.

2005-01-01

A general-purpose method to mechanically transform system requirements into a probably equivalent model has yet to appeal: Such a method represents a necessary step toward high-dependability system engineering for numerous possible application domains, including sensor networks and autonomous systems. Currently available tools and methods that start with a formal model of a system and mechanically produce a probably equivalent implementation are valuable but not su8cient. The "gap" unfilled by such tools and methods is that their. formal models cannot be proven to be equivalent to the system requirements as originated by the customel: For the classes of systems whose behavior can be described as a finite (but significant) set of scenarios, we offer a method for mechanically transforming requirements (expressed in restricted natural language, or in other appropriate graphical notations) into a probably equivalent formal model that can be used as the basis for code generation and other transformations.

NOTE: Solving the ECG forward problem by means of a meshless finite element method

NASA Astrophysics Data System (ADS)

Li, Z. S.; Zhu, S. A.; He, Bin

2007-07-01

The conventional numerical computational techniques such as the finite element method (FEM) and the boundary element method (BEM) require laborious and time-consuming model meshing. The new meshless FEM only uses the boundary description and the node distribution and no meshing of the model is required. This paper presents the fundamentals and implementation of meshless FEM and the meshless FEM method is adapted to solve the electrocardiography (ECG) forward problem. The method is evaluated on a single-layer torso model, in which the analytical solution exists, and tested in a realistic geometry homogeneous torso model, with satisfactory results being obtained. The present results suggest that the meshless FEM may provide an alternative for ECG forward solutions.

Reliable use of determinants to solve nonlinear structural eigenvalue problems efficiently

NASA Technical Reports Server (NTRS)

Williams, F. W.; Kennedy, D.

1988-01-01

The analytical derivation, numerical implementation, and performance of a multiple-determinant parabolic interpolation method (MDPIM) for use in solving transcendental eigenvalue (critical buckling or undamped free vibration) problems in structural mechanics are presented. The overall bounding, eigenvalue-separation, qualified parabolic interpolation, accuracy-confirmation, and convergence-recovery stages of the MDPIM are described in detail, and the numbers of iterations required to solve sample plane-frame problems using the MDPIM are compared with those for a conventional bisection method and for the Newtonian method of Simpson (1984) in extensive tables. The MDPIM is shown to use 31 percent less computation time than bisection when accuracy of 0.0001 is required, but 62 percent less when accuracy of 10 to the -8th is required; the time savings over the Newtonian method are about 10 percent.

Spectrum response estimation for deep-water floating platforms via retardation function representation

NASA Astrophysics Data System (ADS)

Liu, Fushun; Liu, Chengcheng; Chen, Jiefeng; Wang, Bin

2017-08-01

The key concept of spectrum response estimation with commercial software, such as the SESAM software tool, typically includes two main steps: finding a suitable loading spectrum and computing the response amplitude operators (RAOs) subjected to a frequency-specified wave component. In this paper, we propose a nontraditional spectrum response estimation method that uses a numerical representation of the retardation functions. Based on estimated added mass and damping matrices of the structure, we decompose and replace the convolution terms with a series of poles and corresponding residues in the Laplace domain. Then, we estimate the power density corresponding to each frequency component using the improved periodogram method. The advantage of this approach is that the frequency-dependent motion equations in the time domain can be transformed into the Laplace domain without requiring Laplace-domain expressions for the added mass and damping. To validate the proposed method, we use a numerical semi-submerged pontoon from the SESAM. The numerical results show that the responses of the proposed method match well with those obtained from the traditional method. Furthermore, the estimated spectrum also matches well, which indicates its potential application to deep-water floating structures.

Solving phase appearance/disappearance two-phase flow problems with high resolution staggered grid and fully implicit schemes by the Jacobian-free Newton–Krylov Method

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

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-04-01

The phase appearance/disappearance issue presents serious numerical challenges in two-phase flow simulations. Many existing reactor safety analysis codes use different kinds of treatments for the phase appearance/disappearance problem. However, to our best knowledge, there are no fully satisfactory solutions. Additionally, the majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many situations, it is desirable to use high-resolution spatial discretization and fully implicit time integration schemes to reduce numerical errors. In this work, we adapted a high-resolution spatial discretization scheme on staggered grid mesh and fully implicit time integrationmore » methods (such as BDF1 and BDF2) to solve the two-phase flow problems. The discretized nonlinear system was solved by the Jacobian-free Newton Krylov (JFNK) method, which does not require the derivation and implementation of analytical Jacobian matrix. These methods were tested with a few two-phase flow problems with phase appearance/disappearance phenomena considered, such as a linear advection problem, an oscillating manometer problem, and a sedimentation problem. The JFNK method demonstrated extremely robust and stable behaviors in solving the two-phase flow problems with phase appearance/disappearance. No special treatments such as water level tracking or void fraction limiting were used. High-resolution spatial discretization and second- order fully implicit method also demonstrated their capabilities in significantly reducing numerical errors.« less

Implicit and Multigrid Method for Ideal Multigrid Convergence: Direct Numerical Simulation of Separated Flow Around NACA 0012 Airfoil

NASA Technical Reports Server (NTRS)

Liu, Chao-Qun; Shan, H.; Jiang, L.

1999-01-01

Numerical investigation of flow separation over a NACA 0012 airfoil at large angles of attack has been carried out. The numerical calculation is performed by solving the full Navier-Stokes equations in generalized curvilinear coordinates. The second-order LU-SGS implicit scheme is applied for time integration. This scheme requires no tridiagonal inversion and is capable of being completely vectorized, provided the corresponding Jacobian matrices are properly selected. A fourth-order centered compact scheme is used for spatial derivatives. In order to reduce numerical oscillation, a sixth-order implicit filter is employed. Non-reflecting boundary conditions are imposed at the far-field and outlet boundaries to avoid possible non-physical wave reflection. Complex flow separation and vortex shedding phenomenon have been observed and discussed.

Suspension system vibration analysis with regard to variable type ability to smooth road irregularities

NASA Astrophysics Data System (ADS)

Rykov, S. P.; Rykova, O. A.; Koval, V. S.; Makhno, D. E.; Fedotov, K. V.

2018-03-01

The paper aims to analyze vibrations of the dynamic system equivalent of the suspension system with regard to tyre ability to smooth road irregularities. The research is based on static dynamics for linear systems of automated control, methods of correlation, spectral and numerical analysis. Input of new data on the smoothing effect of the pneumatic tyre reflecting changes of a contact area between the wheel and road under vibrations of the suspension makes the system non-linear which requires using numerical analysis methods. Taking into account the variable smoothing ability of the tyre when calculating suspension vibrations, one can approximate calculation and experimental results and improve the constant smoothing ability of the tyre.

Optimization of design parameters of low-energy buildings

NASA Astrophysics Data System (ADS)

Vala, Jiří; Jarošová, Petra

2017-07-01

Evaluation of temperature development and related consumption of energy required for heating, air-conditioning, etc. in low-energy buildings requires the proper physical analysis, covering heat conduction, convection and radiation, including beam and diffusive components of solar radiation, on all building parts and interfaces. The system approach and the Fourier multiplicative decomposition together with the finite element technique offers the possibility of inexpensive and robust numerical and computational analysis of corresponding direct problems, as well as of the optimization ones with several design variables, using the Nelder-Mead simplex method. The practical example demonstrates the correlation between such numerical simulations and the time series of measurements of energy consumption on a small family house in Ostrov u Macochy (35 km northern from Brno).

An alternative method for determining particle-size distribution of forest road aggregate and soil with large-sized particles

Treesearch

Hakjun Rhee; Randy B. Foltz; James L. Fridley; Finn Krogstad; Deborah S. Page-Dumroese

2014-01-01

Measurement of particle-size distribution (PSD) of soil with large-sized particles (e.g., 25.4 mm diameter) requires a large sample and numerous particle-size analyses (PSAs). A new method is needed that would reduce time, effort, and cost for PSAs of the soil and aggregate material with large-sized particles. We evaluated a nested method for sampling and PSA by...

Generations of orthogonal surface coordinates

NASA Technical Reports Server (NTRS)

Blottner, F. G.; Moreno, J. B.

1980-01-01

Two generation methods were developed for three dimensional flows where the computational domain normal to the surface is small. With this restriction the coordinate system requires orthogonality only at the body surface. The first method uses the orthogonal condition in finite-difference form to determine the surface coordinates with the metric coefficients and curvature of the coordinate lines calculated numerically. The second method obtains analytical expressions for the metric coefficients and for the curvature of the coordinate lines.

Modeling for free surface flow with phase change and its application to fusion technology

NASA Astrophysics Data System (ADS)

Luo, Xiaoyong

The development of predictive capabilities for free surface flow with phase change is essential to evaluate liquid wall protection schemes for various fusion chambers. With inertial fusion energy (IFE) concepts such as HYLIFE-II, rapid condensation into cold liquid surfaces is required when using liquid curtains for protecting reactor walls from blasts and intense neutron radiation. With magnetic fusion energy (MFE) concepts, droplets are injected onto the free surface of the liquid to minimize evaporation by minimizing the surface temperature. This dissertation presents a numerical methodology for free surface flow with phase change to help resolve feasibility issues encountered in the aforementioned fusion engineering fields, especially spray droplet condensation efficiency in IFE and droplet heat transfer enhancement on free surface liquid divertors in MFE. The numerical methodology is being conducted within the framework of the incompressible flow with the phase change model. A new second-order projection method is presented in conjunction with Approximate-Factorization techniques (AF method) for incompressible Navier-Stokes equations. A sub-cell conception is introduced and the Ghost Fluid Method in extended in a modified mass transfer model to accurately calculate the mass transfer across the interface. The Crank-Nicholson method is used for the diffusion term to eliminate the numerical viscous stability restriction. The third-order ENO scheme is used for the convective term to guarantee the accuracy of the method. The level set method is used to capture accurately the free surface of the flow and the deformation of the droplets. This numerical investigation identifies the physics characterizing transient heat and mass transfer of the droplet and the free surface flow. The results show that the numerical methodology is quite successful in modeling the free surface with phase change even though some severe deformations such as breaking and merging occur. The versatility of the numerical methodology shows that the work can easily handle complex physical conditions that occur in the fusion science and engineering.

Hybrid Upwind Splitting (HUS) by a Field-by-Field Decomposition

NASA Technical Reports Server (NTRS)

Coquel, Frederic; Liou, Meng-Sing

1995-01-01

We introduce and develop a new approach for upwind biasing: the hybrid upwind splitting (HUS) method. This original procedure is based on a suitable hybridization of current prominent flux vector splitting (FVS) and flux difference splitting (FDS) methods. The HUS method is designed to naturally combine the respective strengths of the above methods while excluding their main deficiencies. Specifically, the HUS strategy yields a family of upwind methods that exhibit the robustness of FVS schemes in the capture of nonlinear waves and the accuracy of some FDS schemes in the resolution of linear waves. We give a detailed construction of the HUS methods following a general and systematic procedure directly performed at the basic level of the field by field (i.e. waves) decomposition involved in FDS methods. For such a given decomposition, each field is endowed either with FVS or FDS numerical fluxes, depending on the nonlinear nature of the field under consideration. Such a design principle is made possible thanks to the introduction of a convenient formalism that provides us with a unified framework for upwind methods. The HUS methods we propose bring significant improvements over current methods in terms of accuracy and robustness. They yield entropy-satisfying approximate solutions as they are strongly supported in numerical experiments. Field by field hybrid numerical fluxes also achieve fairly simple and explicit expressions and hence require a computational effort between that of the FVS and FDS. Several numerical experiments ranging from stiff 1D shock-tube to high speed viscous flows problems are displayed, intending to illustrate the benefits of the present approach. We assess in particular the relevance of our HUS schemes to viscous flow calculations.

Indirect synthesis of multi-degree of freedom transient systems. [linear programming for a kinematically linear system

NASA Technical Reports Server (NTRS)

Pilkey, W. D.; Chen, Y. H.

1974-01-01

An indirect synthesis method is used in the efficient optimal design of multi-degree of freedom, multi-design element, nonlinear, transient systems. A limiting performance analysis which requires linear programming for a kinematically linear system is presented. The system is selected using system identification methods such that the designed system responds as closely as possible to the limiting performance. The efficiency is a result of the method avoiding the repetitive systems analyses accompanying other numerical optimization methods.

Formalizing New Navigation Requirements for NASA's Space Shuttle

NASA Technical Reports Server (NTRS)

DiVito, Ben L.

1996-01-01

We describe a recent NASA-sponsored pilot project intended to gauge the effectiveness of using formal methods in Space Shuttle software requirements analysis. Several Change Requests (CRs) were selected as promising targets to demonstrate the utility of formal methods in this demanding application domain. A CR to add new navigation capabilities to the Shuttle, based on Global Positioning System (GPS) technology, is the focus of this industrial usage report. Portions of the GPS CR were modeled using the language of SRI's Prototype Verification System (PVS). During a limited analysis conducted on the formal specifications, numerous requirements issues were discovered. We present a summary of these encouraging results and conclusions we have drawn from the pilot project.

A Numerical Combination of Extended Boundary Condition Method and Invariant Imbedding Method Applied to Light Scattering by Large Spheroids and Cylinders

NASA Technical Reports Server (NTRS)

Bi, Lei; Yang, Ping; Kattawar, George W.; Mishchenko, Michael I.

2013-01-01

The extended boundary condition method (EBCM) and invariant imbedding method (IIM) are two fundamentally different T-matrix methods for the solution of light scattering by nonspherical particles. The standard EBCM is very efficient but encounters a loss of precision when the particle size is large, the maximum size being sensitive to the particle aspect ratio. The IIM can be applied to particles in a relatively large size parameter range but requires extensive computational time due to the number of spherical layers in the particle volume discretization. A numerical combination of the EBCM and the IIM (hereafter, the EBCM+IIM) is proposed to overcome the aforementioned disadvantages of each method. Even though the EBCM can fail to obtain the T-matrix of a considered particle, it is valuable for decreasing the computational domain (i.e., the number of spherical layers) of the IIM by providing the initial T-matrix associated with an iterative procedure in the IIM. The EBCM+IIM is demonstrated to be more efficient than the IIM in obtaining the optical properties of large size parameter particles beyond the convergence limit of the EBCM. The numerical performance of the EBCM+IIM is illustrated through representative calculations in spheroidal and cylindrical particle cases.

On the numerical treatment of selected oscillatory evolutionary problems

NASA Astrophysics Data System (ADS)

Cardone, Angelamaria; Conte, Dajana; D'Ambrosio, Raffaele; Paternoster, Beatrice

2017-07-01

We focus on evolutionary problems whose qualitative behaviour is known a-priori and exploited in order to provide efficient and accurate numerical schemes. For classical numerical methods, depending on constant coefficients, the required computational effort could be quite heavy, due to the necessary employ of very small stepsizes needed to accurately reproduce the qualitative behaviour of the solution. In these situations, it may be convenient to use special purpose formulae, i.e. non-polynomially fitted formulae on basis functions adapted to the problem (see [16, 17] and references therein). We show examples of special purpose strategies to solve two families of evolutionary problems exhibiting periodic solutions, i.e. partial differential equations and Volterra integral equations.

Personal computer study of finite-difference methods for the transonic small disturbance equation

NASA Technical Reports Server (NTRS)

Bland, Samuel R.

1989-01-01

Calculation of unsteady flow phenomena requires careful attention to the numerical treatment of the governing partial differential equations. The personal computer provides a convenient and useful tool for the development of meshes, algorithms, and boundary conditions needed to provide time accurate solution of these equations. The one-dimensional equation considered provides a suitable model for the study of wave propagation in the equations of transonic small disturbance potential flow. Numerical results for effects of mesh size, extent, and stretching, time step size, and choice of far-field boundary conditions are presented. Analysis of the discretized model problem supports these numerical results. Guidelines for suitable mesh and time step choices are given.

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.

On the Minimal Accuracy Required for Simulating Self-gravitating Systems by Means of Direct N-body Methods

NASA Astrophysics Data System (ADS)

Portegies Zwart, Simon; Boekholt, Tjarda

2014-04-01

The conservation of energy, linear momentum, and angular momentum are important drivers of our physical understanding of the evolution of the universe. These quantities are also conserved in Newton's laws of motion under gravity. Numerical integration of the associated equations of motion is extremely challenging, in particular due to the steady growth of numerical errors (by round-off and discrete time-stepping and the exponential divergence between two nearby solutions. As a result, numerical solutions to the general N-body problem are intrinsically questionable. Using brute force integrations to arbitrary numerical precision we demonstrate empirically that ensembles of different realizations of resonant three-body interactions produce statistically indistinguishable results. Although individual solutions using common integration methods are notoriously unreliable, we conjecture that an ensemble of approximate three-body solutions accurately represents an ensemble of true solutions, so long as the energy during integration is conserved to better than 1/10. We therefore provide an independent confirmation that previous work on self-gravitating systems can actually be trusted, irrespective of the intrinsically chaotic nature of the N-body problem.

Numerical simulation of a bubble rising in an environment consisting of Xanthan gum

NASA Astrophysics Data System (ADS)

Aguirre, Víctor A.; Castillo, Byron A.; Narvaez, Christian P.

2017-09-01

An improved numerical algorithm for front tracking method is developed to simulate a bubble rising in viscous liquid. In the new numerical algorithm, volume correction is introduced to conserve the bubble volume while tracking the bubble's rising and deforming. Volume flux conservation is adopted to solve the Navier-Stokes equation for fluid flow using finite volume method. Non-Newtonian fluids are widely used in industry such as feed and energy industries. In this research we used Xanthan gum which is a microbiological polysaccharide. In order to obtain the properties of the Xanthan gum, such as viscosity, storage and loss modulus, shear rate, etc., it was necessary to do an amplitude sweep and steady flow test in a rheometer with a concentric cylinder as geometry. Based on the data given and using a numerical regression, the coefficients required by Giesekus model are obtained. With these coefficients, it is possible to simulate the comportment of the fluid by the use of the developed algorithm. Once the data given by OpenFOAM is acquired, it is compared with the experimental data.

Adaptive mesh refinement and adjoint methods in geophysics simulations

NASA Astrophysics Data System (ADS)

Burstedde, Carsten

2013-04-01

It is an ongoing challenge to increase the resolution that can be achieved by numerical geophysics simulations. This applies to considering sub-kilometer mesh spacings in global-scale mantle convection simulations as well as to using frequencies up to 1 Hz in seismic wave propagation simulations. One central issue is the numerical cost, since for three-dimensional space discretizations, possibly combined with time stepping schemes, a doubling of resolution can lead to an increase in storage requirements and run time by factors between 8 and 16. A related challenge lies in the fact that an increase in resolution also increases the dimensionality of the model space that is needed to fully parametrize the physical properties of the simulated object (a.k.a. earth). Systems that exhibit a multiscale structure in space are candidates for employing adaptive mesh refinement, which varies the resolution locally. An example that we found well suited is the mantle, where plate boundaries and fault zones require a resolution on the km scale, while deeper area can be treated with 50 or 100 km mesh spacings. This approach effectively reduces the number of computational variables by several orders of magnitude. While in this case it is possible to derive the local adaptation pattern from known physical parameters, it is often unclear what are the most suitable criteria for adaptation. We will present the goal-oriented error estimation procedure, where such criteria are derived from an objective functional that represents the observables to be computed most accurately. Even though this approach is well studied, it is rarely used in the geophysics community. A related strategy to make finer resolution manageable is to design methods that automate the inference of model parameters. Tweaking more than a handful of numbers and judging the quality of the simulation by adhoc comparisons to known facts and observations is a tedious task and fundamentally limited by the turnaround times required by human intervention and analysis. Specifying an objective functional that quantifies the misfit between the simulation outcome and known constraints and then minimizing it through numerical optimization can serve as an automated technique for parameter identification. As suggested by the similarity in formulation, the numerical algorithm is closely related to the one used for goal-oriented error estimation. One common point is that the so-called adjoint equation needs to be solved numerically. We will outline the derivation and implementation of these methods and discuss some of their pros and cons, supported by numerical results.

Robust stability of linear systems: Some computational considerations

NASA Technical Reports Server (NTRS)

Laub, A. J.

1979-01-01

The cases of both additive and multiplicative perturbations were discussed and a number of relationships between the two cases were given. A number of computational aspects of the theory were also discussed, including a proposed new method for evaluating general transfer or frequency response matrices. The new method is numerically stable and efficient, requiring only operations to update for new values of the frequency parameter.

A two-dimensional, TVD numerical scheme for inviscid, high Mach number flows in chemical equilibrium

NASA Technical Reports Server (NTRS)

Eberhardt, S.; Palmer, G.

1986-01-01

A new algorithm has been developed for hypervelocity flows in chemical equilibrium. Solutions have been achieved for Mach numbers up to 15 with no adverse effect on convergence. Two methods of coupling an equilibrium chemistry package have been tested, with the simpler method proving to be more robust. Improvements in boundary conditions are still required for a production-quality code.

Some analytical and numerical approaches to understanding trap counts resulting from pest insect immigration.

PubMed

Bearup, Daniel; Petrovskaya, Natalia; Petrovskii, Sergei

2015-05-01

Monitoring of pest insects is an important part of the integrated pest management. It aims to provide information about pest insect abundance at a given location. This includes data collection, usually using traps, and their subsequent analysis and/or interpretation. However, interpretation of trap count (number of insects caught over a fixed time) remains a challenging problem. First, an increase in either the population density or insects activity can result in a similar increase in the number of insects trapped (the so called "activity-density" problem). Second, a genuine increase of the local population density can be attributed to qualitatively different ecological mechanisms such as multiplication or immigration. Identification of the true factor causing an increase in trap count is important as different mechanisms require different control strategies. In this paper, we consider a mean-field mathematical model of insect trapping based on the diffusion equation. Although the diffusion equation is a well-studied model, its analytical solution in closed form is actually available only for a few special cases, whilst in a more general case the problem has to be solved numerically. We choose finite differences as the baseline numerical method and show that numerical solution of the problem, especially in the realistic 2D case, is not at all straightforward as it requires a sufficiently accurate approximation of the diffusion fluxes. Once the numerical method is justified and tested, we apply it to the corresponding boundary problem where different types of boundary forcing describe different scenarios of pest insect immigration and reveal the corresponding patterns in the trap count growth. Copyright © 2015 Elsevier Inc. All rights reserved.

Dynamic Responses of Flexible Cylinders with Low Mass Ratio

NASA Astrophysics Data System (ADS)

Olaoye, Abiodun; Wang, Zhicheng; Triantafyllou, Michael

2017-11-01

Flexible cylinders with low mass ratios such as composite risers are attractive in the offshore industry because they require lower top tension and are less likely to buckle under self-weight compared to steel risers. However, their relatively low stiffness characteristics make them more vulnerable to vortex induced vibrations. Additionally, numerical investigation of the dynamic responses of such structures based on realistic conditions is limited by high Reynolds number, complex sheared flow profile, large aspect ratio and low mass ratio challenges. In the framework of Fourier spectral/hp element method, the current technique employs entropy-viscosity method (EVM) based large-eddy simulation approach for flow solver and fictitious added mass method for structure solver. The combination of both methods can handle fluid-structure interaction problems at high Reynolds number with low mass ratio. A validation of the numerical approach is provided by comparison with experiments.

Evaluation of the matrix exponential for use in ground-water-flow and solute-transport simulations; theoretical framework

USGS Publications Warehouse

Umari, A.M.; Gorelick, S.M.

1986-01-01

It is possible to obtain analytic solutions to the groundwater flow and solute transport equations if space variables are discretized but time is left continuous. From these solutions, hydraulic head and concentration fields for any future time can be obtained without ' marching ' through intermediate time steps. This analytical approach involves matrix exponentiation and is referred to as the Matrix Exponential Time Advancement (META) method. Two algorithms are presented for the META method, one for symmetric and the other for non-symmetric exponent matrices. A numerical accuracy indicator, referred to as the matrix condition number, was defined and used to determine the maximum number of significant figures that may be lost in the META method computations. The relative computational and storage requirements of the META method with respect to the time marching method increase with the number of nodes in the discretized problem. The potential greater accuracy of the META method and the associated greater reliability through use of the matrix condition number have to be weighed against this increased relative computational and storage requirements of this approach as the number of nodes becomes large. For a particular number of nodes, the META method may be computationally more efficient than the time-marching method, depending on the size of time steps used in the latter. A numerical example illustrates application of the META method to a sample ground-water-flow problem. (Author 's abstract)

Multibody Parachute Flight Simulations for Planetary Entry Trajectories Using "Equilibrium Points"

NASA Technical Reports Server (NTRS)

Raiszadeh, Ben

2003-01-01

A method has been developed to reduce numerical stiffness and computer CPU requirements of high fidelity multibody flight simulations involving parachutes for planetary entry trajectories. Typical parachute entry configurations consist of entry bodies suspended from a parachute, connected by flexible lines. To accurately calculate line forces and moments, the simulations need to keep track of the point where the flexible lines meet (confluence point). In previous multibody parachute flight simulations, the confluence point has been modeled as a point mass. Using a point mass for the confluence point tends to make the simulation numerically stiff, because its mass is typically much less that than the main rigid body masses. One solution for stiff differential equations is to use a very small integration time step. However, this results in large computer CPU requirements. In the method described in the paper, the need for using a mass as the confluence point has been eliminated. Instead, the confluence point is modeled using an "equilibrium point". This point is calculated at every integration step as the point at which sum of all line forces is zero (static equilibrium). The use of this "equilibrium point" has the advantage of both reducing the numerical stiffness of the simulations, and eliminating the dynamical equations associated with vibration of a lumped mass on a high-tension string.

Improved methods for simulating nearly extremal binary black holes

NASA Astrophysics Data System (ADS)

Scheel, Mark A.; Giesler, Matthew; Hemberger, Daniel A.; Lovelace, Geoffrey; Kuper, Kevin; Boyle, Michael; Szilágyi, Béla; Kidder, Lawrence E.

2015-05-01

Astrophysical black holes could be nearly extremal (that is, rotating nearly as fast as possible); therefore, nearly extremal black holes could be among the binaries that current and future gravitational-wave observatories will detect. Predicting the gravitational waves emitted by merging black holes requires numerical-relativity simulations, but these simulations are especially challenging when one or both holes have mass m and spin S exceeding the Bowen-York limit of S/{{m}2}=0.93. We present improved methods that enable us to simulate merging, nearly extremal black holes (i.e., black holes with S/{{m}2}\\gt 0.93) more robustly and more efficiently. We use these methods to simulate an unequal-mass, precessing binary black hole (BBH) coalescence, where the larger black hole has S/{{m}2}=0.99. We also use these methods to simulate a non-precessing BBH coalescence, where both black holes have S/{{m}2}=0.994, nearly reaching the Novikov-Thorne upper bound for holes spun up by thin accretion disks. We demonstrate numerical convergence and estimate the numerical errors of the waveforms; we compare numerical waveforms from our simulations with post-Newtonian and effective-one-body waveforms; we compare the evolution of the black hole masses and spins with analytic predictions; and we explore the effect of increasing spin magnitude on the orbital dynamics (the so-called ‘orbital hangup’ effect).

2-D transmitral flows simulation by means of the immersed boundary method on unstructured grids

NASA Astrophysics Data System (ADS)

Denaro, F. M.; Sarghini, F.

2002-04-01

Interaction between computational fluid dynamics and clinical researches recently allowed a deeper understanding of the physiology of complex phenomena involving cardio-vascular mechanisms. The aim of this paper is to develop a simplified numerical model based on the Immersed Boundary Method and to perform numerical simulations in order to study the cardiac diastolic phase during which the left ventricle is filled with blood flowing from the atrium throughout the mitral valve. As one of the diagnostic problems to be faced by clinicians is the lack of a univocal definition of the diastolic performance from the velocity measurements obtained by Eco-Doppler techniques, numerical simulations are supposed to provide an insight both into the physics of the diastole and into the interpretation of experimental data. An innovative application of the Immersed Boundary Method on unstructured grids is presented, fulfilling accuracy requirements related to the development of a thin boundary layer along the moving immersed boundary. It appears that this coupling between unstructured meshes and the Immersed Boundary Method is a promising technique when a wide range of spatial scales is involved together with a moving boundary. Numerical simulations are performed in a range of physiological parameters and a qualitative comparison with experimental data is presented, in order to demonstrate that, despite the simplified model, the main physiological characteristics of the diastole are well represented. Copyright

Continuous control of chaos based on the stability criterion.

PubMed

Yu, Hong Jie; Liu, Yan Zhu; Peng, Jian Hua

2004-06-01

A method of chaos control based on stability criterion is proposed in the present paper. This method can stabilize chaotic systems onto a desired periodic orbit by a small time-continuous perturbation nonlinear feedback. This method does not require linearization of the system around the stabilized orbit and only an approximate location of the desired periodic orbit is required which can be automatically detected in the control process. The control can be started at any moment by choosing appropriate perturbation restriction condition. It seems that more flexibility and convenience are the main advantages of this method. The discussions on control of attitude motion of a spacecraft, Rössler system, and two coupled Duffing oscillators are given as numerical examples.

SpF: Enabling Petascale Performance for Pseudospectral Dynamo Models

NASA Astrophysics Data System (ADS)

Jiang, W.; Clune, T.; Vriesema, J.; Gutmann, G.

2013-12-01

Pseudospectral (PS) methods possess a number of characteristics (e.g., efficiency, accuracy, natural boundary conditions) that are extremely desirable for dynamo models. Unfortunately, dynamo models based upon PS methods face a number of daunting challenges, which include exposing additional parallelism, leveraging hardware accelerators, exploiting hybrid parallelism, and improving the scalability of global memory transposes. Although these issues are a concern for most models, solutions for PS methods tend to require far more pervasive changes to underlying data and control structures. Further, improvements in performance in one model are difficult to transfer to other models, resulting in significant duplication of effort across the research community. We have developed an extensible software framework for pseudospectral methods called SpF that is intended to enable extreme scalability and optimal performance. High-level abstractions provided by SpF unburden applications of the responsibility of managing domain decomposition and load balance while reducing the changes in code required to adapt to new computing architectures. The key design concept in SpF is that each phase of the numerical calculation is partitioned into disjoint numerical 'kernels' that can be performed entirely in-processor. The granularity of domain-decomposition provided by SpF is only constrained by the data-locality requirements of these kernels. SpF builds on top of optimized vendor libraries for common numerical operations such as transforms, matrix solvers, etc., but can also be configured to use open source alternatives for portability. SpF includes several alternative schemes for global data redistribution and is expected to serve as an ideal testbed for further research into optimal approaches for different network architectures. In this presentation, we will describe the basic architecture of SpF as well as preliminary performance data and experience with adapting legacy dynamo codes. We will conclude with a discussion of planned extensions to SpF that will provide pseudospectral applications with additional flexibility with regard to time integration, linear solvers, and discretization in the radial direction.

An efficient soil water balance model based on hybrid numerical and statistical methods

NASA Astrophysics Data System (ADS)

Mao, Wei; Yang, Jinzhong; Zhu, Yan; Ye, Ming; Liu, Zhao; Wu, Jingwei

2018-04-01

Most soil water balance models only consider downward soil water movement driven by gravitational potential, and thus cannot simulate upward soil water movement driven by evapotranspiration especially in agricultural areas. In addition, the models cannot be used for simulating soil water movement in heterogeneous soils, and usually require many empirical parameters. To resolve these problems, this study derives a new one-dimensional water balance model for simulating both downward and upward soil water movement in heterogeneous unsaturated zones. The new model is based on a hybrid of numerical and statistical methods, and only requires four physical parameters. The model uses three governing equations to consider three terms that impact soil water movement, including the advective term driven by gravitational potential, the source/sink term driven by external forces (e.g., evapotranspiration), and the diffusive term driven by matric potential. The three governing equations are solved separately by using the hybrid numerical and statistical methods (e.g., linear regression method) that consider soil heterogeneity. The four soil hydraulic parameters required by the new models are as follows: saturated hydraulic conductivity, saturated water content, field capacity, and residual water content. The strength and weakness of the new model are evaluated by using two published studies, three hypothetical examples and a real-world application. The evaluation is performed by comparing the simulation results of the new model with corresponding results presented in the published studies, obtained using HYDRUS-1D and observation data. The evaluation indicates that the new model is accurate and efficient for simulating upward soil water flow in heterogeneous soils with complex boundary conditions. The new model is used for evaluating different drainage functions, and the square drainage function and the power drainage function are recommended. Computational efficiency of the new model makes it particularly suitable for large-scale simulation of soil water movement, because the new model can be used with coarse discretization in space and time.

Two-dimensional Euler and Navier-Stokes Time accurate simulations of fan rotor flows

NASA Technical Reports Server (NTRS)

Boretti, A. A.

1990-01-01

Two numerical methods are presented which describe the unsteady flow field in the blade-to-blade plane of an axial fan rotor. These methods solve the compressible, time-dependent, Euler and the compressible, turbulent, time-dependent, Navier-Stokes conservation equations for mass, momentum, and energy. The Navier-Stokes equations are written in Favre-averaged form and are closed with an approximate two-equation turbulence model with low Reynolds number and compressibility effects included. The unsteady aerodynamic component is obtained by superposing inflow or outflow unsteadiness to the steady conditions through time-dependent boundary conditions. The integration in space is performed by using a finite volume scheme, and the integration in time is performed by using k-stage Runge-Kutta schemes, k = 2,5. The numerical integration algorithm allows the reduction of the computational cost of an unsteady simulation involving high frequency disturbances in both CPU time and memory requirements. Less than 200 sec of CPU time are required to advance the Euler equations in a computational grid made up of about 2000 grid during 10,000 time steps on a CRAY Y-MP computer, with a required memory of less than 0.3 megawords.

Computational ecology as an emerging science

PubMed Central

Petrovskii, Sergei; Petrovskaya, Natalia

2012-01-01

It has long been recognized that numerical modelling and computer simulations can be used as a powerful research tool to understand, and sometimes to predict, the tendencies and peculiarities in the dynamics of populations and ecosystems. It has been, however, much less appreciated that the context of modelling and simulations in ecology is essentially different from those that normally exist in other natural sciences. In our paper, we review the computational challenges arising in modern ecology in the spirit of computational mathematics, i.e. with our main focus on the choice and use of adequate numerical methods. Somewhat paradoxically, the complexity of ecological problems does not always require the use of complex computational methods. This paradox, however, can be easily resolved if we recall that application of sophisticated computational methods usually requires clear and unambiguous mathematical problem statement as well as clearly defined benchmark information for model validation. At the same time, many ecological problems still do not have mathematically accurate and unambiguous description, and available field data are often very noisy, and hence it can be hard to understand how the results of computations should be interpreted from the ecological viewpoint. In this scientific context, computational ecology has to deal with a new paradigm: conventional issues of numerical modelling such as convergence and stability become less important than the qualitative analysis that can be provided with the help of computational techniques. We discuss this paradigm by considering computational challenges arising in several specific ecological applications. PMID:23565336

Numerical Approach to Modeling and Characterization of Refractive Index Changes for a Long-Period Fiber Grating Fabricated by Femtosecond Laser

PubMed Central

Saad, Akram; Cho, Yonghyun; Ahmed, Farid; Jun, Martin Byung-Guk

2016-01-01

A 3D finite element model constructed to predict the intensity-dependent refractive index profile induced by femtosecond laser radiation is presented. A fiber core irradiated by a pulsed laser is modeled as a cylinder subject to predefined boundary conditions using COMSOL5.2 Multiphysics commercial package. The numerically obtained refractive index change is used to numerically design and experimentally fabricate long-period fiber grating (LPFG) in pure silica core single-mode fiber employing identical laser conditions. To reduce the high computational requirements, the beam envelope method approach is utilized in the aforementioned numerical models. The number of periods, grating length, and grating period considered in this work are numerically quantified. The numerically obtained spectral growth of the modeled LPFG seems to be consistent with the transmission of the experimentally fabricated LPFG single mode fiber. The sensing capabilities of the modeled LPFG are tested by varying the refractive index of the surrounding medium. The numerically obtained spectrum corresponding to the varied refractive index shows good agreement with the experimental findings. PMID:28774060

Numerical Approach to Modeling and Characterization of Refractive Index Changes for a Long-Period Fiber Grating Fabricated by Femtosecond Laser.

PubMed

Saad, Akram; Cho, Yonghyun; Ahmed, Farid; Jun, Martin Byung-Guk

2016-11-21

A 3D finite element model constructed to predict the intensity-dependent refractive index profile induced by femtosecond laser radiation is presented. A fiber core irradiated by a pulsed laser is modeled as a cylinder subject to predefined boundary conditions using COMSOL5.2 Multiphysics commercial package. The numerically obtained refractive index change is used to numerically design and experimentally fabricate long-period fiber grating (LPFG) in pure silica core single-mode fiber employing identical laser conditions. To reduce the high computational requirements, the beam envelope method approach is utilized in the aforementioned numerical models. The number of periods, grating length, and grating period considered in this work are numerically quantified. The numerically obtained spectral growth of the modeled LPFG seems to be consistent with the transmission of the experimentally fabricated LPFG single mode fiber. The sensing capabilities of the modeled LPFG are tested by varying the refractive index of the surrounding medium. The numerically obtained spectrum corresponding to the varied refractive index shows good agreement with the experimental findings.

Mapping implicit spectral methods to distributed memory architectures

NASA Technical Reports Server (NTRS)

Overman, Andrea L.; Vanrosendale, John

1991-01-01

Spectral methods were proven invaluable in numerical simulation of PDEs (Partial Differential Equations), but the frequent global communication required raises a fundamental barrier to their use on highly parallel architectures. To explore this issue, a 3-D implicit spectral method was implemented on an Intel hypercube. Utilization of about 50 percent was achieved on a 32 node iPSC/860 hypercube, for a 64 x 64 x 64 Fourier-spectral grid; finer grids yield higher utilizations. Chebyshev-spectral grids are more problematic, since plane-relaxation based multigrid is required. However, by using a semicoarsening multigrid algorithm, and by relaxing all multigrid levels concurrently, relatively high utilizations were also achieved in this harder case.

Infants and young children modeling method for numerical dosimetry studies: application to plane wave exposure

NASA Astrophysics Data System (ADS)

Dahdouh, S.; Varsier, N.; Nunez Ochoa, M. A.; Wiart, J.; Peyman, A.; Bloch, I.

2016-02-01

Numerical dosimetry studies require the development of accurate numerical 3D models of the human body. This paper proposes a novel method for building 3D heterogeneous young children models combining results obtained from a semi-automatic multi-organ segmentation algorithm and an anatomy deformation method. The data consist of 3D magnetic resonance images, which are first segmented to obtain a set of initial tissues. A deformation procedure guided by the segmentation results is then developed in order to obtain five young children models ranging from the age of 5 to 37 months. By constraining the deformation of an older child model toward a younger one using segmentation results, we assure the anatomical realism of the models. Using the proposed framework, five models, containing thirteen tissues, are built. Three of these models are used in a prospective dosimetry study to analyze young child exposure to radiofrequency electromagnetic fields. The results lean to show the existence of a relationship between age and whole body exposure. The results also highlight the necessity to specifically study and develop measurements of child tissues dielectric properties.

Applications of MMPBSA to Membrane Proteins I: Efficient Numerical Solutions of Periodic Poisson-Boltzmann Equation

PubMed Central

Botello-Smith, Wesley M.; Luo, Ray

2016-01-01

Continuum solvent models have been widely used in biomolecular modeling applications. Recently much attention has been given to inclusion of implicit membrane into existing continuum Poisson-Boltzmann solvent models to extend their applications to membrane systems. Inclusion of an implicit membrane complicates numerical solutions of the underlining Poisson-Boltzmann equation due to the dielectric inhomogeneity on the boundary surfaces of a computation grid. This can be alleviated by the use of the periodic boundary condition, a common practice in electrostatic computations in particle simulations. The conjugate gradient and successive over-relaxation methods are relatively straightforward to be adapted to periodic calculations, but their convergence rates are quite low, limiting their applications to free energy simulations that require a large number of conformations to be processed. To accelerate convergence, the Incomplete Cholesky preconditioning and the geometric multi-grid methods have been extended to incorporate periodicity for biomolecular applications. Impressive convergence behaviors were found as in the previous applications of these numerical methods to tested biomolecules and MMPBSA calculations. PMID:26389966

ULTRA-SHARP nonoscillatory convection schemes for high-speed steady multidimensional flow

NASA Technical Reports Server (NTRS)

Leonard, B. P.; Mokhtari, Simin

1990-01-01

For convection-dominated flows, classical second-order methods are notoriously oscillatory and often unstable. For this reason, many computational fluid dynamicists have adopted various forms of (inherently stable) first-order upwinding over the past few decades. Although it is now well known that first-order convection schemes suffer from serious inaccuracies attributable to artificial viscosity or numerical diffusion under high convection conditions, these methods continue to enjoy widespread popularity for numerical heat transfer calculations, apparently due to a perceived lack of viable high accuracy alternatives. But alternatives are available. For example, nonoscillatory methods used in gasdynamics, including currently popular TVD schemes, can be easily adapted to multidimensional incompressible flow and convective transport. This, in itself, would be a major advance for numerical convective heat transfer, for example. But, as is shown, second-order TVD schemes form only a small, overly restrictive, subclass of a much more universal, and extremely simple, nonoscillatory flux-limiting strategy which can be applied to convection schemes of arbitrarily high order accuracy, while requiring only a simple tridiagonal ADI line-solver, as used in the majority of general purpose iterative codes for incompressible flow and numerical heat transfer. The new universal limiter and associated solution procedures form the so-called ULTRA-SHARP alternative for high resolution nonoscillatory multidimensional steady state high speed convective modelling.

Recursive linearization of multibody dynamics equations of motion

NASA Technical Reports Server (NTRS)

Lin, Tsung-Chieh; Yae, K. Harold

1989-01-01

The equations of motion of a multibody system are nonlinear in nature, and thus pose a difficult problem in linear control design. One approach is to have a first-order approximation through the numerical perturbations at a given configuration, and to design a control law based on the linearized model. Here, a linearized model is generated analytically by following the footsteps of the recursive derivation of the equations of motion. The equations of motion are first written in a Newton-Euler form, which is systematic and easy to construct; then, they are transformed into a relative coordinate representation, which is more efficient in computation. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient because of its recursive nature. It has also turned out to be more accurate because of the fact that analytical perturbation circumvents numerical differentiation and other associated numerical operations that may accumulate computational error, thus requiring only analytical operations of matrices and vectors. The power of the proposed linearization algorithm is demonstrated, in comparison to a numerical perturbation method, with a two-link manipulator and a seven degrees of freedom robotic manipulator. Its application to control design is also demonstrated.

Time-Accurate Local Time Stepping and High-Order Time CESE Methods for Multi-Dimensional Flows Using Unstructured Meshes

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan; Venkatachari, Balaji Shankar; Cheng, Gary

2013-01-01

With the wide availability of affordable multiple-core parallel supercomputers, next generation numerical simulations of flow physics are being focused on unsteady computations for problems involving multiple time scales and multiple physics. These simulations require higher solution accuracy than most algorithms and computational fluid dynamics codes currently available. This paper focuses on the developmental effort for high-fidelity multi-dimensional, unstructured-mesh flow solvers using the space-time conservation element, solution element (CESE) framework. Two approaches have been investigated in this research in order to provide high-accuracy, cross-cutting numerical simulations for a variety of flow regimes: 1) time-accurate local time stepping and 2) highorder CESE method. The first approach utilizes consistent numerical formulations in the space-time flux integration to preserve temporal conservation across the cells with different marching time steps. Such approach relieves the stringent time step constraint associated with the smallest time step in the computational domain while preserving temporal accuracy for all the cells. For flows involving multiple scales, both numerical accuracy and efficiency can be significantly enhanced. The second approach extends the current CESE solver to higher-order accuracy. Unlike other existing explicit high-order methods for unstructured meshes, the CESE framework maintains a CFL condition of one for arbitrarily high-order formulations while retaining the same compact stencil as its second-order counterpart. For large-scale unsteady computations, this feature substantially enhances numerical efficiency. Numerical formulations and validations using benchmark problems are discussed in this paper along with realistic examples.

On Computations of Duct Acoustics with Near Cut-Off Frequency

NASA Technical Reports Server (NTRS)

Dong, Thomas Z.; Povinelli, Louis A.

1997-01-01

The cut-off is a unique feature associated with duct acoustics due to the presence of duct walls. A study of this cut-off effect on the computations of duct acoustics is performed in the present work. The results show that the computation of duct acoustic modes near cut-off requires higher numerical resolutions than others to avoid being numerically cut off. Duct acoustic problems in Category 2 are solved by the DRP finite difference scheme with the selective artificial damping method and results are presented and compared to reference solutions.

High-order ENO schemes applied to two- and three-dimensional compressible flow

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang; Erlebacher, Gordon; Zang, Thomas A.; Whitaker, David; Osher, Stanley

1991-01-01

High order essentially non-oscillatory (ENO) finite difference schemes are applied to the 2-D and 3-D compressible Euler and Navier-Stokes equations. Practical issues, such as vectorization, efficiency of coding, cost comparison with other numerical methods, and accuracy degeneracy effects, are discussed. Numerical examples are provided which are representative of computational problems of current interest in transition and turbulence physics. These require both nonoscillatory shock capturing and high resolution for detailed structures in the smooth regions and demonstrate the advantage of ENO schemes.

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.

Wavelet-based adaptation methodology combined with finite difference WENO to solve ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Do, Seongju; Li, Haojun; Kang, Myungjoo

2017-06-01

In this paper, we present an accurate and efficient wavelet-based adaptive weighted essentially non-oscillatory (WENO) scheme for hydrodynamics and ideal magnetohydrodynamics (MHD) equations arising from the hyperbolic conservation systems. The proposed method works with the finite difference weighted essentially non-oscillatory (FD-WENO) method in space and the third order total variation diminishing (TVD) Runge-Kutta (RK) method in time. The philosophy of this work is to use the lifted interpolating wavelets as not only detector for singularities but also interpolator. Especially, flexible interpolations can be performed by an inverse wavelet transformation. When the divergence cleaning method introducing auxiliary scalar field ψ is applied to the base numerical schemes for imposing divergence-free condition to the magnetic field in a MHD equation, the approximations to derivatives of ψ require the neighboring points. Moreover, the fifth order WENO interpolation requires large stencil to reconstruct high order polynomial. In such cases, an efficient interpolation method is necessary. The adaptive spatial differentiation method is considered as well as the adaptation of grid resolutions. In order to avoid the heavy computation of FD-WENO, in the smooth regions fixed stencil approximation without computing the non-linear WENO weights is used, and the characteristic decomposition method is replaced by a component-wise approach. Numerical results demonstrate that with the adaptive method we are able to resolve the solutions that agree well with the solution of the corresponding fine grid.

Evaluation of magnetic nanoparticle samples made from biocompatible ferucarbotran by time-correlation magnetic particle imaging reconstruction method

PubMed Central

2013-01-01

Background Molecular imaging using magnetic nanoparticles (MNPs)—magnetic particle imaging (MPI)—has attracted interest for the early diagnosis of cancer and cardiovascular disease. However, because a steep local magnetic field distribution is required to obtain a defined image, sophisticated hardware is required. Therefore, it is desirable to realize excellent image quality even with low-performance hardware. In this study, the spatial resolution of MPI was evaluated using an image reconstruction method based on the correlation information of the magnetization signal in a time domain and by applying MNP samples made from biocompatible ferucarbotran that have adjusted particle diameters. Methods The magnetization characteristics and particle diameters of four types of MNP samples made from ferucarbotran were evaluated. A numerical analysis based on our proposed method that calculates the image intensity from correlation information between the magnetization signal generated from MNPs and the system function was attempted, and the obtained image quality was compared with that using the prototype in terms of image resolution and image artifacts. Results MNP samples obtained by adjusting ferucarbotran showed superior properties to conventional ferucarbotran samples, and numerical analysis showed that the same image quality could be obtained using a gradient magnetic field generator with 0.6 times the performance. However, because image blurring was included theoretically by the proposed method, an algorithm will be required to improve performance. Conclusions MNP samples obtained by adjusting ferucarbotran showed magnetizing properties superior to conventional ferucarbotran samples, and by using such samples, comparable image quality (spatial resolution) could be obtained with a lower gradient magnetic field intensity. PMID:23734917

Spline Approximation of Thin Shell Dynamics

NASA Technical Reports Server (NTRS)

delRosario, R. C. H.; Smith, R. C.

1996-01-01

A spline-based method for approximating thin shell dynamics is presented here. While the method is developed in the context of the Donnell-Mushtari thin shell equations, it can be easily extended to the Byrne-Flugge-Lur'ye equations or other models for shells of revolution as warranted by applications. The primary requirements for the method include accuracy, flexibility and efficiency in smart material applications. To accomplish this, the method was designed to be flexible with regard to boundary conditions, material nonhomogeneities due to sensors and actuators, and inputs from smart material actuators such as piezoceramic patches. The accuracy of the method was also of primary concern, both to guarantee full resolution of structural dynamics and to facilitate the development of PDE-based controllers which ultimately require real-time implementation. Several numerical examples provide initial evidence demonstrating the efficacy of the method.

A feasible DY conjugate gradient method for linear equality constraints

NASA Astrophysics Data System (ADS)

LI, Can

2017-09-01

In this paper, we propose a feasible conjugate gradient method for solving linear equality constrained optimization problem. The method is an extension of the Dai-Yuan conjugate gradient method proposed by Dai and Yuan to linear equality constrained optimization problem. It can be applied to solve large linear equality constrained problem due to lower storage requirement. An attractive property of the method is that the generated direction is always feasible and descent direction. Under mild conditions, the global convergence of the proposed method with exact line search is established. Numerical experiments are also given which show the efficiency of the method.

Introducing a new family of short-range potentials and their numerical solutions using the asymptotic iteration method

NASA Astrophysics Data System (ADS)

Assi, I. A.; Sous, A. J.

2018-05-01

The goal of this work is to derive a new class of short-range potentials that could have a wide range of physical applications, specially in molecular physics. The tridiagonal representation approach has been developed beyond its limitations to produce new potentials by requiring the representation of the Schrödinger wave operator to be multidiagonal and symmetric. This produces a family of Hulthén potentials that has a specific structure, as mentioned in the introduction. As an example, we have solved the nonrelativistic wave equation for the new four-parameter short-range screening potential numerically using the asymptotic iteration method, where we tabulated the eigenvalues for both s -wave and arbitrary l -wave cases in tables.

Development of Condensing Mesh Method for Corner Domain at Numerical Simulation Magnetic System

NASA Astrophysics Data System (ADS)

Perepelkin, E.; Tarelkin, A.; Polyakova, R.; Kovalenko, A.

2018-05-01

A magnetostatic problem arises in searching for the distribution of the magnetic field generated by magnet systems of many physics research facilities, e.g., accelerators. The domain in which the boundaryvalue problem is solved often has a piecewise smooth boundary. In this case, numerical calculations of the problem require the consideration of the solution behavior in the corner domain. In this work we obtained the upper estimation of the magnetic field growth and propose a method of condensing the differential grid near the corner domain of vacuum in case of 3-dimensional space based on this estimation. An example of calculating a real model problem for SDP NICA in the domain containing a corner point is given.

Computation of Static Shapes and Voltages for Micromachined Deformable Mirrors with Nonlinear Electrostatic Actuators

NASA Technical Reports Server (NTRS)

Wang, P. K. C.; Hadaegh, F. Y.

1996-01-01

In modeling micromachined deformable mirrors with electrostatic actuators whose gap spacings are of the same order of magnitude as those of the surface deformations, it is necessary to use nonlinear models for the actuators. In this paper, we consider micromachined deformable mirrors modeled by a membrane or plate equation with nonlinear electrostatic actuator characteristics. Numerical methods for computing the mirror deformation due to given actuator voltages and the actuator voltages required for producing the desired deformations at the actuator locations are presented. The application of the proposed methods to circular deformable mirrors whose surfaces are modeled by elastic membranes is discussed in detail. Numerical results are obtained for a typical circular micromachined mirror with electrostatic actuators.

Semi-implicit finite difference methods for three-dimensional shallow water flow

USGS Publications Warehouse

Casulli, Vincenzo; Cheng, Ralph T.

1992-01-01

A semi-implicit finite difference method for the numerical solution of three-dimensional shallow water flows is presented and discussed. The governing equations are the primitive three-dimensional turbulent mean flow equations where the pressure distribution in the vertical has been assumed to be hydrostatic. In the method of solution a minimal degree of implicitness has been adopted in such a fashion that the resulting algorithm is stable and gives a maximal computational efficiency at a minimal computational cost. At each time step the numerical method requires the solution of one large linear system which can be formally decomposed into a set of small three-diagonal systems coupled with one five-diagonal system. All these linear systems are symmetric and positive definite. Thus the existence and uniquencess of the numerical solution are assured. When only one vertical layer is specified, this method reduces as a special case to a semi-implicit scheme for solving the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm has been shown to be fast, accurate and mass-conservative and can also be applied to simulate flooding and drying of tidal mud-flats in conjunction with three-dimensional flows. Furthermore, the resulting algorithm is fully vectorizable for an efficient implementation on modern vector computers.

An Estimating Equations Approach for the LISCOMP Model.

ERIC Educational Resources Information Center

Reboussin, Beth A.; Liang, Kung-Lee

1998-01-01

A quadratic estimating equations approach for the LISCOMP model is proposed that only requires specification of the first two moments. This method is compared with a three-stage generalized least squares approach through a numerical study and application to a study of life events and neurotic illness. (SLD)

Decision Support for Environmental Management of Industrial Non-Hazardous Secondary Materials: New Analytical Methods Combined with Simulation and Optimization Modeling

EPA Science Inventory

Non-hazardous solid materials from industrial processes, once regarded as waste and disposed in landfills, offer numerous environmental and economic advantages when put to beneficial uses (BUs). Proper management of these industrial non-hazardous secondary materials (INSM) requir...

WASP (Write a Scientific Paper) using Excel - 10: Contingency tables.

PubMed

Grech, Victor

2018-06-01

Contingency tables may be required to perform chi-test analyses. This provides pointers as to how to do this in Microsoft Excel and explains how to set up methods to calculate confidence intervals for proportions, including proportions with zero numerators. Copyright © 2018 Elsevier B.V. All rights reserved.

Cooperative Learning in Reservoir Simulation Classes: Overcoming Disparate Entry Skills

ERIC Educational Resources Information Center

Awang, Mariyamni

2006-01-01

Reservoir simulation is one of the core courses in the petroleum engineering curriculum and it requires knowledge and skills in three major disciplines, namely programming, numerical methods and reservoir engineering. However, there were often gaps in the students' readiness to undertake the course, even after completing the necessary…

77 FR 59998 - Self-Regulatory Organizations; The Options Clearing Corporation; Advance Notice Relating to the...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-10-01

... System for Theoretical Analysis and Numerical Simulations (``STANS''). STANS calculates margin with...'' simulations designed to measure the additional asset value required in any portfolio to eliminate an... Commission process and review your comments more efficiently, please use only one method. The Commission will...

Using Rubrics to Assess Learning in Course-Integrated Library Instruction

ERIC Educational Resources Information Center

Gariepy, Laura W.; Stout, Jennifer A.; Hodge, Megan L.

2016-01-01

Librarians face numerous challenges when designing effective, sustainable methods for assessing student learning outcomes in one-shot, course-integrated library instruction sessions. We explore the use of rubrics to programmatically assess authentic learning exercises completed in one-shot library sessions for a large, required sophomore-level…

Dispersion of Lamb waves in a honeycomb composite sandwich panel.

PubMed

Baid, Harsh; Schaal, Christoph; Samajder, Himadri; Mal, Ajit

2015-02-01

Composite materials are increasingly being used in advanced aircraft and aerospace structures. Despite their many advantages, composites are often susceptible to hidden damages that may occur during manufacturing and/or service of the structure. Therefore, safe operation of composite structures requires careful monitoring of the initiation and growth of such defects. Ultrasonic methods using guided waves offer a reliable and cost effective method for defects monitoring in advanced structures due to their long propagation range and their sensitivity to defects in their propagation path. In this paper, some of the useful properties of guided Lamb type waves are investigated, using analytical, numerical and experimental methods, in an effort to provide the knowledge base required for the development of viable structural health monitoring systems for composite structures. The laboratory experiments involve a pitch-catch method in which a pair of movable transducers is placed on the outside surface of the structure for generating and recording the wave signals. The specific cases considered include an aluminum plate, a woven composite laminate and an aluminum honeycomb sandwich panel. The agreement between experimental, numerical and theoretical results are shown to be excellent in certain frequency ranges, providing a guidance for the design of effective inspection systems. Copyright © 2014 Elsevier B.V. All rights reserved.

Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a k-space pseudospectral method.

PubMed

Treeby, Bradley E; Jaros, Jiri; Rendell, Alistair P; Cox, B T

2012-06-01

The simulation of nonlinear ultrasound propagation through tissue realistic media has a wide range of practical applications. However, this is a computationally difficult problem due to the large size of the computational domain compared to the acoustic wavelength. Here, the k-space pseudospectral method is used to reduce the number of grid points required per wavelength for accurate simulations. The model is based on coupled first-order acoustic equations valid for nonlinear wave propagation in heterogeneous media with power law absorption. These are derived from the equations of fluid mechanics and include a pressure-density relation that incorporates the effects of nonlinearity, power law absorption, and medium heterogeneities. The additional terms accounting for convective nonlinearity and power law absorption are expressed as spatial gradients making them efficient to numerically encode. The governing equations are then discretized using a k-space pseudospectral technique in which the spatial gradients are computed using the Fourier-collocation method. This increases the accuracy of the gradient calculation and thus relaxes the requirement for dense computational grids compared to conventional finite difference methods. The accuracy and utility of the developed model is demonstrated via several numerical experiments, including the 3D simulation of the beam pattern from a clinical ultrasound probe.

Numerical Modeling of Fluorescence Emission Energy Dispersion in Luminescent Solar Concentrator

NASA Astrophysics Data System (ADS)

Li, Lanfang; Sheng, Xing; Rogers, John; Nuzzo, Ralph

2013-03-01

We present a numerical modeling method and the corresponding experimental results, to address fluorescence emission dispersion for applications such as luminescent solar concentrator and light emitting diode color correction. Previously established modeling methods utilized a statistic-thermodynamic theory (Kenard-Stepnov etc.) that required a thorough understanding of the free energy landscape of the fluorophores. Some more recent work used an empirical approximation of the measured emission energy dispersion profile without considering anti-Stokes shifting during absorption and emission. In this work we present a technique for modeling fluorescence absorption and emission that utilizes the experimentally measured spectrum and approximates the observable Frank-Condon vibronic states as a continuum and takes into account thermodynamic energy relaxation by allowing thermal fluctuations. This new approximation method relaxes the requirement for knowledge of the fluorophore system and reduces demand on computing resources while still capturing the essence of physical process. We present simulation results of the energy distribution of emitted photons and compare them with experimental results with good agreement in terms of peak red-shift and intensity attenuation in a luminescent solar concentrator. This work is supported by the DOE `Light-Material Interactions in Energy Conversion' Energy Frontier Research Center under grant DE-SC0001293.

Numerical calculation of charge exchange cross sections for plasma diagnostics

NASA Astrophysics Data System (ADS)

Mendez, Luis

2016-09-01

The diagnostics of impurity density and temperature in the plasma core in tokamak plasmas is carried out by applying the charge exchange recombination spectroscopy (CXRS) technique, where a fast beam of H atoms collides with the plasma particles leading to electron capture reactions with the impurity ions. The diagnostics is based on the emission of the excited ions formed in the electron capture. The application of the CXRS requires the knowledge of accurate state-selective cross sections, which in general are not accessible experimentally, and the calculation of cross sections for the high n capture levels, required for the diagnostics in the intermediate energy domain of the probe beam, is particularly difficult. In this work, we present a lattice numerical method to solve the time dependent Schrödinger equation. The method is based on the GridTDSE package, it is applicable in the wide energy range 1 - 500 keV/u and can be used to assess the accuracy of previous calculations. The application of the method will be illustrated with calculations for collisions of multiply charged ions with H. Work partially supported by project ENE2014-52432-R (Secretaria de Estado de I+D+i, Spain).

Improving the efficiency of configurational-bias Monte Carlo: A density-guided method for generating bending angle trials for linear and branched molecules

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

Sepehri, Aliasghar; Loeffler, Troy D.; Chen, Bin, E-mail: binchen@lsu.edu

2014-08-21

A new method has been developed to generate bending angle trials to improve the acceptance rate and the speed of configurational-bias Monte Carlo. Whereas traditionally the trial geometries are generated from a uniform distribution, in this method we attempt to use the exact probability density function so that each geometry generated is likely to be accepted. In actual practice, due to the complexity of this probability density function, a numerical representation of this distribution function would be required. This numerical table can be generated a priori from the distribution function. This method has been tested on a united-atom model ofmore » alkanes including propane, 2-methylpropane, and 2,2-dimethylpropane, that are good representatives of both linear and branched molecules. It has been shown from these test cases that reasonable approximations can be made especially for the highly branched molecules to reduce drastically the dimensionality and correspondingly the amount of the tabulated data that is needed to be stored. Despite these approximations, the dependencies between the various geometrical variables can be still well considered, as evident from a nearly perfect acceptance rate achieved. For all cases, the bending angles were shown to be sampled correctly by this method with an acceptance rate of at least 96% for 2,2-dimethylpropane to more than 99% for propane. Since only one trial is required to be generated for each bending angle (instead of thousands of trials required by the conventional algorithm), this method can dramatically reduce the simulation time. The profiling results of our Monte Carlo simulation code show that trial generation, which used to be the most time consuming process, is no longer the time dominating component of the simulation.« less

Approximate Solution Methods for Spectral Radiative Transfer in High Refractive Index Layers

NASA Technical Reports Server (NTRS)

Siegel, R.; Spuckler, C. M.

1994-01-01

Some ceramic materials for high temperature applications are partially transparent for radiative transfer. The refractive indices of these materials can be substantially greater than one which influences internal radiative emission and reflections. Heat transfer behavior of single and laminated layers has been obtained in the literature by numerical solutions of the radiative transfer equations coupled with heat conduction and heating at the boundaries by convection and radiation. Two-flux and diffusion methods are investigated here to obtain approximate solutions using a simpler formulation than required for exact numerical solutions. Isotropic scattering is included. The two-flux method for a single layer yields excellent results for gray and two band spectral calculations. The diffusion method yields a good approximation for spectral behavior in laminated multiple layers if the overall optical thickness is larger than about ten. A hybrid spectral model is developed using the two-flux method in the optically thin bands, and radiative diffusion in bands that are optically thick.

Gaussian representation of high-intensity focused ultrasound beams.

PubMed

Soneson, Joshua E; Myers, Matthew R

2007-11-01

A method for fast numerical simulation of high-intensity focused ultrasound beams is derived. The method is based on the frequency-domain representation of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, and assumes for each harmonic a Gaussian transverse pressure distribution at all distances from the transducer face. The beamwidths of the harmonics are constrained to vary inversely with the square root of the harmonic number, and as such this method may be viewed as an extension of a quasilinear approximation. The technique is capable of determining pressure or intensity fields of moderately nonlinear high-intensity focused ultrasound beams in water or biological tissue, usually requiring less than a minute of computer time on a modern workstation. Moreover, this method is particularly well suited to high-gain simulations since, unlike traditional finite-difference methods, it is not subject to resolution limitations in the transverse direction. Results are shown to be in reasonable agreement with numerical solutions of the full KZK equation in both tissue and water for moderately nonlinear beams.

Adaptive [theta]-methods for pricing American options

NASA Astrophysics Data System (ADS)

Khaliq, Abdul Q. M.; Voss, David A.; Kazmi, Kamran

2008-12-01

We develop adaptive [theta]-methods for solving the Black-Scholes PDE for American options. By adding a small, continuous term, the Black-Scholes PDE becomes an advection-diffusion-reaction equation on a fixed spatial domain. Standard implementation of [theta]-methods would require a Newton-type iterative procedure at each time step thereby increasing the computational complexity of the methods. Our linearly implicit approach avoids such complications. We establish a general framework under which [theta]-methods satisfy a discrete version of the positivity constraint characteristic of American options, and numerically demonstrate the sensitivity of the constraint. The positivity results are established for the single-asset and independent two-asset models. In addition, we have incorporated and analyzed an adaptive time-step control strategy to increase the computational efficiency. Numerical experiments are presented for one- and two-asset American options, using adaptive exponential splitting for two-asset problems. The approach is compared with an iterative solution of the two-asset problem in terms of computational efficiency.

Global optimisation methods for poroelastic material characterisation using a clamped sample in a Kundt tube setup

NASA Astrophysics Data System (ADS)

Vanhuyse, Johan; Deckers, Elke; Jonckheere, Stijn; Pluymers, Bert; Desmet, Wim

2016-02-01

The Biot theory is commonly used for the simulation of the vibro-acoustic behaviour of poroelastic materials. However, it relies on a number of material parameters. These can be hard to characterize and require dedicated measurement setups, yielding a time-consuming and costly characterisation. This paper presents a characterisation method which is able to identify all material parameters using only an impedance tube. The method relies on the assumption that the sample is clamped within the tube, that the shear wave is excited and that the acoustic field is no longer one-dimensional. This paper numerically shows the potential of the developed method. It therefore performs a sensitivity analysis of the quantification parameters, i.e. reflection coefficients and relative pressures, and a parameter estimation using global optimisation methods. A 3-step procedure is developed and validated. It is shown that even in the presence of numerically simulated noise this procedure leads to a robust parameter estimation.

A compressible multiphase framework for simulating supersonic atomization

NASA Astrophysics Data System (ADS)

Regele, Jonathan D.; Garrick, Daniel P.; Hosseinzadeh-Nik, Zahra; Aslani, Mohamad; Owkes, Mark

2016-11-01

The study of atomization in supersonic combustors is critical in designing efficient and high performance scramjets. Numerical methods incorporating surface tension effects have largely focused on the incompressible regime as most atomization applications occur at low Mach numbers. Simulating surface tension effects in high speed compressible flow requires robust numerical methods that can handle discontinuities caused by both material interfaces and shocks. A shock capturing/diffused interface method is developed to simulate high-speed compressible gas-liquid flows with surface tension effects using the five-equation model. This includes developments that account for the interfacial pressure jump that occurs in the presence of surface tension. A simple and efficient method for computing local interface curvature is developed and an acoustic non-dimensional scaling for the surface tension force is proposed. The method successfully captures a variety of droplet breakup modes over a range of Weber numbers and demonstrates the impact of surface tension in countering droplet deformation in both subsonic and supersonic cross flows.

Prediction of Aerodynamic Coefficient using Genetic Algorithm Optimized Neural Network for Sparse Data

NASA Technical Reports Server (NTRS)

Rajkumar, T.; Bardina, Jorge; Clancy, Daniel (Technical Monitor)

2002-01-01

Wind tunnels use scale models to characterize aerodynamic coefficients, Wind tunnel testing can be slow and costly due to high personnel overhead and intensive power utilization. Although manual curve fitting can be done, it is highly efficient to use a neural network to define the complex relationship between variables. Numerical simulation of complex vehicles on the wide range of conditions required for flight simulation requires static and dynamic data. Static data at low Mach numbers and angles of attack may be obtained with simpler Euler codes. Static data of stalled vehicles where zones of flow separation are usually present at higher angles of attack require Navier-Stokes simulations which are costly due to the large processing time required to attain convergence. Preliminary dynamic data may be obtained with simpler methods based on correlations and vortex methods; however, accurate prediction of the dynamic coefficients requires complex and costly numerical simulations. A reliable and fast method of predicting complex aerodynamic coefficients for flight simulation I'S presented using a neural network. The training data for the neural network are derived from numerical simulations and wind-tunnel experiments. The aerodynamic coefficients are modeled as functions of the flow characteristics and the control surfaces of the vehicle. The basic coefficients of lift, drag and pitching moment are expressed as functions of angles of attack and Mach number. The modeled and training aerodynamic coefficients show good agreement. This method shows excellent potential for rapid development of aerodynamic models for flight simulation. Genetic Algorithms (GA) are used to optimize a previously built Artificial Neural Network (ANN) that reliably predicts aerodynamic coefficients. Results indicate that the GA provided an efficient method of optimizing the ANN model to predict aerodynamic coefficients. The reliability of the ANN using the GA includes prediction of aerodynamic coefficients to an accuracy of 110% . In our problem, we would like to get an optimized neural network architecture and minimum data set. This has been accomplished within 500 training cycles of a neural network. After removing training pairs (outliers), the GA has produced much better results. The neural network constructed is a feed forward neural network with a back propagation learning mechanism. The main goal has been to free the network design process from constraints of human biases, and to discover better forms of neural network architectures. The automation of the network architecture search by genetic algorithms seems to have been the best way to achieve this goal.

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

Jing Yanfei, E-mail: yanfeijing@uestc.edu.c; Huang Tingzhu, E-mail: tzhuang@uestc.edu.c; Duan Yong, E-mail: duanyong@yahoo.c

This study is mainly focused on iterative solutions with simple diagonal preconditioning to two complex-valued nonsymmetric systems of linear equations arising from a computational chemistry model problem proposed by Sherry Li of NERSC. Numerical experiments show the feasibility of iterative methods to some extent when applied to the problems and reveal the competitiveness of our recently proposed Lanczos biconjugate A-orthonormalization methods to other classic and popular iterative methods. By the way, experiment results also indicate that application specific preconditioners may be mandatory and required for accelerating convergence.

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.

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.

A p-version finite element method for steady incompressible fluid flow and convective heat transfer

NASA Technical Reports Server (NTRS)

Winterscheidt, Daniel L.

1993-01-01

A new p-version finite element formulation for steady, incompressible fluid flow and convective heat transfer problems is presented. The steady-state residual equations are obtained by considering a limiting case of the least-squares formulation for the transient problem. The method circumvents the Babuska-Brezzi condition, permitting the use of equal-order interpolation for velocity and pressure, without requiring the use of arbitrary parameters. Numerical results are presented to demonstrate the accuracy and generality of the method.

A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries.

PubMed

Ge, Liang; Sotiropoulos, Fotis

2007-08-01

A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [1]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus.

A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries

PubMed Central

Ge, Liang; Sotiropoulos, Fotis

2008-01-01

A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [1]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus. PMID:19194533

3-D numerical simulations of earthquake ground motion in sedimentary basins: testing accuracy through stringent models

NASA Astrophysics Data System (ADS)

Chaljub, Emmanuel; Maufroy, Emeline; Moczo, Peter; Kristek, Jozef; Hollender, Fabrice; Bard, Pierre-Yves; Priolo, Enrico; Klin, Peter; de Martin, Florent; Zhang, Zhenguo; Zhang, Wei; Chen, Xiaofei

2015-04-01

Differences between 3-D numerical predictions of earthquake ground motion in the Mygdonian basin near Thessaloniki, Greece, led us to define four canonical stringent models derived from the complex realistic 3-D model of the Mygdonian basin. Sediments atop an elastic bedrock are modelled in the 1D-sharp and 1D-smooth models using three homogeneous layers and smooth velocity distribution, respectively. The 2D-sharp and 2D-smooth models are extensions of the 1-D models to an asymmetric sedimentary valley. In all cases, 3-D wavefields include strongly dispersive surface waves in the sediments. We compared simulations by the Fourier pseudo-spectral method (FPSM), the Legendre spectral-element method (SEM) and two formulations of the finite-difference method (FDM-S and FDM-C) up to 4 Hz. The accuracy of individual solutions and level of agreement between solutions vary with type of seismic waves and depend on the smoothness of the velocity model. The level of accuracy is high for the body waves in all solutions. However, it strongly depends on the discrete representation of the material interfaces (at which material parameters change discontinuously) for the surface waves in the sharp models. An improper discrete representation of the interfaces can cause inaccurate numerical modelling of surface waves. For all the numerical methods considered, except SEM with mesh of elements following the interfaces, a proper implementation of interfaces requires definition of an effective medium consistent with the interface boundary conditions. An orthorhombic effective medium is shown to significantly improve accuracy and preserve the computational efficiency of modelling. The conclusions drawn from the analysis of the results of the canonical cases greatly help to explain differences between numerical predictions of ground motion in realistic models of the Mygdonian basin. We recommend that any numerical method and code that is intended for numerical prediction of earthquake ground motion should be verified through stringent models that would make it possible to test the most important aspects of accuracy.

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

Li, C.; Yu, G.; Wang, K.

The physical designs of the new concept reactors which have complex structure, various materials and neutronic energy spectrum, have greatly improved the requirements to the calculation methods and the corresponding computing hardware. Along with the widely used parallel algorithm, heterogeneous platforms architecture has been introduced into numerical computations in reactor physics. Because of the natural parallel characteristics, the CPU-FPGA architecture is often used to accelerate numerical computation. This paper studies the application and features of this kind of heterogeneous platforms used in numerical calculation of reactor physics through practical examples. After the designed neutron diffusion module based on CPU-FPGA architecturemore » achieves a 11.2 speed up factor, it is proved to be feasible to apply this kind of heterogeneous platform into reactor physics. (authors)« less

Some variance reduction methods for numerical stochastic homogenization

PubMed Central

Blanc, X.; Le Bris, C.; Legoll, F.

2016-01-01

We give an overview of a series of recent studies devoted to variance reduction techniques for numerical stochastic homogenization. Numerical homogenization requires that a set of problems is solved at the microscale, the so-called corrector problems. In a random environment, these problems are stochastic and therefore need to be repeatedly solved, for several configurations of the medium considered. An empirical average over all configurations is then performed using the Monte Carlo approach, so as to approximate the effective coefficients necessary to determine the macroscopic behaviour. Variance severely affects the accuracy and the cost of such computations. Variance reduction approaches, borrowed from other contexts in the engineering sciences, can be useful. Some of these variance reduction techniques are presented, studied and tested here. PMID:27002065

Numerical Investigation of the Performance of a Supersonic Combustion Chamber and Comparison with Experiments

NASA Astrophysics Data System (ADS)

Banica, M. C.; Chun, J.; Scheuermann, T.; Weigand, B.; Wolfersdorf, J. v.

2009-01-01

Scramjet powered vehicles can decrease costs for access to space but substantial obstacles still exist in their realization. For example, experiments in the relevant Mach number regime are difficult to perform and flight testing is expensive. Therefore, numerical methods are often employed for system layout but they require validation against experimental data. Here, we validate the commercial code CFD++ against experimental results for hydrogen combustion in the supersonic combustion facility of the Institute of Aerospace Thermodynamics (ITLR) at the Universität Stuttgart. Fuel is injected through a lobed a strut injector, which provides rapid mixing. Our numerical data shows reasonable agreement with experiments. We further investigate effects of varying equivalence ratios on several important performance parameters.

Gradient optimization and nonlinear control

NASA Technical Reports Server (NTRS)

Hasdorff, L.

1976-01-01

The book represents an introduction to computation in control by an iterative, gradient, numerical method, where linearity is not assumed. The general language and approach used are those of elementary functional analysis. The particular gradient method that is emphasized and used is conjugate gradient descent, a well known method exhibiting quadratic convergence while requiring very little more computation than simple steepest descent. Constraints are not dealt with directly, but rather the approach is to introduce them as penalty terms in the criterion. General conjugate gradient descent methods are developed and applied to problems in control.

Boundedness and convergence of online gradient method with penalty for feedforward neural networks.

PubMed

Zhang, Huisheng; Wu, Wei; Liu, Fei; Yao, Mingchen

2009-06-01

In this brief, we consider an online gradient method with penalty for training feedforward neural networks. Specifically, the penalty is a term proportional to the norm of the weights. Its roles in the method are to control the magnitude of the weights and to improve the generalization performance of the network. By proving that the weights are automatically bounded in the network training with penalty, we simplify the conditions that are required for convergence of online gradient method in literature. A numerical example is given to support the theoretical analysis.

A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation

NASA Technical Reports Server (NTRS)

Jones, Brandon A.; Anderson, Rodney L.

2012-01-01

Demands on numerical integration algorithms for astrodynamics applications continue to increase. Common methods, like explicit Runge-Kutta, meet the orbit propagation needs of most scenarios, but more specialized scenarios require new techniques to meet both computational efficiency and accuracy needs. This paper provides an extensive survey on the application of symplectic and collocation methods to astrodynamics. Both of these methods benefit from relatively recent theoretical developments, which improve their applicability to artificial satellite orbit propagation. This paper also details their implementation, with several tests demonstrating their advantages and disadvantages.

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.

Gaussian process regression to accelerate geometry optimizations relying on numerical differentiation

NASA Astrophysics Data System (ADS)

Schmitz, Gunnar; Christiansen, Ove

2018-06-01

We study how with means of Gaussian Process Regression (GPR) geometry optimizations, which rely on numerical gradients, can be accelerated. The GPR interpolates a local potential energy surface on which the structure is optimized. It is found to be efficient to combine results on a low computational level (HF or MP2) with the GPR-calculated gradient of the difference between the low level method and the target method, which is a variant of explicitly correlated Coupled Cluster Singles and Doubles with perturbative Triples correction CCSD(F12*)(T) in this study. Overall convergence is achieved if both the potential and the geometry are converged. Compared to numerical gradient-based algorithms, the number of required single point calculations is reduced. Although introducing an error due to the interpolation, the optimized structures are sufficiently close to the minimum of the target level of theory meaning that the reference and predicted minimum only vary energetically in the μEh regime.

The Robin Hood method - A novel numerical method for electrostatic problems based on a non-local charge transfer

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

Lazic, Predrag; Stefancic, Hrvoje; Abraham, Hrvoje

2006-03-20

We introduce a novel numerical method, named the Robin Hood method, of solving electrostatic problems. The approach of the method is closest to the boundary element methods, although significant conceptual differences exist with respect to this class of methods. The method achieves equipotentiality of conducting surfaces by iterative non-local charge transfer. For each of the conducting surfaces, non-local charge transfers are performed between surface elements, which differ the most from the targeted equipotentiality of the surface. The method is tested against analytical solutions and its wide range of application is demonstrated. The method has appealing technical characteristics. For the problemmore » with N surface elements, the computational complexity of the method essentially scales with N {sup {alpha}}, where {alpha} < 2, the required computer memory scales with N, while the error of the potential decreases exponentially with the number of iterations for many orders of magnitude of the error, without the presence of the Critical Slowing Down. The Robin Hood method could prove useful in other classical or even quantum problems. Some future development ideas for possible applications outside electrostatics are addressed.« less

Analysis of the iteratively regularized Gauss-Newton method under a heuristic rule

NASA Astrophysics Data System (ADS)

Jin, Qinian; Wang, Wei

2018-03-01

The iteratively regularized Gauss-Newton method is one of the most prominent regularization methods for solving nonlinear ill-posed inverse problems when the data is corrupted by noise. In order to produce a useful approximate solution, this iterative method should be terminated properly. The existing a priori and a posteriori stopping rules require accurate information on the noise level, which may not be available or reliable in practical applications. In this paper we propose a heuristic selection rule for this regularization method, which requires no information on the noise level. By imposing certain conditions on the noise, we derive a posteriori error estimates on the approximate solutions under various source conditions. Furthermore, we establish a convergence result without using any source condition. Numerical results are presented to illustrate the performance of our heuristic selection rule.

7 CFR 51.2927 - Marking and packing requirements.

Code of Federal Regulations, 2012 CFR

2012-01-01

... and packing requirements. The minimum size or numerical count of the apricots in any package shall be plainly labeled, stenciled, or otherwise marked on the package. (a) Numerical count. When the numerical...

7 CFR 51.2927 - Marking and packing requirements.

Code of Federal Regulations, 2010 CFR

2010-01-01

... and packing requirements. The minimum size or numerical count of the apricots in any package shall be plainly labeled, stenciled, or otherwise marked on the package. (a) Numerical count. When the numerical...

7 CFR 51.2927 - Marking and packing requirements.

Code of Federal Regulations, 2011 CFR

2011-01-01

... and packing requirements. The minimum size or numerical count of the apricots in any package shall be plainly labeled, stenciled, or otherwise marked on the package. (a) Numerical count. When the numerical...

7 CFR 51.2927 - Marking and packing requirements.

Code of Federal Regulations, 2013 CFR

2013-01-01

... Requirements § 51.2927 Marking and packing requirements. The minimum size or numerical count of the apricots in any package shall be plainly labeled, stenciled, or otherwise marked on the package. (a) Numerical count. When the numerical count is used the fruit in any sample shall not vary more than one-fourth inch...

7 CFR 51.2927 - Marking and packing requirements.

Code of Federal Regulations, 2014 CFR

2014-01-01

... Requirements § 51.2927 Marking and packing requirements. The minimum size or numerical count of the apricots in any package shall be plainly labeled, stenciled, or otherwise marked on the package. (a) Numerical count. When the numerical count is used the fruit in any sample shall not vary more than one-fourth inch...

A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates

NASA Astrophysics Data System (ADS)

Läuter, Matthias; Giraldo, Francis X.; Handorf, Dörthe; Dethloff, Klaus

2008-12-01

A global model of the atmosphere is presented governed by the shallow water equations and discretized by a Runge-Kutta discontinuous Galerkin method on an unstructured triangular grid. The shallow water equations on the sphere, a two-dimensional surface in R3, are locally represented in terms of spherical triangular coordinates, the appropriate local coordinate mappings on triangles. On every triangular grid element, this leads to a two-dimensional representation of tangential momentum and therefore only two discrete momentum equations. The discontinuous Galerkin method consists of an integral formulation which requires both area (elements) and line (element faces) integrals. Here, we use a Rusanov numerical flux to resolve the discontinuous fluxes at the element faces. A strong stability-preserving third-order Runge-Kutta method is applied for the time discretization. The polynomial space of order k on each curved triangle of the grid is characterized by a Lagrange basis and requires high-order quadature rules for the integration over elements and element faces. For the presented method no mass matrix inversion is necessary, except in a preprocessing step. The validation of the atmospheric model has been done considering standard tests from Williamson et al. [D.L. Williamson, J.B. Drake, J.J. Hack, R. Jakob, P.N. Swarztrauber, A standard test set for numerical approximations to the shallow water equations in spherical geometry, J. Comput. Phys. 102 (1992) 211-224], unsteady analytical solutions of the nonlinear shallow water equations and a barotropic instability caused by an initial perturbation of a jet stream. A convergence rate of O(Δx) was observed in the model experiments. Furthermore, a numerical experiment is presented, for which the third-order time-integration method limits the model error. Thus, the time step Δt is restricted by both the CFL-condition and accuracy demands. Conservation of mass was shown up to machine precision and energy conservation converges for both increasing grid resolution and increasing polynomial order k.

Analytical solutions for coagulation and condensation kinetics of composite particles

NASA Astrophysics Data System (ADS)

Piskunov, Vladimir N.

2013-04-01

The processes of composite particles formation consisting of a mixture of different materials are essential for many practical problems: for analysis of the consequences of accidental releases in atmosphere; for simulation of precipitation formation in clouds; for description of multi-phase processes in chemical reactors and industrial facilities. Computer codes developed for numerical simulation of these processes require optimization of computational methods and verification of numerical programs. Kinetic equations of composite particle formation are given in this work in a concise form (impurity integrated). Coagulation, condensation and external sources associated with nucleation are taken into account. Analytical solutions were obtained in a number of model cases. The general laws for fraction redistribution of impurities were defined. The results can be applied to develop numerical algorithms considerably reducing the simulation effort, as well as to verify the numerical programs for calculation of the formation kinetics of composite particles in the problems of practical importance.

Energy conserving numerical methods for the computation of complex vortical flows

NASA Astrophysics Data System (ADS)

Allaneau, Yves

One of the original goals of this thesis was to develop numerical tools to help with the design of micro air vehicles. Micro Air Vehicles (MAVs) are small flying devices of only a few inches in wing span. Some people consider that as their size becomes smaller and smaller, it would be increasingly more difficult to keep all the classical control surfaces such as the rudders, the ailerons and the usual propellers. Over the years, scientists took inspiration from nature. Birds, by flapping and deforming their wings, are capable of accurate attitude control and are able to generate propulsion. However, the biomimicry design has its own limitations and it is difficult to place a hummingbird in a wind tunnel to study precisely the motion of its wings. Our approach was to use numerical methods to tackle this challenging problem. In order to precisely evaluate the lift and drag generated by the wings, one needs to be able to capture with high fidelity the extremely complex vortical flow produced in the wake. This requires a numerical method that is stable yet not too dissipative, so that the vortices do not get diffused in an unphysical way. We solved this problem by developing a new Discontinuous Galerkin scheme that, in addition to conserving mass, momentum and total energy locally, also preserves kinetic energy globally. This property greatly improves the stability of the simulations, especially in the special case p=0 when the approximation polynomials are taken to be piecewise constant (we recover a finite volume scheme). In addition to needing an adequate numerical scheme, a high fidelity solution requires many degrees of freedom in the computations to represent the flow field. The size of the smallest eddies in the flow is given by the Kolmogoroff scale. Capturing these eddies requires a mesh counting in the order of Re³ cells, where Re is the Reynolds number of the flow. We show that under-resolving the system, to a certain extent, is acceptable. However our simulations still required meshes containing tens of millions of degrees of freedom. Such computations can only be done in reasonable amounts of time by spreading the work on multiple CPUs via domain decomposition. Further speed-up efforts were made by implementing a version of the code for GPUs using Nvidia's CUDA programming language. Finally we searched for optimal wing motions by coupling our computational fluid dynamics code with the optimization package SNOPT. The wing motion was parameterized by a few angles describing the local curvature and the twisting of the wing. These were expressed in terms of truncated Fourier series, the Fourier coefficients being our optimization parameters. With this approach we were able to obtain propulsive efficiencies of around 50% (thrust power/power input).

Numerical Simulation of Two Phase Flows

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

2001-01-01

Two phase flows can be found in broad situations in nature, biology, and industry devices and can involve diverse and complex mechanisms. While the physical models may be specific for certain situations, the mathematical formulation and numerical treatment for solving the governing equations can be general. Hence, we will require information concerning each individual phase as needed in a single phase. but also the interactions between them. These interaction terms, however, pose additional numerical challenges because they are beyond the basis that we use to construct modern numerical schemes, namely the hyperbolicity of equations. Moreover, due to disparate differences in time scales, fluid compressibility and nonlinearity become acute, further complicating the numerical procedures. In this paper, we will show the ideas and procedure how the AUSM-family schemes are extended for solving two phase flows problems. Specifically, both phases are assumed in thermodynamic equilibrium, namely, the time scales involved in phase interactions are extremely short in comparison with those in fluid speeds and pressure fluctuations. Details of the numerical formulation and issues involved are discussed and the effectiveness of the method are demonstrated for several industrial examples.

A frequency dependent preconditioned wavelet method for atmospheric tomography

NASA Astrophysics Data System (ADS)

Yudytskiy, Mykhaylo; Helin, Tapio; Ramlau, Ronny

2013-12-01

Atmospheric tomography, i.e. the reconstruction of the turbulence in the atmosphere, is a main task for the adaptive optics systems of the next generation telescopes. For extremely large telescopes, such as the European Extremely Large Telescope, this problem becomes overly complex and an efficient algorithm is needed to reduce numerical costs. Recently, a conjugate gradient method based on wavelet parametrization of turbulence layers was introduced [5]. An iterative algorithm can only be numerically efficient when the number of iterations required for a sufficient reconstruction is low. A way to achieve this is to design an efficient preconditioner. In this paper we propose a new frequency-dependent preconditioner for the wavelet method. In the context of a multi conjugate adaptive optics (MCAO) system simulated on the official end-to-end simulation tool OCTOPUS of the European Southern Observatory we demonstrate robustness and speed of the preconditioned algorithm. We show that three iterations are sufficient for a good reconstruction.

On Efficient Multigrid Methods for Materials Processing Flows with Small Particles

NASA Technical Reports Server (NTRS)

Thomas, James (Technical Monitor); Diskin, Boris; Harik, VasylMichael

2004-01-01

Multiscale modeling of materials requires simulations of multiple levels of structural hierarchy. The computational efficiency of numerical methods becomes a critical factor for simulating large physical systems with highly desperate length scales. Multigrid methods are known for their superior efficiency in representing/resolving different levels of physical details. The efficiency is achieved by employing interactively different discretizations on different scales (grids). To assist optimization of manufacturing conditions for materials processing with numerous particles (e.g., dispersion of particles, controlling flow viscosity and clusters), a new multigrid algorithm has been developed for a case of multiscale modeling of flows with small particles that have various length scales. The optimal efficiency of the algorithm is crucial for accurate predictions of the effect of processing conditions (e.g., pressure and velocity gradients) on the local flow fields that control the formation of various microstructures or clusters.

Particle swarm optimization and gravitational wave data analysis: Performance on a binary inspiral testbed

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

Wang Yan; Mohanty, Soumya D.; Center for Gravitational Wave Astronomy, Department of Physics and Astronomy, University of Texas at Brownsville, 80 Fort Brown, Brownsville, Texas 78520

2010-03-15

The detection and estimation of gravitational wave signals belonging to a parameterized family of waveforms requires, in general, the numerical maximization of a data-dependent function of the signal parameters. Because of noise in the data, the function to be maximized is often highly multimodal with numerous local maxima. Searching for the global maximum then becomes computationally expensive, which in turn can limit the scientific scope of the search. Stochastic optimization is one possible approach to reducing computational costs in such applications. We report results from a first investigation of the particle swarm optimization method in this context. The method ismore » applied to a test bed motivated by the problem of detection and estimation of a binary inspiral signal. Our results show that particle swarm optimization works well in the presence of high multimodality, making it a viable candidate method for further applications in gravitational wave data analysis.« less

The spectral cell method in nonlinear earthquake modeling

NASA Astrophysics Data System (ADS)

Giraldo, Daniel; Restrepo, Doriam

2017-12-01

This study examines the applicability of the spectral cell method (SCM) to compute the nonlinear earthquake response of complex basins. SCM combines fictitious-domain concepts with the spectral-version of the finite element method to solve the wave equations in heterogeneous geophysical domains. Nonlinear behavior is considered by implementing the Mohr-Coulomb and Drucker-Prager yielding criteria. We illustrate the performance of SCM with numerical examples of nonlinear basins exhibiting physically and computationally challenging conditions. The numerical experiments are benchmarked with results from overkill solutions, and using MIDAS GTS NX, a finite element software for geotechnical applications. Our findings show good agreement between the two sets of results. Traditional spectral elements implementations allow points per wavelength as low as PPW = 4.5 for high-order polynomials. Our findings show that in the presence of nonlinearity, high-order polynomials (p ≥ 3) require mesh resolutions above of PPW ≥ 10 to ensure displacement errors below 10%.

On the rate of convergence of the alternating projection method in finite dimensional spaces

NASA Astrophysics Data System (ADS)

Galántai, A.

2005-10-01

Using the results of Smith, Solmon, and Wagner [K. Smith, D. Solomon, S. Wagner, Practical and mathematical aspects of the problem of reconstructing objects from radiographs, Bull. Amer. Math. Soc. 83 (1977) 1227-1270] and Nelson and Neumann [S. Nelson, M. Neumann, Generalizations of the projection method with application to SOR theory for Hermitian positive semidefinite linear systems, Numer. Math. 51 (1987) 123-141] we derive new estimates for the speed of the alternating projection method and its relaxed version in . These estimates can be computed in at most O(m3) arithmetic operations unlike the estimates in papers mentioned above that require spectral information. The new and old estimates are equivalent in many practical cases. In cases when the new estimates are weaker, the numerical testing indicates that they approximate the original bounds in papers mentioned above quite well.

Numerical solution of the incompressible Navier-Stokes equations. Ph.D. Thesis - Stanford Univ., Mar. 1989

NASA Technical Reports Server (NTRS)

Rogers, Stuart E.

1990-01-01

The current work is initiated in an effort to obtain an efficient, accurate, and robust algorithm for the numerical solution of the incompressible Navier-Stokes equations in two- and three-dimensional generalized curvilinear coordinates for both steady-state and time-dependent flow problems. This is accomplished with the use of the method of artificial compressibility and a high-order flux-difference splitting technique for the differencing of the convective terms. Time accuracy is obtained in the numerical solutions by subiterating the equations in psuedo-time for each physical time step. The system of equations is solved with a line-relaxation scheme which allows the use of very large pseudo-time steps leading to fast convergence for steady-state problems as well as for the subiterations of time-dependent problems. Numerous laminar test flow problems are computed and presented with a comparison against analytically known solutions or experimental results. These include the flow in a driven cavity, the flow over a backward-facing step, the steady and unsteady flow over a circular cylinder, flow over an oscillating plate, flow through a one-dimensional inviscid channel with oscillating back pressure, the steady-state flow through a square duct with a 90 degree bend, and the flow through an artificial heart configuration with moving boundaries. An adequate comparison with the analytical or experimental results is obtained in all cases. Numerical comparisons of the upwind differencing with central differencing plus artificial dissipation indicates that the upwind differencing provides a much more robust algorithm, which requires significantly less computing time. The time-dependent problems require on the order of 10 to 20 subiterations, indicating that the elliptical nature of the problem does require a substantial amount of computing effort.

Parametric State Space Structuring

NASA Technical Reports Server (NTRS)

Ciardo, Gianfranco; Tilgner, Marco

1997-01-01

Structured approaches based on Kronecker operators for the description and solution of the infinitesimal generator of a continuous-time Markov chains are receiving increasing interest. However, their main advantage, a substantial reduction in the memory requirements during the numerical solution, comes at a price. Methods based on the "potential state space" allocate a probability vector that might be much larger than actually needed. Methods based on the "actual state space", instead, have an additional logarithmic overhead. We present an approach that realizes the advantages of both methods with none of their disadvantages, by partitioning the local state spaces of each submodel. We apply our results to a model of software rendezvous, and show how they reduce memory requirements while, at the same time, improving the efficiency of the computation.

Numerical methods for the weakly compressible Generalized Langevin Model in Eulerian reference frame

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

Azarnykh, Dmitrii, E-mail: d.azarnykh@tum.de; Litvinov, Sergey; Adams, Nikolaus A.

2016-06-01

A well established approach for the computation of turbulent flow without resolving all turbulent flow scales is to solve a filtered or averaged set of equations, and to model non-resolved scales by closures derived from transported probability density functions (PDF) for velocity fluctuations. Effective numerical methods for PDF transport employ the equivalence between the Fokker–Planck equation for the PDF and a Generalized Langevin Model (GLM), and compute the PDF by transporting a set of sampling particles by GLM (Pope (1985) [1]). The natural representation of GLM is a system of stochastic differential equations in a Lagrangian reference frame, typically solvedmore » by particle methods. A representation in a Eulerian reference frame, however, has the potential to significantly reduce computational effort and to allow for the seamless integration into a Eulerian-frame numerical flow solver. GLM in a Eulerian frame (GLMEF) formally corresponds to the nonlinear fluctuating hydrodynamic equations derived by Nakamura and Yoshimori (2009) [12]. Unlike the more common Landau–Lifshitz Navier–Stokes (LLNS) equations these equations are derived from the underdamped Langevin equation and are not based on a local equilibrium assumption. Similarly to LLNS equations the numerical solution of GLMEF requires special considerations. In this paper we investigate different numerical approaches to solving GLMEF with respect to the correct representation of stochastic properties of the solution. We find that a discretely conservative staggered finite-difference scheme, adapted from a scheme originally proposed for turbulent incompressible flow, in conjunction with a strongly stable (for non-stochastic PDE) Runge–Kutta method performs better for GLMEF than schemes adopted from those proposed previously for the LLNS. We show that equilibrium stochastic fluctuations are correctly reproduced.« less

Computational Issues in Damping Identification for Large Scale Problems

NASA Technical Reports Server (NTRS)

Pilkey, Deborah L.; Roe, Kevin P.; Inman, Daniel J.

1997-01-01

Two damping identification methods are tested for efficiency in large-scale applications. One is an iterative routine, and the other a least squares method. Numerical simulations have been performed on multiple degree-of-freedom models to test the effectiveness of the algorithm and the usefulness of parallel computation for the problems. High Performance Fortran is used to parallelize the algorithm. Tests were performed using the IBM-SP2 at NASA Ames Research Center. The least squares method tested incurs high communication costs, which reduces the benefit of high performance computing. This method's memory requirement grows at a very rapid rate meaning that larger problems can quickly exceed available computer memory. The iterative method's memory requirement grows at a much slower pace and is able to handle problems with 500+ degrees of freedom on a single processor. This method benefits from parallelization, and significant speedup can he seen for problems of 100+ degrees-of-freedom.

THC-MP: High performance numerical simulation of reactive transport and multiphase flow in porous media

NASA Astrophysics Data System (ADS)

Wei, Xiaohui; Li, Weishan; Tian, Hailong; Li, Hongliang; Xu, Haixiao; Xu, Tianfu

2015-07-01

The numerical simulation of multiphase flow and reactive transport in the porous media on complex subsurface problem is a computationally intensive application. To meet the increasingly computational requirements, this paper presents a parallel computing method and architecture. Derived from TOUGHREACT that is a well-established code for simulating subsurface multi-phase flow and reactive transport problems, we developed a high performance computing THC-MP based on massive parallel computer, which extends greatly on the computational capability for the original code. The domain decomposition method was applied to the coupled numerical computing procedure in the THC-MP. We designed the distributed data structure, implemented the data initialization and exchange between the computing nodes and the core solving module using the hybrid parallel iterative and direct solver. Numerical accuracy of the THC-MP was verified through a CO2 injection-induced reactive transport problem by comparing the results obtained from the parallel computing and sequential computing (original code). Execution efficiency and code scalability were examined through field scale carbon sequestration applications on the multicore cluster. The results demonstrate successfully the enhanced performance using the THC-MP on parallel computing facilities.

ON THE MINIMAL ACCURACY REQUIRED FOR SIMULATING SELF-GRAVITATING SYSTEMS BY MEANS OF DIRECT N-BODY METHODS

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

Portegies Zwart, Simon; Boekholt, Tjarda

2014-04-10

The conservation of energy, linear momentum, and angular momentum are important drivers of our physical understanding of the evolution of the universe. These quantities are also conserved in Newton's laws of motion under gravity. Numerical integration of the associated equations of motion is extremely challenging, in particular due to the steady growth of numerical errors (by round-off and discrete time-stepping and the exponential divergence between two nearby solutions. As a result, numerical solutions to the general N-body problem are intrinsically questionable. Using brute force integrations to arbitrary numerical precision we demonstrate empirically that ensembles of different realizations of resonant three-bodymore » interactions produce statistically indistinguishable results. Although individual solutions using common integration methods are notoriously unreliable, we conjecture that an ensemble of approximate three-body solutions accurately represents an ensemble of true solutions, so long as the energy during integration is conserved to better than 1/10. We therefore provide an independent confirmation that previous work on self-gravitating systems can actually be trusted, irrespective of the intrinsically chaotic nature of the N-body problem.« less

A comparative analysis of numerical approaches to the mechanics of elastic sheets

NASA Astrophysics Data System (ADS)

Taylor, Michael; Davidovitch, Benny; Qiu, Zhanlong; Bertoldi, Katia

2015-06-01

Numerically simulating deformations in thin elastic sheets is a challenging problem in computational mechanics due to destabilizing compressive stresses that result in wrinkling. Determining the location, structure, and evolution of wrinkles in these problems has important implications in design and is an area of increasing interest in the fields of physics and engineering. In this work, several numerical approaches previously proposed to model equilibrium deformations in thin elastic sheets are compared. These include standard finite element-based static post-buckling approaches as well as a recently proposed method based on dynamic relaxation, which are applied to the problem of an annular sheet with opposed tractions where wrinkling is a key feature. Numerical solutions are compared to analytic predictions of the ground state, enabling a quantitative evaluation of the predictive power of the various methods. Results indicate that static finite element approaches produce local minima that are highly sensitive to initial imperfections, relying on a priori knowledge of the equilibrium wrinkling pattern to generate optimal results. In contrast, dynamic relaxation is much less sensitive to initial imperfections and can generate low-energy solutions for a wide variety of loading conditions without requiring knowledge of the equilibrium solution beforehand.

A Superior Kirchhoff Method for Aeroacoustic Noise Prediction: The Ffowcs Williams-Hawkings Equation

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.

1997-01-01

The prediction of aeroacoustic noise is important; all new aircraft must meet noise certification requirements. Local noise standards can be even more stringent. The NASA noise reduction goal is to reduce perceived noise levels by a factor of two in 10 years. The objective of this viewgraph presentation is to demonstrate the superiority of the FW-H approach over the Kirchoff method for aeroacoustics, both analytically and numerically.

Dynamic earthquake rupture simulation on nonplanar faults embedded in 3D geometrically complex, heterogeneous Earth models

NASA Astrophysics Data System (ADS)

Duru, K.; Dunham, E. M.; Bydlon, S. A.; Radhakrishnan, H.

2014-12-01

Dynamic propagation of shear ruptures on a frictional interface is a useful idealization of a natural earthquake.The conditions relating slip rate and fault shear strength are often expressed as nonlinear friction laws.The corresponding initial boundary value problems are both numerically and computationally challenging.In addition, seismic waves generated by earthquake ruptures must be propagated, far away from fault zones, to seismic stations and remote areas.Therefore, reliable and efficient numerical simulations require both provably stable and high order accurate numerical methods.We present a numerical method for:a) enforcing nonlinear friction laws, in a consistent and provably stable manner, suitable for efficient explicit time integration;b) dynamic propagation of earthquake ruptures along rough faults; c) accurate propagation of seismic waves in heterogeneous media with free surface topography.We solve the first order form of the 3D elastic wave equation on a boundary-conforming curvilinear mesh, in terms of particle velocities and stresses that are collocated in space and time, using summation-by-parts finite differences in space. The finite difference stencils are 6th order accurate in the interior and 3rd order accurate close to the boundaries. Boundary and interface conditions are imposed weakly using penalties. By deriving semi-discrete energy estimates analogous to the continuous energy estimates we prove numerical stability. Time stepping is performed with a 4th order accurate explicit low storage Runge-Kutta scheme. We have performed extensive numerical experiments using a slip-weakening friction law on non-planar faults, including recent SCEC benchmark problems. We also show simulations on fractal faults revealing the complexity of rupture dynamics on rough faults. We are presently extending our method to rate-and-state friction laws and off-fault plasticity.

A faster numerical scheme for a coupled system modeling soil erosion and sediment transport

NASA Astrophysics Data System (ADS)

Le, M.-H.; Cordier, S.; Lucas, C.; Cerdan, O.

2015-02-01

Overland flow and soil erosion play an essential role in water quality and soil degradation. Such processes, involving the interactions between water flow and the bed sediment, are classically described by a well-established system coupling the shallow water equations and the Hairsine-Rose model. Numerical approximation of this coupled system requires advanced methods to preserve some important physical and mathematical properties; in particular, the steady states and the positivity of both water depth and sediment concentration. Recently, finite volume schemes based on Roe's solver have been proposed by Heng et al. (2009) and Kim et al. (2013) for one and two-dimensional problems. In their approach, an additional and artificial restriction on the time step is required to guarantee the positivity of sediment concentration. This artificial condition can lead the computation to be costly when dealing with very shallow flow and wet/dry fronts. The main result of this paper is to propose a new and faster scheme for which only the CFL condition of the shallow water equations is sufficient to preserve the positivity of sediment concentration. In addition, the numerical procedure of the erosion part can be used with any well-balanced and positivity preserving scheme of the shallow water equations. The proposed method is tested on classical benchmarks and also on a realistic configuration.

Recent progress in inverse methods in France

NASA Technical Reports Server (NTRS)

Bry, Pierre-Francois; Jacquotte, Olivier-Pierre; Lepape, Marie-Claire

1991-01-01

Given the current level of jet engine performance, improvement of the various turbomachinery components requires the use of advanced methods in aerodynamics, heat transfer, and aeromechanics. In particular, successful blade design can only be achieved via numerical design methods which make it possible to reach optimized solutions in a much shorter time than ever before. Two design methods which are currently being used throughout the French turbomachinery industry to obtain optimized blade geometries are presented. Examples are presented for compressor and turbine applications. The status of these methods as far as improvement and extension to new fields of applications is also reported.

An Iterative Solver in the Presence and Absence of Multiplicity for Nonlinear Equations

PubMed Central

Özkum, Gülcan

2013-01-01

We develop a high-order fixed point type method to approximate a multiple root. By using three functional evaluations per full cycle, a new class of fourth-order methods for this purpose is suggested and established. The methods from the class require the knowledge of the multiplicity. We also present a method in the absence of multiplicity for nonlinear equations. In order to attest the efficiency of the obtained methods, we employ numerical comparisons alongside obtaining basins of attraction to compare them in the complex plane according to their convergence speed and chaotic behavior. PMID:24453914

Reconstruction of fluorescence molecular tomography with a cosinoidal level set method.

PubMed

Zhang, Xuanxuan; Cao, Xu; Zhu, Shouping

2017-06-27

Implicit shape-based reconstruction method in fluorescence molecular tomography (FMT) is capable of achieving higher image clarity than image-based reconstruction method. However, the implicit shape method suffers from a low convergence speed and performs unstably due to the utilization of gradient-based optimization methods. Moreover, the implicit shape method requires priori information about the number of targets. A shape-based reconstruction scheme of FMT with a cosinoidal level set method is proposed in this paper. The Heaviside function in the classical implicit shape method is replaced with a cosine function, and then the reconstruction can be accomplished with the Levenberg-Marquardt method rather than gradient-based methods. As a result, the priori information about the number of targets is not required anymore and the choice of step length is avoided. Numerical simulations and phantom experiments were carried out to validate the proposed method. Results of the proposed method show higher contrast to noise ratios and Pearson correlations than the implicit shape method and image-based reconstruction method. Moreover, the number of iterations required in the proposed method is much less than the implicit shape method. The proposed method performs more stably, provides a faster convergence speed than the implicit shape method, and achieves higher image clarity than the image-based reconstruction method.

24 CFR 135.30 - Numerical goals for meeting the greatest extent feasible requirement.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 24 Housing and Urban Development 1 2012-04-01 2012-04-01 false Numerical goals for meeting the... Concerns § 135.30 Numerical goals for meeting the greatest extent feasible requirement. (a) General. (1... of section 3 by meeting the numerical goals set forth in this section for providing training...

24 CFR 135.30 - Numerical goals for meeting the greatest extent feasible requirement.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 24 Housing and Urban Development 1 2013-04-01 2013-04-01 false Numerical goals for meeting the... Concerns § 135.30 Numerical goals for meeting the greatest extent feasible requirement. (a) General. (1... of section 3 by meeting the numerical goals set forth in this section for providing training...

24 CFR 135.30 - Numerical goals for meeting the greatest extent feasible requirement.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 24 Housing and Urban Development 1 2011-04-01 2011-04-01 false Numerical goals for meeting the... Concerns § 135.30 Numerical goals for meeting the greatest extent feasible requirement. (a) General. (1... of section 3 by meeting the numerical goals set forth in this section for providing training...

24 CFR 135.30 - Numerical goals for meeting the greatest extent feasible requirement.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 24 Housing and Urban Development 1 2014-04-01 2014-04-01 false Numerical goals for meeting the... Concerns § 135.30 Numerical goals for meeting the greatest extent feasible requirement. (a) General. (1... of section 3 by meeting the numerical goals set forth in this section for providing training...

Stability analysis of cylinders with circular cutouts

NASA Technical Reports Server (NTRS)

Almroth, B. O.; Brogan, F. A.; Marlowe, M. B.

1973-01-01

The stability of axially compressed cylinders with circular cutouts is analyzed numerically. An extension of the finite-difference method is used which removes the requirement that displacement components be defined in the directions of the grid lines. The results of this nonlinear analysis are found to be in good agreement with earlier experimental results.

New methods in hydrologic modeling and decision support for culvert flood risk under climate change

NASA Astrophysics Data System (ADS)

Rosner, A.; Letcher, B. H.; Vogel, R. M.; Rees, P. S.

2015-12-01

Assessing culvert flood vulnerability under climate change poses an unusual combination of challenges. We seek a robust method of planning for an uncertain future, and therefore must consider a wide range of plausible future conditions. Culverts in our case study area, northwestern Massachusetts, USA, are predominantly found in small, ungaged basins. The need to predict flows both at numerous sites and under numerous plausible climate conditions requires a statistical model with low data and computational requirements. We present a statistical streamflow model that is driven by precipitation and temperature, allowing us to predict flows without reliance on reference gages of observed flows. The hydrological analysis is used to determine each culvert's risk of failure under current conditions. We also explore the hydrological response to a range of plausible future climate conditions. These results are used to determine the tolerance of each culvert to future increases in precipitation. In a decision support context, current flood risk as well as tolerance to potential climate changes are used to provide a robust assessment and prioritization for culvert replacements.

Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE scheme

DOE PAGES

Burton, Donald E.; Morgan, Nathaniel Ray; Charest, Marc Robert Joseph; ...

2017-11-22

From the very origins of numerical hydrodynamics in the Lagrangian work of von Neumann and Richtmyer [83], the issue of total energy conservation as well as entropy production has been problematic. Because of well known problems with mesh deformation, Lagrangian schemes have evolved into Arbitrary Lagrangian–Eulerian (ALE) methods [39] that combine the best properties of Lagrangian and Eulerian methods. Energy issues have persisted for this class of methods. We believe that fundamental issues of energy conservation and entropy production in ALE require further examination. The context of the paper is an ALE scheme that is extended in the sense thatmore » it permits cyclic or periodic remap of data between grids of the same or differing connectivity. The principal design goals for a remap method then consist of total energy conservation, bounded internal energy, and compatibility of kinetic energy and momentum. We also have secondary objectives of limiting velocity and stress in a non-directional manner, keeping primitive variables monotone, and providing a higher than second order reconstruction of remapped variables. Particularly, the new contributions fall into three categories associated with: energy conservation and entropy production, reconstruction and bounds preservation of scalar and tensor fields, and conservative remap of nonlinear fields. Our paper presents a derivation of the methods, details of implementation, and numerical results for a number of test problems. The methods requires volume integration of polynomial functions in polytopal cells with planar facets, and the requisite expressions are derived for arbitrary order.« less

Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE scheme

NASA Astrophysics Data System (ADS)

Burton, D. E.; Morgan, N. R.; Charest, M. R. J.; Kenamond, M. A.; Fung, J.

2018-02-01

From the very origins of numerical hydrodynamics in the Lagrangian work of von Neumann and Richtmyer [83], the issue of total energy conservation as well as entropy production has been problematic. Because of well known problems with mesh deformation, Lagrangian schemes have evolved into Arbitrary Lagrangian-Eulerian (ALE) methods [39] that combine the best properties of Lagrangian and Eulerian methods. Energy issues have persisted for this class of methods. We believe that fundamental issues of energy conservation and entropy production in ALE require further examination. The context of the paper is an ALE scheme that is extended in the sense that it permits cyclic or periodic remap of data between grids of the same or differing connectivity. The principal design goals for a remap method then consist of total energy conservation, bounded internal energy, and compatibility of kinetic energy and momentum. We also have secondary objectives of limiting velocity and stress in a non-directional manner, keeping primitive variables monotone, and providing a higher than second order reconstruction of remapped variables. In particular, the new contributions fall into three categories associated with: energy conservation and entropy production, reconstruction and bounds preservation of scalar and tensor fields, and conservative remap of nonlinear fields. The paper presents a derivation of the methods, details of implementation, and numerical results for a number of test problems. The methods requires volume integration of polynomial functions in polytopal cells with planar facets, and the requisite expressions are derived for arbitrary order.

Multiplex SNaPshot-a new simple and efficient CYP2D6 and ADRB1 genotyping method.

PubMed

Ben, Songtao; Cooper-DeHoff, Rhonda M; Flaten, Hanna K; Evero, Oghenero; Ferrara, Tracey M; Spritz, Richard A; Monte, Andrew A

2016-04-23

Reliable, inexpensive, high-throughput genotyping methods are required for clinical trials. Traditional assays require numerous enzyme digestions or are too expensive for large sample volumes. Our objective was to develop an inexpensive, efficient, and reliable assay for CYP2D6 and ADRB1 accounting for numerous polymorphisms including gene duplications. We utilized the multiplex SNaPshot® custom genotype method to genotype CYP2D6 and ADRB1. We compared the method to reference standards genotyped using the Taqman Copy Number Variant Assay followed by pyrosequencing quantification and determined assigned genotype concordance. We genotyped 119 subjects. Seven (5.9 %) were found to be CYP2D6 poor metabolizers (PMs), 18 (15.1 %) intermediate metabolizers (IMs), 89 (74.8 %) extensive metabolizers (EMs), and 5 (4.2 %) ultra-rapid metabolizers (UMs). We genotyped two variants in the β1-adrenoreceptor, rs1801253 (Gly389Arg) and rs1801252 (Ser49Gly). The Gly389Arg genotype is Gly/Gly 18 (15.1 %), Gly/Arg 58 (48.7 %), and Arg/Arg 43 (36.1 %). The Ser49Gly genotype is Ser/Ser 82 (68.9 %), Ser/Gly 32 (26.9), and Gly/Gly 5 (4.2 %). The multiplex SNaPshot method was concordant with genotypes in reference samples. The multiplex SNaPshot method allows for specific and accurate detection of CYP2D6 genotypes and ADRB1 genotypes and haplotypes. This platform is simple and efficient and suited for high throughput.

Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE scheme

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

Burton, Donald E.; Morgan, Nathaniel Ray; Charest, Marc Robert Joseph

From the very origins of numerical hydrodynamics in the Lagrangian work of von Neumann and Richtmyer [83], the issue of total energy conservation as well as entropy production has been problematic. Because of well known problems with mesh deformation, Lagrangian schemes have evolved into Arbitrary Lagrangian–Eulerian (ALE) methods [39] that combine the best properties of Lagrangian and Eulerian methods. Energy issues have persisted for this class of methods. We believe that fundamental issues of energy conservation and entropy production in ALE require further examination. The context of the paper is an ALE scheme that is extended in the sense thatmore » it permits cyclic or periodic remap of data between grids of the same or differing connectivity. The principal design goals for a remap method then consist of total energy conservation, bounded internal energy, and compatibility of kinetic energy and momentum. We also have secondary objectives of limiting velocity and stress in a non-directional manner, keeping primitive variables monotone, and providing a higher than second order reconstruction of remapped variables. Particularly, the new contributions fall into three categories associated with: energy conservation and entropy production, reconstruction and bounds preservation of scalar and tensor fields, and conservative remap of nonlinear fields. Our paper presents a derivation of the methods, details of implementation, and numerical results for a number of test problems. The methods requires volume integration of polynomial functions in polytopal cells with planar facets, and the requisite expressions are derived for arbitrary order.« less

The ADER-DG method for seismic wave propagation and earthquake rupture dynamics

NASA Astrophysics Data System (ADS)

Pelties, Christian; Gabriel, Alice; Ampuero, Jean-Paul; de la Puente, Josep; Käser, Martin

2013-04-01

We will present the Arbitrary high-order DERivatives Discontinuous Galerkin (ADER-DG) method for solving the combined elastodynamic wave propagation and dynamic rupture problem. The ADER-DG method enables high-order accuracy in space and time while being implemented on unstructured tetrahedral meshes. A tetrahedral element discretization provides rapid and automatized mesh generation as well as geometrical flexibility. Features as mesh coarsening and local time stepping schemes can be applied to reduce computational efforts without introducing numerical artifacts. The method is well suited for parallelization and large scale high-performance computing since only directly neighboring elements exchange information via numerical fluxes. The concept of fluxes is a key ingredient of the numerical scheme as it governs the numerical dispersion and diffusion properties and allows to accommodate for boundary conditions, empirical friction laws of dynamic rupture processes, or the combination of different element types and non-conforming mesh transitions. After introducing fault dynamics into the ADER-DG framework, we will demonstrate its specific advantages in benchmarking test scenarios provided by the SCEC/USGS Spontaneous Rupture Code Verification Exercise. An important result of the benchmark is that the ADER-DG method avoids spurious high-frequency contributions in the slip rate spectra and therefore does not require artificial Kelvin-Voigt damping, filtering or other modifications of the produced synthetic seismograms. To demonstrate the capabilities of the proposed scheme we simulate an earthquake scenario, inspired by the 1992 Landers earthquake, that includes branching and curved fault segments. Furthermore, topography is respected in the discretized model to capture the surface waves correctly. The advanced geometrical flexibility combined with an enhanced accuracy will make the ADER-DG method a useful tool to study earthquake dynamics on complex fault systems in realistic rheologies.

Computational Challenges of Viscous Incompressible Flows

NASA Technical Reports Server (NTRS)

Kwak, Dochan; Kiris, Cetin; Kim, Chang Sung

2004-01-01

Over the past thirty years, numerical methods and simulation tools for incompressible flows have been advanced as a subset of the computational fluid dynamics (CFD) discipline. Although incompressible flows are encountered in many areas of engineering, simulation of compressible flow has been the major driver for developing computational algorithms and tools. This is probably due to the rather stringent requirements for predicting aerodynamic performance characteristics of flight vehicles, while flow devices involving low-speed or incompressible flow could be reasonably well designed without resorting to accurate numerical simulations. As flow devices are required to be more sophisticated and highly efficient CFD took become increasingly important in fluid engineering for incompressible and low-speed flow. This paper reviews some of the successes made possible by advances in computational technologies during the same period, and discusses some of the current challenges faced in computing incompressible flows.

Successes and Challenges of Incompressible Flow Simulation

NASA Technical Reports Server (NTRS)

Kwak, Dochan; Kiris, Cetin

2003-01-01

During the past thirty years, numerical methods and simulation tools for incompressible flows have been advanced as a subset of CFD discipline. Even though incompressible flows are encountered in many areas of engineering, simulation of compressible flow has been the major driver for developing computational algorithms and tools. This is probably due to rather stringent requirements for predicting aerodynamic performance characteristics of flight vehicles, while flow devices involving low speed or incompressible flow could be reasonably well designed without resorting to accurate numerical simulations. As flow devices are required to be more sophisticated and highly efficient, CFD tools become indispensable in fluid engineering for incompressible and low speed flow. This paper is intended to review some of the successes made possible by advances in computational technologies during the same period, and discuss some of the current challenges.

The MINERVA Software Development Process

NASA Technical Reports Server (NTRS)

Narkawicz, Anthony; Munoz, Cesar A.; Dutle, Aaron M.

2017-01-01

This paper presents a software development process for safety-critical software components of cyber-physical systems. The process is called MINERVA, which stands for Mirrored Implementation Numerically Evaluated against Rigorously Verified Algorithms. The process relies on formal methods for rigorously validating code against its requirements. The software development process uses: (1) a formal specification language for describing the algorithms and their functional requirements, (2) an interactive theorem prover for formally verifying the correctness of the algorithms, (3) test cases that stress the code, and (4) numerical evaluation on these test cases of both the algorithm specifications and their implementations in code. The MINERVA process is illustrated in this paper with an application to geo-containment algorithms for unmanned aircraft systems. These algorithms ensure that the position of an aircraft never leaves a predetermined polygon region and provide recovery maneuvers when the region is inadvertently exited.

Efficient method for the calculation of mean extinction. II. Analyticity of the complex extinction efficiency of homogeneous spheroids and finite cylinders.

PubMed

Xing, Z F; Greenberg, J M

1994-08-20

The analyticity of the complex extinction efficiency is examined numerically in the size-parameter domain for homogeneous prolate and oblate spheroids and finite cylinders. The T-matrix code, which is the most efficient program available to date, is employed to calculate the individual particle-extinction efficiencies. Because of its computational limitations in the size-parameter range, a slightly modified Hilbert-transform algorithm is required to establish the analyticity numerically. The findings concerning analyticity that we reported for spheres (Astrophys. J. 399, 164-175, 1992) apply equally to these nonspherical particles.

Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul

1993-01-01

We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems. First, a roper summation-by-parts formula is found for the approximate derivative. A 'simultaneous approximation term' (SAT) is then introduced to treat the boundary conditions. This procedure leads to time-stable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach.

Numerical Inverse Scattering for the Toda Lattice

NASA Astrophysics Data System (ADS)

Bilman, Deniz; Trogdon, Thomas

2017-06-01

We present a method to compute the inverse scattering transform (IST) for the famed Toda lattice by solving the associated Riemann-Hilbert (RH) problem numerically. Deformations for the RH problem are incorporated so that the IST can be evaluated in O(1) operations for arbitrary points in the ( n, t)-domain, including short- and long-time regimes. No time-stepping is required to compute the solution because ( n, t) appear as parameters in the associated RH problem. The solution of the Toda lattice is computed in long-time asymptotic regions where the asymptotics are not known rigorously.

Designs for thermal harvesting with nonlinear coordinate transformation

NASA Astrophysics Data System (ADS)

Ji, Qingxiang; Fang, Guodong; Liang, Jun

2018-04-01

In this paper a thermal concentrating design method was proposed based on the concept of generating function without knowing the needed coordinate transformation beforehand. The thermal harvesting performance was quantitatively characterized by heat concentrating efficiency and external temperature perturbation. Nonlinear transformations of different forms were employed to design high order thermal concentrators, and corresponding harvesting performances were investigated by numerical simulations. The numerical results shows that the form of coordinate transformation directly influences the distributions of heat flows inside the concentrator, consequently, influences the thermal harvesting behaviors significantly. The concentrating performance can be actively controlled and optimized by changing the form of coordinate transformations. The analysis in this paper offers a beneficial method to flexibly tune the harvesting performance of the thermal concentrator according to the requirements of practical applications.

Aerodynamic loads on a Darrieus rotor blade

NASA Astrophysics Data System (ADS)

Wilson, R. E.; McKie, W. R.; Lissaman, P. B. S.; James, M.

1983-03-01

A method is presented for the free vortex analysis of a Darrieus rotor blade in nonsteady motion, which employs the circle theorem to map the moving rotor airfoil into the circle plane and models the wake generated in terms of point vortices. Nascent vortex strength and position are taken from the Kutta condition, so that the nascent vortex has the same strength as a vortex sheet of uniform strength. Pressure integration over the plate and wake vortex impulse methods yields the same numerical results. The numerical results presented for a one-bladed Darrieus rotor at a tip/speed ratio of three, and two different chord sizes, indicate that the moment on the blade can be adequately approximated by quasi-steady relationships, although the accurate determination of local velocity and circulation are still required.

A three-dimensional Dirichlet-to-Neumann operator for water waves over topography

NASA Astrophysics Data System (ADS)

Andrade, D.; Nachbin, A.

2018-06-01

Surface water waves are considered propagating over highly variable non-smooth topographies. For this three dimensional problem a Dirichlet-to-Neumann (DtN) operator is constructed reducing the numerical modeling and evolution to the two dimensional free surface. The corresponding Fourier-type operator is defined through a matrix decomposition. The topographic component of the decomposition requires special care and a Galerkin method is provided accordingly. One dimensional numerical simulations, along the free surface, validate the DtN formulation in the presence of a large amplitude, rapidly varying topography. An alternative, conformal mapping based, method is used for benchmarking. A two dimensional simulation in the presence of a Luneburg lens (a particular submerged mound) illustrates the accurate performance of the three dimensional DtN operator.

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.

Un algorithme efficace d'intégration plastique pour un matériau obéissant au critère anisotrope de Hill

NASA Astrophysics Data System (ADS)

Titeux, Isabelle; Li, Yuming M.; Debray, Karl; Guo, Ying-Qiao

2004-11-01

This Note deals with an efficient algorithm to carry out the plastic integration and compute the stresses due to large strains for materials satisfying the Hill's anisotropic yield criterion. The classical algorithm of plastic integration such as 'Return Mapping Method' is largely used for nonlinear analyses of structures and numerical simulations of forming processes, but it requires an iterative schema and may have convergence problems. A new direct algorithm based on a scalar method is developed which allows us to directly obtain the plastic multiplier without an iteration procedure; thus the computation time is largely reduced and the numerical problems are avoided. To cite this article: I. Titeux et al., C. R. Mecanique 332 (2004).

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.

Bessel function expansion to reduce the calculation time and memory usage for cylindrical computer-generated holograms.

PubMed

Sando, Yusuke; Barada, Daisuke; Jackin, Boaz Jessie; Yatagai, Toyohiko

2017-07-10

This study proposes a method to reduce the calculation time and memory usage required for calculating cylindrical computer-generated holograms. The wavefront on the cylindrical observation surface is represented as a convolution integral in the 3D Fourier domain. The Fourier transformation of the kernel function involving this convolution integral is analytically performed using a Bessel function expansion. The analytical solution can drastically reduce the calculation time and the memory usage without any cost, compared with the numerical method using fast Fourier transform to Fourier transform the kernel function. In this study, we present the analytical derivation, the efficient calculation of Bessel function series, and a numerical simulation. Furthermore, we demonstrate the effectiveness of the analytical solution through comparisons of calculation time and memory usage.

The use of transition region characteristics to improve the numerical simulation of heat transfer in bypass transitional flows

NASA Technical Reports Server (NTRS)

Simon, Frederick F.

1993-01-01

A method is presented for improving the numerical prediction of bypass transition heat transfer on a flat plate in a high-disturbance environment with zero or favorable pressure gradient. The method utilizes low Reynolds number k-epsilon turbulence models in combination with the characteristic parameters of the transition region. The parameters representing the characteristics of the transition region used are the intermittency, transition length and turbulent spot properties. An analysis is made of the transition length in terms of turbulent spot variables. The nondimensional spot formation rate, required for the prediction of the transition length, is shown by the analysis to be a function of the spot spreading angle, the dimensionless spot velocity ratio and the dimensionless spot area ratio. The intermittency form of the k-epsilon equations were derived from conditionally averaged equations which have been shown to be an improvement over global-time-averaged equations for the numerical calculation of the transition region. The numerical predictions are in general good agreement with the experimental data and indicate the potential use of the method in accelerating flows. Turbulence models of the k-epsilon type are known to underpredict the transition length. The present work demonstrates how incorporating transition region characteristics improves the ability of two-equation turbulence models to simulate bypass transition for flat plates with potential application to turbine vanes and blades.

Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) Collocation Method for Solving Linear and Nonlinear Fokker-Planck Equations

NASA Astrophysics Data System (ADS)

Parand, K.; Latifi, S.; Moayeri, M. M.; Delkhosh, M.

2018-05-01

In this study, we have constructed a new numerical approach for solving the time-dependent linear and nonlinear Fokker-Planck equations. In fact, we have discretized the time variable with Crank-Nicolson method and for the space variable, a numerical method based on Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) collocation method is applied. It leads to in solving the equation in a series of time steps and at each time step, the problem is reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. One can observe that the proposed method is simple and accurate. Indeed, one of its merits is that it is derivative-free and by proposing a formula for derivative matrices, the difficulty aroused in calculation is overcome, along with that it does not need to calculate the General Lagrange basis and matrices; they have Kronecker property. Linear and nonlinear Fokker-Planck equations are given as examples and the results amply demonstrate that the presented method is very valid, effective, reliable and does not require any restrictive assumptions for nonlinear terms.

A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields

DOE PAGES

Osborn, Sarah; Vassilevski, Panayot S.; Villa, Umberto

2017-10-26

In this paper, we propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen--Loève (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving amore » mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Lastly, numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method.« less

A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields

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

Osborn, Sarah; Vassilevski, Panayot S.; Villa, Umberto

In this paper, we propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen--Loève (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving amore » mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Lastly, numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method.« less

Efficient solution of parabolic equations by Krylov approximation methods

NASA Technical Reports Server (NTRS)

Gallopoulos, E.; Saad, Y.

1990-01-01

Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.

Numerical form-finding method for large mesh reflectors with elastic rim trusses

NASA Astrophysics Data System (ADS)

Yang, Dongwu; Zhang, Yiqun; Li, Peng; Du, Jingli

2018-06-01

Traditional methods for designing a mesh reflector usually treat the rim truss as rigid. Due to large aperture, light weight and high accuracy requirements on spaceborne reflectors, the rim truss deformation is indeed not negligible. In order to design a cable net with asymmetric boundaries for the front and rear nets, a cable-net form-finding method is firstly introduced. Then, the form-finding method is embedded into an iterative approach for designing a mesh reflector considering the elasticity of the supporting rim truss. By iterations on form-findings of the cable-net based on the updated boundary conditions due to the rim truss deformation, a mesh reflector with a fairly uniform tension distribution in its equilibrium state could be finally designed. Applications on offset mesh reflectors with both circular and elliptical rim trusses are illustrated. The numerical results show the effectiveness of the proposed approach and that a circular rim truss is more stable than an elliptical rim truss.

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.

Efficient Wideband Numerical Simulations for Nanostructures Employing a Drude-Critical Points (DCP) Dispersive Model.

PubMed

Ren, Qiang; Nagar, Jogender; Kang, Lei; Bian, Yusheng; Werner, Ping; Werner, Douglas H

2017-05-18

A highly efficient numerical approach for simulating the wideband optical response of nano-architectures comprised of Drude-Critical Points (DCP) media (e.g., gold and silver) is proposed and validated through comparing with commercial computational software. The kernel of this algorithm is the subdomain level discontinuous Galerkin time domain (DGTD) method, which can be viewed as a hybrid of the spectral-element time-domain method (SETD) and the finite-element time-domain (FETD) method. An hp-refinement technique is applied to decrease the Degrees-of-Freedom (DoFs) and computational requirements. The collocated E-J scheme facilitates solving the auxiliary equations by converting the inversions of matrices to simpler vector manipulations. A new hybrid time stepping approach, which couples the Runge-Kutta and Newmark methods, is proposed to solve the temporal auxiliary differential equations (ADEs) with a high degree of efficiency. The advantages of this new approach, in terms of computational resource overhead and accuracy, are validated through comparison with well-known commercial software for three diverse cases, which cover both near-field and far-field properties with plane wave and lumped port sources. The presented work provides the missing link between DCP dispersive models and FETD and/or SETD based algorithms. It is a competitive candidate for numerically studying the wideband plasmonic properties of DCP media.

Variational data assimilation for the initial-value dynamo problem.

PubMed

Li, Kuan; Jackson, Andrew; Livermore, Philip W

2011-11-01

The secular variation of the geomagnetic field as observed at the Earth's surface results from the complex magnetohydrodynamics taking place in the fluid core of the Earth. One way to analyze this system is to use the data in concert with an underlying dynamical model of the system through the technique of variational data assimilation, in much the same way as is employed in meteorology and oceanography. The aim is to discover an optimal initial condition that leads to a trajectory of the system in agreement with observations. Taking the Earth's core to be an electrically conducting fluid sphere in which convection takes place, we develop the continuous adjoint forms of the magnetohydrodynamic equations that govern the dynamical system together with the corresponding numerical algorithms appropriate for a fully spectral method. These adjoint equations enable a computationally fast iterative improvement of the initial condition that determines the system evolution. The initial condition depends on the three dimensional form of quantities such as the magnetic field in the entire sphere. For the magnetic field, conservation of the divergence-free condition for the adjoint magnetic field requires the introduction of an adjoint pressure term satisfying a zero boundary condition. We thus find that solving the forward and adjoint dynamo system requires different numerical algorithms. In this paper, an efficient algorithm for numerically solving this problem is developed and tested for two illustrative problems in a whole sphere: one is a kinematic problem with prescribed velocity field, and the second is associated with the Hall-effect dynamo, exhibiting considerable nonlinearity. The algorithm exhibits reliable numerical accuracy and stability. Using both the analytical and the numerical techniques of this paper, the adjoint dynamo system can be solved directly with the same order of computational complexity as that required to solve the forward problem. These numerical techniques form a foundation for ultimate application to observations of the geomagnetic field over the time scale of centuries.

Bubble Augmented Propulsor Mixture Flow Simulation near Choked Flow Condition

NASA Astrophysics Data System (ADS)

Choi, Jin-Keun; Hsiao, Chao-Tsung; Chahine, Georges

2013-03-01

The concept of waterjet thrust augmentation through bubble injection has been the subject of many patents and publications over the past several decades, and computational and experimental evidences of the augmentation of the jet thrust through bubble growth in the jet stream have been reported. Through our experimental studies, we have demonstrated net thrust augmentation as high as 70%for air volume fractions as high as 50%. However, in order to enable practical designs, an adequately validated modeling tool is required. In our previous numerical studies, we developed and validated a numerical code to simulate and predict the performance of a two-phase flow water jet propulsion system for low void fractions. In the present work, we extend the numerical method to handle higher void fractions to enable simulations for the high thrust augmentation conditions. At high void fractions, the speed of sound in the bubbly mixture decreases substantially and could be as low as 20 m/s, and the mixture velocity can approach the speed of sound in the medium. In this numerical study, we extend our numerical model, which is based on the two-way coupling between the mixture flow field and Lagrangian tracking of a large number of bubbles, to accommodate compressible flow regimes. Numerical methods used and the validation studies for various flow conditions in the bubble augmented propulsor will be presented. This work is supported by Office of Naval Research through contract N00014-11-C-0482 monitored by Dr. Ki-Han Kim.

Numerical study on response time of a parallel plate capacitive polyimide humidity sensor based on microhole upper electrode

NASA Astrophysics Data System (ADS)

Zhou, Wenhe; He, Xuan; Wu, Jianyun; Wang, Liangbi; Wang, Liangcheng

2017-07-01

The parallel plate capacitive humidity sensor based on the grid upper electrode is considered to be a promising one in some fields which require a humidity sensor with better dynamic characteristics. To strengthen the structure and balance the electric charge of the grid upper electrode, a strip is needed. However, it is the strip that keeps the dynamic characteristics of the sensor from being further improved. The numerical method is time- and cost-saving, but the numerical study on the response time of the sensor is just of bits and pieces. The numerical models presented by these studies did not consider the porosity effect of the polymer film on the dynamic characteristics. To overcome the defect of the grid upper electrode, a new structure of the upper electrode is provided by this paper first, and then a model considering the porosity effects of the polymer film on the dynamic characteristics is presented and validated. Finally, with the help of software FLUENT, parameter effects on the response time of the humidity sensor based on the microhole upper electrode are studied by the numerical method. The numerical results show that the response time of the microhole upper electrode sensor is 86% better than that of the grid upper electrode sensor, the response time of humidity sensor can be improved by reducing the hole spacing, increasing the aperture, reducing film thickness, and reasonably enlarging the porosity of the film.

Computational time analysis of the numerical solution of 3D electrostatic Poisson's equation

NASA Astrophysics Data System (ADS)

Kamboh, Shakeel Ahmed; Labadin, Jane; Rigit, Andrew Ragai Henri; Ling, Tech Chaw; Amur, Khuda Bux; Chaudhary, Muhammad Tayyab

2015-05-01

3D Poisson's equation is solved numerically to simulate the electric potential in a prototype design of electrohydrodynamic (EHD) ion-drag micropump. Finite difference method (FDM) is employed to discretize the governing equation. The system of linear equations resulting from FDM is solved iteratively by using the sequential Jacobi (SJ) and sequential Gauss-Seidel (SGS) methods, simulation results are also compared to examine the difference between the results. The main objective was to analyze the computational time required by both the methods with respect to different grid sizes and parallelize the Jacobi method to reduce the computational time. In common, the SGS method is faster than the SJ method but the data parallelism of Jacobi method may produce good speedup over SGS method. In this study, the feasibility of using parallel Jacobi (PJ) method is attempted in relation to SGS method. MATLAB Parallel/Distributed computing environment is used and a parallel code for SJ method is implemented. It was found that for small grid size the SGS method remains dominant over SJ method and PJ method while for large grid size both the sequential methods may take nearly too much processing time to converge. Yet, the PJ method reduces computational time to some extent for large grid sizes.

Solution of the advection-dispersion equation by a finite-volume eulerian-lagrangian local adjoint method

USGS Publications Warehouse

Healy, R.W.; Russell, T.F.

1992-01-01

A finite-volume Eulerian-Lagrangian local adjoint method for solution of the advection-dispersion equation is developed and discussed. The method is mass conservative and can solve advection-dominated ground-water solute-transport problems accurately and efficiently. An integrated finite-difference approach is used in the method. A key component of the method is that the integral representing the mass-storage term is evaluated numerically at the current time level. Integration points, and the mass associated with these points, are then forward tracked up to the next time level. The number of integration points required to reach a specified level of accuracy is problem dependent and increases as the sharpness of the simulated solute front increases. Integration points are generally equally spaced within each grid cell. For problems involving variable coefficients it has been found to be advantageous to include additional integration points at strategic locations in each well. These locations are determined by backtracking. Forward tracking of boundary fluxes by the method alleviates problems that are encountered in the backtracking approaches of most characteristic methods. A test problem is used to illustrate that the new method offers substantial advantages over other numerical methods for a wide range of problems.

Discontinuous Galerkin method with Gaussian artificial viscosity on graphical processing units for nonlinear acoustics

NASA Astrophysics Data System (ADS)

Tripathi, Bharat B.; Marchiano, Régis; Baskar, Sambandam; Coulouvrat, François

2015-10-01

Propagation of acoustical shock waves in complex geometry is a topic of interest in the field of nonlinear acoustics. For instance, simulation of Buzz Saw Noice requires the treatment of shock waves generated by the turbofan through the engines of aeroplanes with complex geometries and wall liners. Nevertheless, from a numerical point of view it remains a challenge. The two main hurdles are to take into account the complex geometry of the domain and to deal with the spurious oscillations (Gibbs phenomenon) near the discontinuities. In this work, first we derive the conservative hyperbolic system of nonlinear acoustics (up to quadratic nonlinear terms) using the fundamental equations of fluid dynamics. Then, we propose to adapt the classical nodal discontinuous Galerkin method to develop a high fidelity solver for nonlinear acoustics. The discontinuous Galerkin method is a hybrid of finite element and finite volume method and is very versatile to handle complex geometry. In order to obtain better performance, the method is parallelized on Graphical Processing Units. Like other numerical methods, discontinuous Galerkin method suffers with the problem of Gibbs phenomenon near the shock, which is a numerical artifact. Among the various ways to manage these spurious oscillations, we choose the method of parabolic regularization. Although, the introduction of artificial viscosity into the system is a popular way of managing shocks, we propose a new approach of introducing smooth artificial viscosity locally in each element, wherever needed. Firstly, a shock sensor using the linear coefficients of the spectral solution is used to locate the position of the discontinuities. Then, a viscosity coefficient depending on the shock sensor is introduced into the hyperbolic system of equations, only in the elements near the shock. The viscosity is applied as a two-dimensional Gaussian patch with its shape parameters depending on the element dimensions, referred here as Element Centered Smooth Artificial Viscosity. Using this numerical solver, various numerical experiments are presented for one and two-dimensional test cases in homogeneous and quiescent medium. This work is funded by CEFIPRA (Indo-French Centre for the Promotion of Advance Research) and partially aided by EGIDE (Campus France).

Ptychographic overlap constraint errors and the limits of their numerical recovery using conjugate gradient descent methods.

PubMed

Tripathi, Ashish; McNulty, Ian; Shpyrko, Oleg G

2014-01-27

Ptychographic coherent x-ray diffractive imaging is a form of scanning microscopy that does not require optics to image a sample. A series of scanned coherent diffraction patterns recorded from multiple overlapping illuminated regions on the sample are inverted numerically to retrieve its image. The technique recovers the phase lost by detecting the diffraction patterns by using experimentally known constraints, in this case the measured diffraction intensities and the assumed scan positions on the sample. The spatial resolution of the recovered image of the sample is limited by the angular extent over which the diffraction patterns are recorded and how well these constraints are known. Here, we explore how reconstruction quality degrades with uncertainties in the scan positions. We show experimentally that large errors in the assumed scan positions on the sample can be numerically determined and corrected using conjugate gradient descent methods. We also explore in simulations the limits, based on the signal to noise of the diffraction patterns and amount of overlap between adjacent scan positions, of just how large these errors can be and still be rendered tractable by this method.

Evaluation of the eigenvalue method in the solution of transient heat conduction problems

NASA Astrophysics Data System (ADS)

Landry, D. W.

1985-01-01

The eigenvalue method is evaluated to determine the advantages and disadvantages of the method as compared to fully explicit, fully implicit, and Crank-Nicolson methods. Time comparisons and accuracy comparisons are made in an effort to rank the eigenvalue method in relation to the comparison schemes. The eigenvalue method is used to solve the parabolic heat equation in multidimensions with transient temperatures. Extensions into three dimensions are made to determine the method's feasibility in handling large geometry problems requiring great numbers of internal mesh points. The eigenvalue method proves to be slightly better in accuracy than the comparison routines because of an exact treatment, as opposed to a numerical approximation, of the time derivative in the heat equation. It has the potential of being a very powerful routine in solving long transient type problems. The method is not well suited to finely meshed grid arrays or large regions because of the time and memory requirements necessary for calculating large sets of eigenvalues and eigenvectors.

Numerical modeling of separated flows at moderate Reynolds numbers appropriate for turbine blades and unmanned aero vehicles

NASA Astrophysics Data System (ADS)

Castiglioni, Giacomo

Flows over airfoils and blades in rotating machinery, for unmanned and micro-aerial vehicles, wind turbines, and propellers consist of a laminar boundary layer near the leading edge that is often followed by a laminar separation bubble and transition to turbulence further downstream. Typical Reynolds averaged Navier-Stokes turbulence models are inadequate for such flows. Direct numerical simulation is the most reliable, but is also the most computationally expensive alternative. This work assesses the capability of immersed boundary methods and large eddy simulations to reduce the computational requirements for such flows and still provide high quality results. Two-dimensional and three-dimensional simulations of a laminar separation bubble on a NACA-0012 airfoil at Rec = 5x104 and at 5° of incidence have been performed with an immersed boundary code and a commercial code using body fitted grids. Several sub-grid scale models have been implemented in both codes and their performance evaluated. For the two-dimensional simulations with the immersed boundary method the results show good agreement with the direct numerical simulation benchmark data for the pressure coefficient Cp and the friction coefficient Cf, but only when using dissipative numerical schemes. There is evidence that this behavior can be attributed to the ability of dissipative schemes to damp numerical noise coming from the immersed boundary. For the three-dimensional simulations the results show a good prediction of the separation point, but an inaccurate prediction of the reattachment point unless full direct numerical simulation resolution is used. The commercial code shows good agreement with the direct numerical simulation benchmark data in both two and three-dimensional simulations, but the presence of significant, unquantified numerical dissipation prevents a conclusive assessment of the actual prediction capabilities of very coarse large eddy simulations with low order schemes in general cases. Additionally, a two-dimensional sweep of angles of attack from 0° to 5° is performed showing a qualitative prediction of the jump in lift and drag coefficients due to the appearance of the laminar separation bubble. The numerical dissipation inhibits the predictive capabilities of large eddy simulations whenever it is of the same order of magnitude or larger than the sub-grid scale dissipation. The need to estimate the numerical dissipation is most pressing for low-order methods employed by commercial computational fluid dynamics codes. Following the recent work of Schranner et al., the equations and procedure for estimating the numerical dissipation rate and the numerical viscosity in a commercial code are presented. The method allows for the computation of the numerical dissipation rate and numerical viscosity in the physical space for arbitrary sub-domains in a self-consistent way, using only information provided by the code in question. The method is first tested for a three-dimensional Taylor-Green vortex flow in a simple cubic domain and compared with benchmark results obtained using an accurate, incompressible spectral solver. Afterwards the same procedure is applied for the first time to a realistic flow configuration, specifically to the above discussed laminar separation bubble flow over a NACA 0012 airfoil. The method appears to be quite robust and its application reveals that for the code and the flow in question the numerical dissipation can be significantly larger than the viscous dissipation or the dissipation of the classical Smagorinsky sub-grid scale model, confirming the previously qualitative finding.

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.

Some variance reduction methods for numerical stochastic homogenization.

PubMed

Blanc, X; Le Bris, C; Legoll, F

2016-04-28

We give an overview of a series of recent studies devoted to variance reduction techniques for numerical stochastic homogenization. Numerical homogenization requires that a set of problems is solved at the microscale, the so-called corrector problems. In a random environment, these problems are stochastic and therefore need to be repeatedly solved, for several configurations of the medium considered. An empirical average over all configurations is then performed using the Monte Carlo approach, so as to approximate the effective coefficients necessary to determine the macroscopic behaviour. Variance severely affects the accuracy and the cost of such computations. Variance reduction approaches, borrowed from other contexts in the engineering sciences, can be useful. Some of these variance reduction techniques are presented, studied and tested here. © 2016 The Author(s).

A new digitized reverse correction method for hypoid gears based on a one-dimensional probe

NASA Astrophysics Data System (ADS)

Li, Tianxing; Li, Jubo; Deng, Xiaozhong; Yang, Jianjun; Li, Genggeng; Ma, Wensuo

2017-12-01

In order to improve the tooth surface geometric accuracy and transmission quality of hypoid gears, a new digitized reverse correction method is proposed based on the measurement data from a one-dimensional probe. The minimization of tooth surface geometrical deviations is realized from the perspective of mathematical analysis and reverse engineering. Combining the analysis of complex tooth surface generation principles and the measurement mechanism of one-dimensional probes, the mathematical relationship between the theoretical designed tooth surface, the actual machined tooth surface and the deviation tooth surface is established, the mapping relation between machine-tool settings and tooth surface deviations is derived, and the essential connection between the accurate calculation of tooth surface deviations and the reverse correction method of machine-tool settings is revealed. Furthermore, a reverse correction model of machine-tool settings is built, a reverse correction strategy is planned, and the minimization of tooth surface deviations is achieved by means of the method of numerical iterative reverse solution. On this basis, a digitized reverse correction system for hypoid gears is developed by the organic combination of numerical control generation, accurate measurement, computer numerical processing, and digitized correction. Finally, the correctness and practicability of the digitized reverse correction method are proved through a reverse correction experiment. The experimental results show that the tooth surface geometric deviations meet the engineering requirements after two trial cuts and one correction.

Control optimization of a lifting body entry problem by an improved and a modified method of perturbation function. Ph.D. Thesis - Houston Univ.

NASA Technical Reports Server (NTRS)

Garcia, F., Jr.

1974-01-01

A study of the solution problem of a complex entry optimization was studied. The problem was transformed into a two-point boundary value problem by using classical calculus of variation methods. Two perturbation methods were devised. These methods attempted to desensitize the contingency of the solution of this type of problem on the required initial co-state estimates. Also numerical results are presented for the optimal solution resulting from a number of different initial co-states estimates. The perturbation methods were compared. It is found that they are an improvement over existing methods.

Design of transonic airfoil sections using a similarity theory

NASA Technical Reports Server (NTRS)

Nixon, D.

1978-01-01

A study of the available methods for transonic airfoil and wing design indicates that the most powerful technique is the numerical optimization procedure. However, the computer time for this method is relatively large because of the amount of computation required in the searches during optimization. The optimization method requires that base and calibration solutions be computed to determine a minimum drag direction. The design space is then computationally searched in this direction; it is these searches that dominate the computation time. A recent similarity theory allows certain transonic flows to be calculated rapidly from the base and calibration solutions. In this paper the application of the similarity theory to design problems is examined with the object of at least partially eliminating the costly searches of the design optimization method. An example of an airfoil design is presented.

Magnetic Field Suppression of Flow in Semiconductor Melt

NASA Technical Reports Server (NTRS)

Fedoseyev, A. I.; Kansa, E. J.; Marin, C.; Volz, M. P.; Ostrogorsky, A. G.

2000-01-01

One of the most promising approaches for the reduction of convection during the crystal growth of conductive melts (semiconductor crystals) is the application of magnetic fields. Current technology allows the experimentation with very intense static fields (up to 80 KGauss) for which nearly convection free results are expected from simple scaling analysis in stabilized systems (vertical Bridgman method with axial magnetic field). However, controversial experimental results were obtained. The computational methods are, therefore, a fundamental tool in the understanding of the phenomena accounting during the solidification of semiconductor materials. Moreover, effects like the bending of the isomagnetic lines, different aspect ratios and misalignments between the direction of the gravity and magnetic field vectors can not be analyzed with analytical methods. The earliest numerical results showed controversial conclusions and are not able to explain the experimental results. Although the generated flows are extremely low, the computational task is a complicated because of the thin boundary layers. That is one of the reasons for the discrepancy in the results that numerical studies reported. Modeling of these magnetically damped crystal growth experiments requires advanced numerical methods. We used, for comparison, three different approaches to obtain the solution of the problem of thermal convection flows: (1) Spectral method in spectral superelement implementation, (2) Finite element method with regularization for boundary layers, (3) Multiquadric method, a novel method with global radial basis functions, that is proven to have exponential convergence. The results obtained by these three methods are presented for a wide region of Rayleigh and Hartman numbers. Comparison and discussion of accuracy, efficiency, reliability and agreement with experimental results will be presented as well.

Calculation of the aerodynamic loading of swept and unswept flexible wings of arbitrary stiffness

NASA Technical Reports Server (NTRS)

Diederich, Franklin W

1950-01-01

A method is presented for calculating the aerodynamic loading, the divergence speed, and certain stability derivatives of swept and unswept wings and tail surfaces of arbitrary stiffness. Provision is made for using either stiffness curves and root rotation constants or structural influence coefficients in the analysis. Computing forms, tables of numerical constants required in the analysis, and an illustrative example are included to facilitate calculations by means of the method.

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.

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.

Dry calibration of electromagnetic flowmeters based on numerical models combining multiple physical phenomena (multiphysics)

NASA Astrophysics Data System (ADS)

Fu, X.; Hu, L.; Lee, K. M.; Zou, J.; Ruan, X. D.; Yang, H. Y.

2010-10-01

This paper presents a method for dry calibration of an electromagnetic flowmeter (EMF). This method, which determines the voltage induced in the EMF as conductive liquid flows through a magnetic field, numerically solves a coupled set of multiphysical equations with measured boundary conditions for the magnetic, electric, and flow fields in the measuring pipe of the flowmeter. Specifically, this paper details the formulation of dry calibration and an efficient algorithm (that adaptively minimizes the number of measurements and requires only the normal component of the magnetic flux density as boundary conditions on the pipe surface to reconstruct the magnetic field involved) for computing the sensitivity of EMF. Along with an in-depth discussion on factors that could significantly affect the final precision of a dry calibrated EMF, the effects of flow disturbance on measuring errors have been experimentally studied by installing a baffle at the inflow port of the EMF. Results of the dry calibration on an actual EMF were compared against flow-rig calibration; excellent agreements (within 0.3%) between dry calibration and flow-rig tests verify the multiphysical computation of the fields and the robustness of the method. As requiring no actual flow, the dry calibration is particularly useful for calibrating large-diameter EMFs where conventional flow-rig methods are often costly and difficult to implement.

Development of Physics-Based Hurricane Wave Response Functions: Application to Selected Sites on the U.S. Gulf Coast

NASA Astrophysics Data System (ADS)

McLaughlin, P. W.; Kaihatu, J. M.; Irish, J. L.; Taylor, N. R.; Slinn, D.

2013-12-01

Recent hurricane activity in the Gulf of Mexico has led to a need for accurate, computationally efficient prediction of hurricane damage so that communities can better assess risk of local socio-economic disruption. This study focuses on developing robust, physics based non-dimensional equations that accurately predict maximum significant wave height at different locations near a given hurricane track. These equations (denoted as Wave Response Functions, or WRFs) were developed from presumed physical dependencies between wave heights and hurricane characteristics and fit with data from numerical models of waves and surge under hurricane conditions. After curve fitting, constraints which correct for fully developed sea state were used to limit the wind wave growth. When applied to the region near Gulfport, MS, back prediction of maximum significant wave height yielded root mean square errors between 0.22-0.42 (m) at open coast stations and 0.07-0.30 (m) at bay stations when compared to the numerical model data. The WRF method was also applied to Corpus Christi, TX and Panama City, FL with similar results. Back prediction errors will be included in uncertainty evaluations connected to risk calculations using joint probability methods. These methods require thousands of simulations to quantify extreme value statistics, thus requiring the use of reduced methods such as the WRF to represent the relevant physical processes.

Computationally efficient simulation of unsteady aerodynamics using POD on the fly

NASA Astrophysics Data System (ADS)

Moreno-Ramos, Ruben; Vega, José M.; Varas, Fernando

2016-12-01

Modern industrial aircraft design requires a large amount of sufficiently accurate aerodynamic and aeroelastic simulations. Current computational fluid dynamics (CFD) solvers with aeroelastic capabilities, such as the NASA URANS unstructured solver FUN3D, require very large computational resources. Since a very large amount of simulation is necessary, the CFD cost is just unaffordable in an industrial production environment and must be significantly reduced. Thus, a more inexpensive, yet sufficiently precise solver is strongly needed. An opportunity to approach this goal could follow some recent results (Terragni and Vega 2014 SIAM J. Appl. Dyn. Syst. 13 330-65 Rapun et al 2015 Int. J. Numer. Meth. Eng. 104 844-68) on an adaptive reduced order model that combines ‘on the fly’ a standard numerical solver (to compute some representative snapshots), proper orthogonal decomposition (POD) (to extract modes from the snapshots), Galerkin projection (onto the set of POD modes), and several additional ingredients such as projecting the equations using a limited amount of points and fairly generic mode libraries. When applied to the complex Ginzburg-Landau equation, the method produces acceleration factors (comparing with standard numerical solvers) of the order of 20 and 300 in one and two space dimensions, respectively. Unfortunately, the extension of the method to unsteady, compressible flows around deformable geometries requires new approaches to deal with deformable meshes, high-Reynolds numbers, and compressibility. A first step in this direction is presented considering the unsteady compressible, two-dimensional flow around an oscillating airfoil using a CFD solver in a rigidly moving mesh. POD on the Fly gives results whose accuracy is comparable to that of the CFD solver used to compute the snapshots.

Measurement Uncertainty of Dew-Point Temperature in a Two-Pressure Humidity Generator

NASA Astrophysics Data System (ADS)

Martins, L. Lages; Ribeiro, A. Silva; Alves e Sousa, J.; Forbes, Alistair B.

2012-09-01

This article describes the measurement uncertainty evaluation of the dew-point temperature when using a two-pressure humidity generator as a reference standard. The estimation of the dew-point temperature involves the solution of a non-linear equation for which iterative solution techniques, such as the Newton-Raphson method, are required. Previous studies have already been carried out using the GUM method and the Monte Carlo method but have not discussed the impact of the approximate numerical method used to provide the temperature estimation. One of the aims of this article is to take this approximation into account. Following the guidelines presented in the GUM Supplement 1, two alternative approaches can be developed: the forward measurement uncertainty propagation by the Monte Carlo method when using the Newton-Raphson numerical procedure; and the inverse measurement uncertainty propagation by Bayesian inference, based on prior available information regarding the usual dispersion of values obtained by the calibration process. The measurement uncertainties obtained using these two methods can be compared with previous results. Other relevant issues concerning this research are the broad application to measurements that require hygrometric conditions obtained from two-pressure humidity generators and, also, the ability to provide a solution that can be applied to similar iterative models. The research also studied the factors influencing both the use of the Monte Carlo method (such as the seed value and the convergence parameter) and the inverse uncertainty propagation using Bayesian inference (such as the pre-assigned tolerance, prior estimate, and standard deviation) in terms of their accuracy and adequacy.

Presenting quantitative information about decision outcomes: a risk communication primer for patient decision aid developers

PubMed Central

2013-01-01

Background Making evidence-based decisions often requires comparison of two or more options. Research-based evidence may exist which quantifies how likely the outcomes are for each option. Understanding these numeric estimates improves patients’ risk perception and leads to better informed decision making. This paper summarises current “best practices” in communication of evidence-based numeric outcomes for developers of patient decision aids (PtDAs) and other health communication tools. Method An expert consensus group of fourteen researchers from North America, Europe, and Australasia identified eleven main issues in risk communication. Two experts for each issue wrote a “state of the art” summary of best evidence, drawing on the PtDA, health, psychological, and broader scientific literature. In addition, commonly used terms were defined and a set of guiding principles and key messages derived from the results. Results The eleven key components of risk communication were: 1) Presenting the chance an event will occur; 2) Presenting changes in numeric outcomes; 3) Outcome estimates for test and screening decisions; 4) Numeric estimates in context and with evaluative labels; 5) Conveying uncertainty; 6) Visual formats; 7) Tailoring estimates; 8) Formats for understanding outcomes over time; 9) Narrative methods for conveying the chance of an event; 10) Important skills for understanding numerical estimates; and 11) Interactive web-based formats. Guiding principles from the evidence summaries advise that risk communication formats should reflect the task required of the user, should always define a relevant reference class (i.e., denominator) over time, should aim to use a consistent format throughout documents, should avoid “1 in x” formats and variable denominators, consider the magnitude of numbers used and the possibility of format bias, and should take into account the numeracy and graph literacy of the audience. Conclusion A substantial and rapidly expanding evidence base exists for risk communication. Developers of tools to facilitate evidence-based decision making should apply these principles to improve the quality of risk communication in practice. PMID:24625237

Estimating times of extinction in the fossil record

PubMed Central

Marshall, Charles R.

2016-01-01

Because the fossil record is incomplete, the last fossil of a taxon is a biased estimate of its true time of extinction. Numerous methods have been developed in the palaeontology literature for estimating the true time of extinction using ages of fossil specimens. These methods, which typically give a confidence interval for estimating the true time of extinction, differ in the assumptions they make and the nature and amount of data they require. We review the literature on such methods and make some recommendations for future directions. PMID:27122005

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

Estimating times of extinction in the fossil record.

PubMed

Wang, Steve C; Marshall, Charles R

2016-04-01

Because the fossil record is incomplete, the last fossil of a taxon is a biased estimate of its true time of extinction. Numerous methods have been developed in the palaeontology literature for estimating the true time of extinction using ages of fossil specimens. These methods, which typically give a confidence interval for estimating the true time of extinction, differ in the assumptions they make and the nature and amount of data they require. We review the literature on such methods and make some recommendations for future directions. © 2016 The Author(s).

Anatomical image-guided fluorescence molecular tomography reconstruction using kernel method

NASA Astrophysics Data System (ADS)

Baikejiang, Reheman; Zhao, Yue; Fite, Brett Z.; Ferrara, Katherine W.; Li, Changqing

2017-05-01

Fluorescence molecular tomography (FMT) is an important in vivo imaging modality to visualize physiological and pathological processes in small animals. However, FMT reconstruction is ill-posed and ill-conditioned due to strong optical scattering in deep tissues, which results in poor spatial resolution. It is well known that FMT image quality can be improved substantially by applying the structural guidance in the FMT reconstruction. An approach to introducing anatomical information into the FMT reconstruction is presented using the kernel method. In contrast to conventional methods that incorporate anatomical information with a Laplacian-type regularization matrix, the proposed method introduces the anatomical guidance into the projection model of FMT. The primary advantage of the proposed method is that it does not require segmentation of targets in the anatomical images. Numerical simulations and phantom experiments have been performed to demonstrate the proposed approach's feasibility. Numerical simulation results indicate that the proposed kernel method can separate two FMT targets with an edge-to-edge distance of 1 mm and is robust to false-positive guidance and inhomogeneity in the anatomical image. For the phantom experiments with two FMT targets, the kernel method has reconstructed both targets successfully, which further validates the proposed kernel method.

Kranc: a Mathematica package to generate numerical codes for tensorial evolution equations

NASA Astrophysics Data System (ADS)

Husa, Sascha; Hinder, Ian; Lechner, Christiane

2006-06-01

We present a suite of Mathematica-based computer-algebra packages, termed "Kranc", which comprise a toolbox to convert certain (tensorial) systems of partial differential evolution equations to parallelized C or Fortran code for solving initial boundary value problems. Kranc can be used as a "rapid prototyping" system for physicists or mathematicians handling very complicated systems of partial differential equations, but through integration into the Cactus computational toolkit we can also produce efficient parallelized production codes. Our work is motivated by the field of numerical relativity, where Kranc is used as a research tool by the authors. In this paper we describe the design and implementation of both the Mathematica packages and the resulting code, we discuss some example applications, and provide results on the performance of an example numerical code for the Einstein equations. Program summaryTitle of program: Kranc Catalogue identifier: ADXS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXS_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computer for which the program is designed and others on which it has been tested: General computers which run Mathematica (for code generation) and Cactus (for numerical simulations), tested under Linux Programming language used: Mathematica, C, Fortran 90 Memory required to execute with typical data: This depends on the number of variables and gridsize, the included ADM example requires 4308 KB Has the code been vectorized or parallelized: The code is parallelized based on the Cactus framework. Number of bytes in distributed program, including test data, etc.: 1 578 142 Number of lines in distributed program, including test data, etc.: 11 711 Nature of physical problem: Solution of partial differential equations in three space dimensions, which are formulated as an initial value problem. In particular, the program is geared towards handling very complex tensorial equations as they appear, e.g., in numerical relativity. The worked out examples comprise the Klein-Gordon equations, the Maxwell equations, and the ADM formulation of the Einstein equations. Method of solution: The method of numerical solution is finite differencing and method of lines time integration, the numerical code is generated through a high level Mathematica interface. Restrictions on the complexity of the program: Typical numerical relativity applications will contain up to several dozen evolution variables and thousands of source terms, Cactus applications have shown scaling up to several thousand processors and grid sizes exceeding 500 3. Typical running time: This depends on the number of variables and the grid size: the included ADM example takes approximately 100 seconds on a 1600 MHz Intel Pentium M processor. Unusual features of the program: based on Mathematica and Cactus

Large scale nonlinear programming for the optimization of spacecraft trajectories

NASA Astrophysics Data System (ADS)

Arrieta-Camacho, Juan Jose

Despite the availability of high fidelity mathematical models, the computation of accurate optimal spacecraft trajectories has never been an easy task. While simplified models of spacecraft motion can provide useful estimates on energy requirements, sizing, and cost; the actual launch window and maneuver scheduling must rely on more accurate representations. We propose an alternative for the computation of optimal transfers that uses an accurate representation of the spacecraft dynamics. Like other methodologies for trajectory optimization, this alternative is able to consider all major disturbances. In contrast, it can handle explicitly equality and inequality constraints throughout the trajectory; it requires neither the derivation of costate equations nor the identification of the constrained arcs. The alternative consist of two steps: (1) discretizing the dynamic model using high-order collocation at Radau points, which displays numerical advantages, and (2) solution to the resulting Nonlinear Programming (NLP) problem using an interior point method, which does not suffer from the performance bottleneck associated with identifying the active set, as required by sequential quadratic programming methods; in this way the methodology exploits the availability of sound numerical methods, and next generation NLP solvers. In practice the methodology is versatile; it can be applied to a variety of aerospace problems like homing, guidance, and aircraft collision avoidance; the methodology is particularly well suited for low-thrust spacecraft trajectory optimization. Examples are presented which consider the optimization of a low-thrust orbit transfer subject to the main disturbances due to Earth's gravity field together with Lunar and Solar attraction. Other example considers the optimization of a multiple asteroid rendezvous problem. In both cases, the ability of our proposed methodology to consider non-standard objective functions and constraints is illustrated. Future research directions are identified, involving the automatic scheduling and optimization of trajectory correction maneuvers. The sensitivity information provided by the methodology is expected to be invaluable in such research pursuit. The collocation scheme and nonlinear programming algorithm presented in this work, complement other existing methodologies by providing reliable and efficient numerical methods able to handle large scale, nonlinear dynamic models.

Highly efficient and exact method for parallelization of grid-based algorithms and its implementation in DelPhi

PubMed Central

Li, Chuan; Li, Lin; Zhang, Jie; Alexov, Emil

2012-01-01

The Gauss-Seidel method is a standard iterative numerical method widely used to solve a system of equations and, in general, is more efficient comparing to other iterative methods, such as the Jacobi method. However, standard implementation of the Gauss-Seidel method restricts its utilization in parallel computing due to its requirement of using updated neighboring values (i.e., in current iteration) as soon as they are available. Here we report an efficient and exact (not requiring assumptions) method to parallelize iterations and to reduce the computational time as a linear/nearly linear function of the number of CPUs. In contrast to other existing solutions, our method does not require any assumptions and is equally applicable for solving linear and nonlinear equations. This approach is implemented in the DelPhi program, which is a finite difference Poisson-Boltzmann equation solver to model electrostatics in molecular biology. This development makes the iterative procedure on obtaining the electrostatic potential distribution in the parallelized DelPhi several folds faster than that in the serial code. Further we demonstrate the advantages of the new parallelized DelPhi by computing the electrostatic potential and the corresponding energies of large supramolecular structures. PMID:22674480

Theory and computation of optimal low- and medium-thrust transfers

NASA Technical Reports Server (NTRS)

Chuang, C.-H.

1994-01-01

This report presents two numerical methods considered for the computation of fuel-optimal, low-thrust orbit transfers in large numbers of burns. The origins of these methods are observations made with the extremal solutions of transfers in small numbers of burns; there seems to exist a trend such that the longer the time allowed to perform an optimal transfer the less fuel that is used. These longer transfers are obviously of interest since they require a motor of low thrust; however, we also find a trend that the longer the time allowed to perform the optimal transfer the more burns are required to satisfy optimality. Unfortunately, this usually increases the difficulty of computation. Both of the methods described use small-numbered burn solutions to determine solutions in large numbers of burns. One method is a homotopy method that corrects for problems that arise when a solution requires a new burn or coast arc for optimality. The other method is to simply patch together long transfers from smaller ones. An orbit correction problem is solved to develop this method. This method may also lead to a good guidance law for transfer orbits with long transfer times.

The Research on Automatic Construction of Domain Model Based on Deep Web Query Interfaces

NASA Astrophysics Data System (ADS)

JianPing, Gu

The integration of services is transparent, meaning that users no longer face the millions of Web services, do not care about the required data stored, but do not need to learn how to obtain these data. In this paper, we analyze the uncertainty of schema matching, and then propose a series of similarity measures. To reduce the cost of execution, we propose the type-based optimization method and schema matching pruning method of numeric data. Based on above analysis, we propose the uncertain schema matching method. The experiments prove the effectiveness and efficiency of our method.

Method for obtaining electron energy-density functions from Langmuir-probe data using a card-programmable calculator

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

Longhurst, G.R.

This paper presents a method for obtaining electron energy density functions from Langmuir probe data taken in cool, dense plasmas where thin-sheath criteria apply and where magnetic effects are not severe. Noise is filtered out by using regression of orthogonal polynomials. The method requires only a programmable calculator (TI-59 or equivalent) to implement and can be used for the most general, nonequilibrium electron energy distribution plasmas. Data from a mercury ion source analyzed using this method are presented and compared with results for the same data using standard numerical techniques.

Prediction of discretization error using the error transport equation

NASA Astrophysics Data System (ADS)

Celik, Ismail B.; Parsons, Don Roscoe

2017-06-01

This study focuses on an approach to quantify the discretization error associated with numerical solutions of partial differential equations by solving an error transport equation (ETE). The goal is to develop a method that can be used to adequately predict the discretization error using the numerical solution on only one grid/mesh. The primary problem associated with solving the ETE is the formulation of the error source term which is required for accurately predicting the transport of the error. In this study, a novel approach is considered which involves fitting the numerical solution with a series of locally smooth curves and then blending them together with a weighted spline approach. The result is a continuously differentiable analytic expression that can be used to determine the error source term. Once the source term has been developed, the ETE can easily be solved using the same solver that is used to obtain the original numerical solution. The new methodology is applied to the two-dimensional Navier-Stokes equations in the laminar flow regime. A simple unsteady flow case is also considered. The discretization error predictions based on the methodology presented in this study are in good agreement with the 'true error'. While in most cases the error predictions are not quite as accurate as those from Richardson extrapolation, the results are reasonable and only require one numerical grid. The current results indicate that there is much promise going forward with the newly developed error source term evaluation technique and the ETE.

Transient electromagnetic sounding for groundwater

USGS Publications Warehouse

Fitterman, David V.; Stewart, Mark T.

1986-01-01

The feasibility of using the transient electromagnetic sounding (TS or TDEM) method for groundwater exploration can be studied by means of numerical models. As examples of its applicability to groundwater exploration, we study four groundwater exploration problems: (1) mapping of alluvial fill and gravel zones over bedrock; (2) mapping of sand and gravel lenses in till; (3) detection of salt or brackish water interfaces in freshwater aquifers; and (4) determination of hydrostratigraphy. These groundwater problems require determination of the depth to bedrock; location of resistive, high‐porosity zones associated with fresh water; determination of formation resistivity to assess water quality; and determination of lithology and geometry, respectively. The TS method is best suited for locating conductive targets, and has very good vertical resolution. Unlike other sounding techniques where the receiver‐transmitter array must be expanded to sound more deeply, the depth of investigation for the TS method is a function of the length of time the transient is recorded. Present equipment limitations require that exploration targets with resistivities of 50 Ω ⋅ m or more be at least 50 m deep to determine their resistivity. The maximum depth of exploration is controlled by the geoelectrical section and background electromagnetic (EM) noise. For a particular exploration problem, numerical studies are recommended to determine if the target is detectable.

Improving finite element results in modeling heart valve mechanics.

PubMed

Earl, Emily; Mohammadi, Hadi

2018-06-01

Finite element analysis is a well-established computational tool which can be used for the analysis of soft tissue mechanics. Due to the structural complexity of the leaflet tissue of the heart valve, the currently available finite element models do not adequately represent the leaflet tissue. A method of addressing this issue is to implement computationally expensive finite element models, characterized by precise constitutive models including high-order and high-density mesh techniques. In this study, we introduce a novel numerical technique that enhances the results obtained from coarse mesh finite element models to provide accuracy comparable to that of fine mesh finite element models while maintaining a relatively low computational cost. Introduced in this study is a method by which the computational expense required to solve linear and nonlinear constitutive models, commonly used in heart valve mechanics simulations, is reduced while continuing to account for large and infinitesimal deformations. This continuum model is developed based on the least square algorithm procedure coupled with the finite difference method adhering to the assumption that the components of the strain tensor are available at all nodes of the finite element mesh model. The suggested numerical technique is easy to implement, practically efficient, and requires less computational time compared to currently available commercial finite element packages such as ANSYS and/or ABAQUS.

From three-dimensional long-term tectonic numerical models to synthetic structural data: semi-automatic extraction of instantaneous & finite strain quantities

NASA Astrophysics Data System (ADS)

Duclaux, Guillaume; May, Dave

2017-04-01

Over the past three decades thermo-mechanical numerical modelling has transformed the way we look at deformation in the lithosphere. More than just generating aesthetically pleasing pictures, the output from a numerical models contains a rich source of quantitative information that can be used to measure deformation quantities in plan view or three-dimensions. Adding value to any numerical experiment requires a thorough post-processing of the modelling results. Such work aims to produce visual information that will resonate to seasoned structural geologists and assist with comparing experimental and observational data. Here we introduce two methods to generate synthetic structural data from numerical model outputs. We first present an image processing and shape recognition workflow developed to extract the active faults orientation from surface velocity gradients. In order to measure the active faults lengths and directions along with their distribution at the surface of the model we implemented an automated sequential mapping technique based on the second invariant of the strain rate tensor and using a suite a python functions. Active fault direction measurements are achieved using a probabilistic method for extracting linear features orientation from any surface. This method has the undeniable advantage to avoid interpretation bias. Strike measurements for individual segments are weighted according to their length and orientation distribution data are presented in an equal-area moving average rose diagrams produced using a weighted method. Finally, we discuss a method for mapping finite strain in three-dimensions. A high-resolution Lagrangian regular grid which advects during the numerical experiment is used to track the progressive deformation within the model. Thanks to this data we can measure the finite strain ellipsoids for any region of interest in the model. This method assumes that the finite strain is homogenous within one unit cell of the grid. We can compute individual ellipsoid's parameters (orientation, shape, etc.) and represent the finite deformation for any region of interest in a Flinn diagram. In addition, we can use the finite strain ellipsoids to estimate the prevailing foliation and/or lineation directions anywhere in the model. These two methods are applied to measure the instantaneous and finite deformation patterns within an oblique rift zone ongoing constant extension in the absence of surface processes.

Supercomputing Aspects for Simulating Incompressible Flow

NASA Technical Reports Server (NTRS)

Kwak, Dochan; Kris, Cetin C.

2000-01-01

The primary objective of this research is to support the design of liquid rocket systems for the Advanced Space Transportation System. Since the space launch systems in the near future are likely to rely on liquid rocket engines, increasing the efficiency and reliability of the engine components is an important task. One of the major problems in the liquid rocket engine is to understand fluid dynamics of fuel and oxidizer flows from the fuel tank to plume. Understanding the flow through the entire turbo-pump geometry through numerical simulation will be of significant value toward design. One of the milestones of this effort is to develop, apply and demonstrate the capability and accuracy of 3D CFD methods as efficient design analysis tools on high performance computer platforms. The development of the Message Passage Interface (MPI) and Multi Level Parallel (MLP) versions of the INS3D code is currently underway. The serial version of INS3D code is a multidimensional incompressible Navier-Stokes solver based on overset grid technology, INS3D-MPI is based on the explicit massage-passing interface across processors and is primarily suited for distributed memory systems. INS3D-MLP is based on multi-level parallel method and is suitable for distributed-shared memory systems. For the entire turbo-pump simulations, moving boundary capability and efficient time-accurate integration methods are built in the flow solver, To handle the geometric complexity and moving boundary problems, an overset grid scheme is incorporated with the solver so that new connectivity data will be obtained at each time step. The Chimera overlapped grid scheme allows subdomains move relative to each other, and provides a great flexibility when the boundary movement creates large displacements. Two numerical procedures, one based on artificial compressibility method and the other pressure projection method, are outlined for obtaining time-accurate solutions of the incompressible Navier-Stokes equations. The performance of the two methods is compared by obtaining unsteady solutions for the evolution of twin vortices behind a flat plate. Calculated results are compared with experimental and other numerical results. For an unsteady flow, which requires small physical time step, the pressure projection method was found to be computationally efficient since it does not require any subiteration procedure. It was observed that the artificial compressibility method requires a fast convergence scheme at each physical time step in order to satisfy the incompressibility condition. This was obtained by using a GMRES-ILU(0) solver in present computations. When a line-relaxation scheme was used, the time accuracy was degraded and time-accurate computations became very expensive.

A no-gold-standard technique for objective assessment of quantitative nuclear-medicine imaging methods

PubMed Central

Jha, Abhinav K; Caffo, Brian; Frey, Eric C

2016-01-01

The objective optimization and evaluation of nuclear-medicine quantitative imaging methods using patient data is highly desirable but often hindered by the lack of a gold standard. Previously, a regression-without-truth (RWT) approach has been proposed for evaluating quantitative imaging methods in the absence of a gold standard, but this approach implicitly assumes that bounds on the distribution of true values are known. Several quantitative imaging methods in nuclear-medicine imaging measure parameters where these bounds are not known, such as the activity concentration in an organ or the volume of a tumor. We extended upon the RWT approach to develop a no-gold-standard (NGS) technique for objectively evaluating such quantitative nuclear-medicine imaging methods with patient data in the absence of any ground truth. Using the parameters estimated with the NGS technique, a figure of merit, the noise-to-slope ratio (NSR), can be computed, which can rank the methods on the basis of precision. An issue with NGS evaluation techniques is the requirement of a large number of patient studies. To reduce this requirement, the proposed method explored the use of multiple quantitative measurements from the same patient, such as the activity concentration values from different organs in the same patient. The proposed technique was evaluated using rigorous numerical experiments and using data from realistic simulation studies. The numerical experiments demonstrated that the NSR was estimated accurately using the proposed NGS technique when the bounds on the distribution of true values were not precisely known, thus serving as a very reliable metric for ranking the methods on the basis of precision. In the realistic simulation study, the NGS technique was used to rank reconstruction methods for quantitative single-photon emission computed tomography (SPECT) based on their performance on the task of estimating the mean activity concentration within a known volume of interest. Results showed that the proposed technique provided accurate ranking of the reconstruction methods for 97.5% of the 50 noise realizations. Further, the technique was robust to the choice of evaluated reconstruction methods. The simulation study pointed to possible violations of the assumptions made in the NGS technique under clinical scenarios. However, numerical experiments indicated that the NGS technique was robust in ranking methods even when there was some degree of such violation. PMID:26982626

A no-gold-standard technique for objective assessment of quantitative nuclear-medicine imaging methods.

PubMed

Jha, Abhinav K; Caffo, Brian; Frey, Eric C

2016-04-07

The objective optimization and evaluation of nuclear-medicine quantitative imaging methods using patient data is highly desirable but often hindered by the lack of a gold standard. Previously, a regression-without-truth (RWT) approach has been proposed for evaluating quantitative imaging methods in the absence of a gold standard, but this approach implicitly assumes that bounds on the distribution of true values are known. Several quantitative imaging methods in nuclear-medicine imaging measure parameters where these bounds are not known, such as the activity concentration in an organ or the volume of a tumor. We extended upon the RWT approach to develop a no-gold-standard (NGS) technique for objectively evaluating such quantitative nuclear-medicine imaging methods with patient data in the absence of any ground truth. Using the parameters estimated with the NGS technique, a figure of merit, the noise-to-slope ratio (NSR), can be computed, which can rank the methods on the basis of precision. An issue with NGS evaluation techniques is the requirement of a large number of patient studies. To reduce this requirement, the proposed method explored the use of multiple quantitative measurements from the same patient, such as the activity concentration values from different organs in the same patient. The proposed technique was evaluated using rigorous numerical experiments and using data from realistic simulation studies. The numerical experiments demonstrated that the NSR was estimated accurately using the proposed NGS technique when the bounds on the distribution of true values were not precisely known, thus serving as a very reliable metric for ranking the methods on the basis of precision. In the realistic simulation study, the NGS technique was used to rank reconstruction methods for quantitative single-photon emission computed tomography (SPECT) based on their performance on the task of estimating the mean activity concentration within a known volume of interest. Results showed that the proposed technique provided accurate ranking of the reconstruction methods for 97.5% of the 50 noise realizations. Further, the technique was robust to the choice of evaluated reconstruction methods. The simulation study pointed to possible violations of the assumptions made in the NGS technique under clinical scenarios. However, numerical experiments indicated that the NGS technique was robust in ranking methods even when there was some degree of such violation.

Numerical study on the Welander oscillatory natural circulation problem using high-order numerical methods

DOE PAGES

Zou, Ling; Zhao, Haihua; Kim, Seung Jun

2016-11-16

In this study, the classical Welander’s oscillatory natural circulation problem is investigated using high-order numerical methods. As originally studied by Welander, the fluid motion in a differentially heated fluid loop can exhibit stable, weakly instable, and strongly instable modes. A theoretical stability map has also been originally derived from the stability analysis. Numerical results obtained in this paper show very good agreement with Welander’s theoretical derivations. For stable cases, numerical results from both the high-order and low-order numerical methods agree well with the non-dimensional flow rate analytically derived. The high-order numerical methods give much less numerical errors compared to themore » low-order methods. For stability analysis, the high-order numerical methods could perfectly predict the stability map, while the low-order numerical methods failed to do so. For all theoretically unstable cases, the low-order methods predicted them to be stable. The result obtained in this paper is a strong evidence to show the benefits of using high-order numerical methods over the low-order ones, when they are applied to simulate natural circulation phenomenon that has already gain increasing interests in many future nuclear reactor designs.« less

The Challenge of Leading Work Teams: Creating a Case Study to Enhance Learning

ERIC Educational Resources Information Center

Schraeder, Mike; Bandow, Diane

2016-01-01

The competitive success of organizations is heavily dependent on the quality of leadership within those organizations. Among the growing list of skills required for effective leadership is the need for leaders to promote the deployment of effective teams in the workplace. There are numerous strategies and methods that have been utilized to prepare…

Supercomputers Of The Future

NASA Technical Reports Server (NTRS)

Peterson, Victor L.; Kim, John; Holst, Terry L.; Deiwert, George S.; Cooper, David M.; Watson, Andrew B.; Bailey, F. Ron

1992-01-01

Report evaluates supercomputer needs of five key disciplines: turbulence physics, aerodynamics, aerothermodynamics, chemistry, and mathematical modeling of human vision. Predicts these fields will require computer speed greater than 10(Sup 18) floating-point operations per second (FLOP's) and memory capacity greater than 10(Sup 15) words. Also, new parallel computer architectures and new structured numerical methods will make necessary speed and capacity available.

Using Predictor-Corrector Methods in Numerical Solutions to Mathematical Problems of Motion

ERIC Educational Resources Information Center

Lewis, Jerome

2005-01-01

In this paper, the author looks at some classic problems in mathematics that involve motion in the plane. Many case problems like these are difficult and beyond the mathematical skills of most undergraduates, but computational approaches often require less insight into the subtleties of the problems and can be used to obtain reliable solutions.…

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.

Fire metrology: Current and future directions in physics-based measurements

Treesearch

Robert L. Kremens; Alistair M.S. Smith; Matthew B. Dickinson

2010-01-01

The robust evaluation of fire impacts on the biota, soil, and atmosphere requires measurement and analysis methods that can characterize combustion processes across a range of temporal and spatial scales. Numerous challenges are apparent in the literature. These challenges have led to novel research to quantify the 1) structure and heterogeneity of the pre-fire...

Multi-hybrid method for investigation of EM scattering from inhomogeneous object above a dielectric rough surface

NASA Astrophysics Data System (ADS)

Li, Jie; Guo, LiXin; He, Qiong; Wei, Bing

2012-10-01

An iterative strategy combining Kirchhoff approximation^(KA) with the hybrid finite element-boundary integral (FE-BI) method is presented in this paper to study the interactions between the inhomogeneous object and the underlying rough surface. KA is applied to study scattering from underlying rough surfaces, whereas FE-BI deals with scattering from the above target. Both two methods use updated excitation sources. Huygens equivalence principle and an iterative strategy are employed to consider the multi-scattering effects. This hybrid FE-BI-KA scheme is an improved and generalized version of previous hybrid Kirchhoff approximation-method of moments (KA-MoM). This newly presented hybrid method has the following advantages: (1) the feasibility of modeling multi-scale scattering problems (large scale underlying surface and small scale target); (2) low memory requirement as in hybrid KA-MoM; (3) the ability to deal with scattering from inhomogeneous (including coated or layered) scatterers above rough surfaces. The numerical results are given to evaluate the accuracy of the multi-hybrid technique; the computing time and memory requirements consumed in specific numerical simulation of FE-BI-KA are compared with those of MoM. The convergence performance is analyzed by studying the iteration number variation caused by related parameters. Then bistatic scattering from inhomogeneous object of different configurations above dielectric Gaussian rough surface is calculated and the influences of dielectric compositions and surface roughness on the scattering pattern are discussed.

A numerical method for solving the 3D unsteady incompressible Navier Stokes equations in curvilinear domains with complex immersed boundaries

NASA Astrophysics Data System (ADS)

Ge, Liang; Sotiropoulos, Fotis

2007-08-01

A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g. the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [A. Gilmanov, F. Sotiropoulos, A hybrid cartesian/immersed boundary method for simulating flows with 3d, geometrically complex, moving bodies, Journal of Computational Physics 207 (2005) 457-492.]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus.

Evaluation of an Eulerian multi-material mixture formulation based on a single inverse deformation gradient tensor field

DOE PAGES

Ghaisas, N. S.; Subramaniam, A.; Lele, S. K.; ...

2017-12-31

We report high energy-density solids undergoing elastic-plastic deformations coupled to compressible fluids are a common occurrence in engineering applications. Examples include problems involving high-velocity impact and penetration, cavitation, and several manufacturing processes, such as cold forming. Numerical simulations of such phenomena require the ability to handle the interaction of shock waves with multi-material interfaces that can undergo large deformations and severe distortions. As opposed to Lagrangian (Benson 1992) and arbitrary Lagrangian-Eulerian (ALE) methods (Donea et al. 2004), fully Eulerian methods use grids that do not change in time. Consequently, Eulerian methods do not suffer from difficulties on account of meshmore » entanglement, and do not require periodic, expensive, remap operations.« less

Evaluation of an Eulerian multi-material mixture formulation based on a single inverse deformation gradient tensor field

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

Ghaisas, N. S.; Subramaniam, A.; Lele, S. K.

We report high energy-density solids undergoing elastic-plastic deformations coupled to compressible fluids are a common occurrence in engineering applications. Examples include problems involving high-velocity impact and penetration, cavitation, and several manufacturing processes, such as cold forming. Numerical simulations of such phenomena require the ability to handle the interaction of shock waves with multi-material interfaces that can undergo large deformations and severe distortions. As opposed to Lagrangian (Benson 1992) and arbitrary Lagrangian-Eulerian (ALE) methods (Donea et al. 2004), fully Eulerian methods use grids that do not change in time. Consequently, Eulerian methods do not suffer from difficulties on account of meshmore » entanglement, and do not require periodic, expensive, remap operations.« less

A modified three-term PRP conjugate gradient algorithm for optimization models.

PubMed

Wu, Yanlin

2017-01-01

The nonlinear conjugate gradient (CG) algorithm is a very effective method for optimization, especially for large-scale problems, because of its low memory requirement and simplicity. Zhang et al. (IMA J. Numer. Anal. 26:629-649, 2006) firstly propose a three-term CG algorithm based on the well known Polak-Ribière-Polyak (PRP) formula for unconstrained optimization, where their method has the sufficient descent property without any line search technique. They proved the global convergence of the Armijo line search but this fails for the Wolfe line search technique. Inspired by their method, we will make a further study and give a modified three-term PRP CG algorithm. The presented method possesses the following features: (1) The sufficient descent property also holds without any line search technique; (2) the trust region property of the search direction is automatically satisfied; (3) the steplengh is bounded from below; (4) the global convergence will be established under the Wolfe line search. Numerical results show that the new algorithm is more effective than that of the normal method.

THE SYSTEMATIC ERROR TEST FOR PSF CORRECTION IN WEAK GRAVITATIONAL LENSING SHEAR MEASUREMENT BY THE ERA METHOD BY IDEALIZING PSF

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

Okura, Yuki; Futamase, Toshifumi, E-mail: yuki.okura@riken.jp

We improve the ellipticity of re-smeared artificial image (ERA) method of point-spread function (PSF) correction in a weak lensing shear analysis in order to treat the realistic shape of galaxies and the PSF. This is done by re-smearing the PSF and the observed galaxy image using a re-smearing function (RSF) and allows us to use a new PSF with a simple shape and to correct the PSF effect without any approximations or assumptions. We perform a numerical test to show that the method applied for galaxies and PSF with some complicated shapes can correct the PSF effect with a systematicmore » error of less than 0.1%. We also apply the ERA method for real data of the Abell 1689 cluster to confirm that it is able to detect the systematic weak lensing shear pattern. The ERA method requires less than 0.1 or 1 s to correct the PSF for each object in a numerical test and a real data analysis, respectively.« less

Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media

NASA Astrophysics Data System (ADS)

Yang, Haijian; Sun, Shuyu; Yang, Chao

2017-03-01

Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.

A new hybrid numerical scheme for simulating fault ruptures with near-fault bulk inhomogeneities

NASA Astrophysics Data System (ADS)

Hajarolasvadi, S.; Elbanna, A. E.

2017-12-01

The Finite Difference (FD) and Boundary Integral (BI) Method have been extensively used to model spontaneously propagating shear cracks, which can serve as a useful idealization of natural earthquakes. While FD suffers from artificial dispersion and numerical dissipation and has a large computational cost as it requires the discretization of the whole volume of interest, it can be applied to a wider range of problems including ones with bulk nonlinearities and heterogeneities. On the other hand, in the BI method, the numerical consideration is confined to the crack path only, with the elastodynamic response of the bulk expressed in terms of integral relations between displacement discontinuities and tractions along the crack. Therefore, this method - its spectral boundary integral (SBI) formulation in particular - is much faster and more computationally efficient than other bulk methods such as FD. However, its application is restricted to linear elastic bulk and planar faults. This work proposes a novel hybrid numerical scheme that combines FD and the SBI to enable treating fault zone nonlinearities and heterogeneities with unprecedented resolution and in a more computationally efficient way. The main idea of the method is to enclose the inhomgeneities in a virtual strip that is introduced for computational purposes only. This strip is then discretized using a volume-based numerical method, chosen here to be the finite difference method while the virtual boundaries of the strip are handled using the SBI formulation that represents the two elastic half spaces outside the strip. Modeling the elastodynamic response in these two halfspaces needs to be carried out by an Independent Spectral Formulation before joining them to the strip with the appropriate boundary conditions. Dirichlet and Neumann boundary conditions are imposed on the strip and the two half-spaces, respectively, at each time step to propagate the solution forward. We demonstrate the validity of the approach using two examples for dynamic rupture propagation: one in the presence of a low velocity layer and the other in which off-fault plasticity is permitted. This approach is more computationally efficient than pure FD and expands the range of applications of SBI beyond the current state of the art.

WATSFAR: numerical simulation of soil WATer and Solute fluxes using a FAst and Robust method

NASA Astrophysics Data System (ADS)

Crevoisier, David; Voltz, Marc

2013-04-01

To simulate the evolution of hydro- and agro-systems, numerous spatialised models are based on a multi-local approach and improvement of simulation accuracy by data-assimilation techniques are now used in many application field. The latest acquisition techniques provide a large amount of experimental data, which increase the efficiency of parameters estimation and inverse modelling approaches. In turn simulations are often run on large temporal and spatial domains which requires a large number of model runs. Eventually, despite the regular increase in computing capacities, the development of fast and robust methods describing the evolution of saturated-unsaturated soil water and solute fluxes is still a challenge. Ross (2003, Agron J; 95:1352-1361) proposed a method, solving 1D Richards' and convection-diffusion equation, that fulfil these characteristics. The method is based on a non iterative approach which reduces the numerical divergence risks and allows the use of coarser spatial and temporal discretisations, while assuring a satisfying accuracy of the results. Crevoisier et al. (2009, Adv Wat Res; 32:936-947) proposed some technical improvements and validated this method on a wider range of agro- pedo- climatic situations. In this poster, we present the simulation code WATSFAR which generalises the Ross method to other mathematical representations of soil water retention curve (i.e. standard and modified van Genuchten model) and includes a dual permeability context (preferential fluxes) for both water and solute transfers. The situations tested are those known to be the less favourable when using standard numerical methods: fine textured and extremely dry soils, intense rainfall and solute fluxes, soils near saturation, ... The results of WATSFAR have been compared with the standard finite element model Hydrus. The analysis of these comparisons highlights two main advantages for WATSFAR, i) robustness: even on fine textured soil or high water and solute fluxes - where Hydrus simulations may fail to converge - no numerical problem appears, and ii) accuracy of simulations even for loose spatial domain discretisations, which can only be obtained by Hydrus with fine discretisations.

High-order cyclo-difference techniques: An alternative to finite differences

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Otto, John C.

1993-01-01

The summation-by-parts energy norm is used to establish a new class of high-order finite-difference techniques referred to here as 'cyclo-difference' techniques. These techniques are constructed cyclically from stable subelements, and require no numerical boundary conditions; when coupled with the simultaneous approximation term (SAT) boundary treatment, they are time asymptotically stable for an arbitrary hyperbolic system. These techniques are similar to spectral element techniques and are ideally suited for parallel implementation, but do not require special collocation points or orthogonal basis functions. The principal focus is on methods of sixth-order formal accuracy or less; however, these methods could be extended in principle to any arbitrary order of accuracy.

In Search of Grid Converged Solutions

NASA Technical Reports Server (NTRS)

Lockard, David P.

2010-01-01

Assessing solution error continues to be a formidable task when numerically solving practical flow problems. Currently, grid refinement is the primary method used for error assessment. The minimum grid spacing requirements to achieve design order accuracy for a structured-grid scheme are determined for several simple examples using truncation error evaluations on a sequence of meshes. For certain methods and classes of problems, obtaining design order may not be sufficient to guarantee low error. Furthermore, some schemes can require much finer meshes to obtain design order than would be needed to reduce the error to acceptable levels. Results are then presented from realistic problems that further demonstrate the challenges associated with using grid refinement studies to assess solution accuracy.

Applying Parallel Adaptive Methods with GeoFEST/PYRAMID to Simulate Earth Surface Crustal Dynamics

NASA Technical Reports Server (NTRS)

Norton, Charles D.; Lyzenga, Greg; Parker, Jay; Glasscoe, Margaret; Donnellan, Andrea; Li, Peggy

2006-01-01

This viewgraph presentation reviews the use Adaptive Mesh Refinement (AMR) in simulating the Crustal Dynamics of Earth's Surface. AMR simultaneously improves solution quality, time to solution, and computer memory requirements when compared to generating/running on a globally fine mesh. The use of AMR in simulating the dynamics of the Earth's Surface is spurred by future proposed NASA missions, such as InSAR for Earth surface deformation and other measurements. These missions will require support for large-scale adaptive numerical methods using AMR to model observations. AMR was chosen because it has been successful in computation fluid dynamics for predictive simulation of complex flows around complex structures.

Determination of full piezoelectric complex parameters using gradient-based optimization algorithm

NASA Astrophysics Data System (ADS)

Kiyono, C. Y.; Pérez, N.; Silva, E. C. N.

2016-02-01

At present, numerical techniques allow the precise simulation of mechanical structures, but the results are limited by the knowledge of the material properties. In the case of piezoelectric ceramics, the full model determination in the linear range involves five elastic, three piezoelectric, and two dielectric complex parameters. A successful solution to obtaining piezoceramic properties consists of comparing the experimental measurement of the impedance curve and the results of a numerical model by using the finite element method (FEM). In the present work, a new systematic optimization method is proposed to adjust the full piezoelectric complex parameters in the FEM model. Once implemented, the method only requires the experimental data (impedance modulus and phase data acquired by an impedometer), material density, geometry, and initial values for the properties. This method combines a FEM routine implemented using an 8-noded axisymmetric element with a gradient-based optimization routine based on the method of moving asymptotes (MMA). The main objective of the optimization procedure is minimizing the quadratic difference between the experimental and numerical electrical conductance and resistance curves (to consider resonance and antiresonance frequencies). To assure the convergence of the optimization procedure, this work proposes restarting the optimization loop whenever the procedure ends in an undesired or an unfeasible solution. Two experimental examples using PZ27 and APC850 samples are presented to test the precision of the method and to check the dependency of the frequency range used, respectively.

Drag reduction in channel flow using nonlinear control

NASA Technical Reports Server (NTRS)

Keefe, Laurence R.

1993-01-01

Two nonlinear control schemes have been applied to the problem of drag reduction in channel flow. Both schemes have been tested using numerical simulations at a mass flux Reynolds numbers of 4408, utilizing 2D nonlinear neutral modes for goal dynamics. The OGY-method, which requires feedback, reduces drag to 60-80 percent of the turbulent value at the same Reynolds number, and employs forcing only within a thin region near the wall. The H-method, or model-based control, fails to achieve any drag reduction when starting from a fully turbulent initial condition, but shows potential for suppressing or retarding laminar-to-turbulent transition by imposing instead a transition to a low drag, nonlinear traveling wave solution to the Navier-Stokes equation. The drag in this state corresponds to that achieved by the OGY-method. Model-based control requires no feedback, but in experiments to date has required the forcing be imposed within a thicker layer than the OGY-method. Control energy expenditures in both methods are small, representing less than 0.1 percent of the uncontrolled flow's energy.

On-the-fly Numerical Surface Integration for Finite-Difference Poisson-Boltzmann Methods.

PubMed

Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

2011-11-01

Most implicit solvation models require the definition of a molecular surface as the interface that separates the solute in atomic detail from the solvent approximated as a continuous medium. Commonly used surface definitions include the solvent accessible surface (SAS), the solvent excluded surface (SES), and the van der Waals surface. In this study, we present an efficient numerical algorithm to compute the SES and SAS areas to facilitate the applications of finite-difference Poisson-Boltzmann methods in biomolecular simulations. Different from previous numerical approaches, our algorithm is physics-inspired and intimately coupled to the finite-difference Poisson-Boltzmann methods to fully take advantage of its existing data structures. Our analysis shows that the algorithm can achieve very good agreement with the analytical method in the calculation of the SES and SAS areas. Specifically, in our comprehensive test of 1,555 molecules, the average unsigned relative error is 0.27% in the SES area calculations and 1.05% in the SAS area calculations at the grid spacing of 1/2Å. In addition, a systematic correction analysis can be used to improve the accuracy for the coarse-grid SES area calculations, with the average unsigned relative error in the SES areas reduced to 0.13%. These validation studies indicate that the proposed algorithm can be applied to biomolecules over a broad range of sizes and structures. Finally, the numerical algorithm can also be adapted to evaluate the surface integral of either a vector field or a scalar field defined on the molecular surface for additional solvation energetics and force calculations.

The analytical and numerical approaches to the theory of the Moon's librations: Modern analysis and results

NASA Astrophysics Data System (ADS)

Petrova, N.; Zagidullin, A.; Nefedyev, Y.; Kosulin, V.; Andreev, A.

2017-11-01

Observing physical librations of celestial bodies and the Moon represents one of the astronomical methods of remotely assessing the internal structure of a celestial body without conducting expensive space experiments. The paper contains a review of recent advances in studying the Moon's structure using various methods of obtaining and applying the lunar physical librations (LPhL) data. In this article LPhL simulation methods of assessing viscoelastic and dissipative properties of the lunar body and lunar core parameters, whose existence has been recently confirmed during the seismic data reprocessing of ;Apollo; space mission, are described. Much attention is paid to physical interpretation of the free librations phenomenon and the methods for its determination. In the paper the practical application of the most accurate analytical LPhL tables (Rambaux and Williams, 2011) is discussed. The tables were built on the basis of complex analytical processing of the residual differences obtained when comparing long-term series of laser observations with the numerical ephemeris DE421. In the paper an efficiency analysis of two approaches to LPhL theory is conducted: the numerical and the analytical ones. It has been shown that in lunar investigation both approaches complement each other in various aspects: the numerical approach provides high accuracy of the theory, which is required for the proper processing of modern observations, the analytical approach allows to comprehend the essence of the phenomena in the lunar rotation, predict and interpret new effects in the observations of lunar body and lunar core parameters.

Numerical weather prediction model tuning via ensemble prediction system

NASA Astrophysics Data System (ADS)

Jarvinen, H.; Laine, M.; Ollinaho, P.; Solonen, A.; Haario, H.

2011-12-01

This paper discusses a novel approach to tune predictive skill of numerical weather prediction (NWP) models. NWP models contain tunable parameters which appear in parameterizations schemes of sub-grid scale physical processes. Currently, numerical values of these parameters are specified manually. In a recent dual manuscript (QJRMS, revised) we developed a new concept and method for on-line estimation of the NWP model parameters. The EPPES ("Ensemble prediction and parameter estimation system") method requires only minimal changes to the existing operational ensemble prediction infra-structure and it seems very cost-effective because practically no new computations are introduced. The approach provides an algorithmic decision making tool for model parameter optimization in operational NWP. In EPPES, statistical inference about the NWP model tunable parameters is made by (i) generating each member of the ensemble of predictions using different model parameter values, drawn from a proposal distribution, and (ii) feeding-back the relative merits of the parameter values to the proposal distribution, based on evaluation of a suitable likelihood function against verifying observations. In the presentation, the method is first illustrated in low-order numerical tests using a stochastic version of the Lorenz-95 model which effectively emulates the principal features of ensemble prediction systems. The EPPES method correctly detects the unknown and wrongly specified parameters values, and leads to an improved forecast skill. Second, results with an atmospheric general circulation model based ensemble prediction system show that the NWP model tuning capacity of EPPES scales up to realistic models and ensemble prediction systems. Finally, a global top-end NWP model tuning exercise with preliminary results is published.

Precise and Fast Computation of the Gravitational Field of a General Finite Body and Its Application to the Gravitational Study of Asteroid Eros

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

Fukushima, Toshio, E-mail: Toshio.Fukushima@nao.ac.jp

In order to obtain the gravitational field of a general finite body inside its Brillouin sphere, we developed a new method to compute the field accurately. First, the body is assumed to consist of some layers in a certain spherical polar coordinate system and the volume mass density of each layer is expanded as a Maclaurin series of the radial coordinate. Second, the line integral with respect to the radial coordinate is analytically evaluated in a closed form. Third, the resulting surface integrals are numerically integrated by the split quadrature method using the double exponential rule. Finally, the associated gravitationalmore » acceleration vector is obtained by numerically differentiating the numerically integrated potential. Numerical experiments confirmed that the new method is capable of computing the gravitational field independently of the location of the evaluation point, namely whether inside, on the surface of, or outside the body. It can also provide sufficiently precise field values, say of 14–15 digits for the potential and of 9–10 digits for the acceleration. Furthermore, its computational efficiency is better than that of the polyhedron approximation. This is because the computational error of the new method decreases much faster than that of the polyhedron models when the number of required transcendental function calls increases. As an application, we obtained the gravitational field of 433 Eros from its shape model expressed as the 24 × 24 spherical harmonic expansion by assuming homogeneity of the object.« less

A note on the uniqueness of 2D elastostatic problems formulated by different types of potential functions

NASA Astrophysics Data System (ADS)

Guerrero, José Luis Morales; Vidal, Manuel Cánovas; Nicolás, José Andrés Moreno; López, Francisco Alhama

2018-05-01

New additional conditions required for the uniqueness of the 2D elastostatic problems formulated in terms of potential functions for the derived Papkovich-Neuber representations, are studied. Two cases are considered, each of them formulated by the scalar potential function plus one of the rectangular non-zero components of the vector potential function. For these formulations, in addition to the original (physical) boundary conditions, two new additional conditions are required. In addition, for the complete Papkovich-Neuber formulation, expressed by the scalar potential plus two components of the vector potential, the additional conditions established previously for the three-dimensional case in z-convex domain can be applied. To show the usefulness of these new conditions in a numerical scheme two applications are numerically solved by the network method for the three cases of potential formulations.

Practical witness for electronic coherences

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

Johnson, Allan S.; Department of Physics, Imperial College London, London; Yuen-Zhou, Joel

2014-12-28

The origin of the coherences in two-dimensional spectroscopy of photosynthetic complexes remains disputed. Recently, it has been shown that in the ultrashort-pulse limit, oscillations in a frequency-integrated pump-probe signal correspond exclusively to electronic coherences, and thus such experiments can be used to form a test for electronic vs. vibrational oscillations in such systems. Here, we demonstrate a method for practically implementing such a test, whereby pump-probe signals are taken at several different pulse durations and used to extrapolate to the ultrashort-pulse limit. We present analytic and numerical results determining requirements for pulse durations and the optimal choice of pulse centralmore » frequency, which can be determined from an absorption spectrum. Our results suggest that for numerous systems, the required experiment could be implemented by many ultrafast spectroscopy laboratories using pulses of tens of femtoseconds in duration. Such experiments could resolve the standing debate over the nature of coherences in photosynthetic complexes.« less

SandiaMRCR

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

2012-01-05

SandiaMCR was developed to identify pure components and their concentrations from spectral data. This software efficiently implements the multivariate calibration regression alternating least squares (MCR-ALS), principal component analysis (PCA), and singular value decomposition (SVD). Version 3.37 also includes the PARAFAC-ALS Tucker-1 (for trilinear analysis) algorithms. The alternating least squares methods can be used to determine the composition without or with incomplete prior information on the constituents and their concentrations. It allows the specification of numerous preprocessing, initialization and data selection and compression options for the efficient processing of large data sets. The software includes numerous options including the definition ofmore » equality and non-negativety constraints to realistically restrict the solution set, various normalization or weighting options based on the statistics of the data, several initialization choices and data compression. The software has been designed to provide a practicing spectroscopist the tools required to routinely analysis data in a reasonable time and without requiring expert intervention.« less

Practical witness for electronic coherences.

PubMed

Johnson, Allan S; Yuen-Zhou, Joel; Aspuru-Guzik, Alán; Krich, Jacob J

2014-12-28

The origin of the coherences in two-dimensional spectroscopy of photosynthetic complexes remains disputed. Recently, it has been shown that in the ultrashort-pulse limit, oscillations in a frequency-integrated pump-probe signal correspond exclusively to electronic coherences, and thus such experiments can be used to form a test for electronic vs. vibrational oscillations in such systems. Here, we demonstrate a method for practically implementing such a test, whereby pump-probe signals are taken at several different pulse durations and used to extrapolate to the ultrashort-pulse limit. We present analytic and numerical results determining requirements for pulse durations and the optimal choice of pulse central frequency, which can be determined from an absorption spectrum. Our results suggest that for numerous systems, the required experiment could be implemented by many ultrafast spectroscopy laboratories using pulses of tens of femtoseconds in duration. Such experiments could resolve the standing debate over the nature of coherences in photosynthetic complexes.

Geometric Integration of Weakly Dissipative Systems

NASA Astrophysics Data System (ADS)

Modin, K.; Führer, C.; Soöderlind, G.

2009-09-01

Some problems in mechanics, e.g. in bearing simulation, contain subsystems that are conservative as well as weakly dissipative subsystems. Our experience is that geometric integration methods are often superior for such systems, as long as the dissipation is weak. Here we develop adaptive methods for dissipative perturbations of Hamiltonian systems. The methods are "geometric" in the sense that the form of the dissipative perturbation is preserved. The methods are linearly explicit, i.e., they require the solution of a linear subsystem. We sketch an analysis in terms of backward error analysis and numerical comparisons with a conventional RK method of the same order is given.

Ef: Software for Nonrelativistic Beam Simulation by Particle-in-Cell Algorithm

NASA Astrophysics Data System (ADS)

Boytsov, A. Yu.; Bulychev, A. A.

2018-04-01

Understanding of particle dynamics is crucial in construction of electron guns, ion sources and other types of nonrelativistic beam devices. Apart from external guiding and focusing systems, a prominent role in evolution of such low-energy beams is played by particle-particle interaction. Numerical simulations taking into account these effects are typically accomplished by a well-known particle-in-cell method. In practice, for convenient work a simulation program should not only implement this method, but also support parallelization, provide integration with CAD systems and allow access to details of the simulation algorithm. To address the formulated requirements, development of a new open source code - Ef - has been started. It's current features and main functionality are presented. Comparison with several analytical models demonstrates good agreement between the numerical results and the theory. Further development plans are discussed.

Chiral thiazoline and thiazole building blocks for the synthesis of peptide-derived natural products.

PubMed

Just-Baringo, Xavier; Albericio, Fernando; Alvarez, Mercedes

2014-01-01

Thiazoline and thiazole heterocycles are privileged motifs found in numerous peptide-derived natural products of biological interest. During the last decades, the synthesis of optically pure building blocks has been addressed by numerous groups, which have developed a plethora of strategies to that end. Efficient and reliable methodologies that are compatible with the intricate and capricious architectures of natural products are a must to further develop their science. Structure confirmation, structure-activity relationship studies and industrial production are fields of paramount importance that require these robust methodologies in order to successfully bring natural products into the clinic. Today's chemist toolbox is assorted with many powerful methods for chiral thiazoline and thiazole synthesis. Ranging from biomimetic approaches to stereoselective alkylations, one is likely to find a suitable method for their needs.

MLFMA-accelerated Nyström method for ultrasonic scattering - Numerical results and experimental validation

NASA Astrophysics Data System (ADS)

Gurrala, Praveen; Downs, Andrew; Chen, Kun; Song, Jiming; Roberts, Ron

2018-04-01

Full wave scattering models for ultrasonic waves are necessary for the accurate prediction of voltage signals received from complex defects/flaws in practical nondestructive evaluation (NDE) measurements. We propose the high-order Nyström method accelerated by the multilevel fast multipole algorithm (MLFMA) as an improvement to the state-of-the-art full-wave scattering models that are based on boundary integral equations. We present numerical results demonstrating improvements in simulation time and memory requirement. Particularly, we demonstrate the need for higher order geom-etry and field approximation in modeling NDE measurements. Also, we illustrate the importance of full-wave scattering models using experimental pulse-echo data from a spherical inclusion in a solid, which cannot be modeled accurately by approximation-based scattering models such as the Kirchhoff approximation.

An efficient method to compute spurious end point contributions in PO solutions. [Physical Optics

NASA Technical Reports Server (NTRS)

Gupta, Inder J.; Burnside, Walter D.; Pistorius, Carl W. I.

1987-01-01

A method is given to compute the spurious endpoint contributions in the physical optics solution for electromagnetic scattering from conducting bodies. The method is applicable to general three-dimensional structures. The only information required to use the method is the radius of curvature of the body at the shadow boundary. Thus, the method is very efficient for numerical computations. As an illustration, the method is applied to several bodies of revolution to compute the endpoint contributions for backscattering in the case of axial incidence. It is shown that in high-frequency situations, the endpoint contributions obtained using the method are equal to the true endpoint contributions.

A modified conjugate gradient coefficient with inexact line search for unconstrained optimization

NASA Astrophysics Data System (ADS)

Aini, Nurul; Rivaie, Mohd; Mamat, Mustafa

2016-11-01

Conjugate gradient (CG) method is a line search algorithm mostly known for its wide application in solving unconstrained optimization problems. Its low memory requirements and global convergence properties makes it one of the most preferred method in real life application such as in engineering and business. In this paper, we present a new CG method based on AMR* and CD method for solving unconstrained optimization functions. The resulting algorithm is proven to have both the sufficient descent and global convergence properties under inexact line search. Numerical tests are conducted to assess the effectiveness of the new method in comparison to some previous CG methods. The results obtained indicate that our method is indeed superior.

Uncertainty Propagation for Turbulent, Compressible Flow in a Quasi-1D Nozzle Using Stochastic Methods

NASA Technical Reports Server (NTRS)

Zang, Thomas A.; Mathelin, Lionel; Hussaini, M. Yousuff; Bataille, Francoise

2003-01-01

This paper describes a fully spectral, Polynomial Chaos method for the propagation of uncertainty in numerical simulations of compressible, turbulent flow, as well as a novel stochastic collocation algorithm for the same application. The stochastic collocation method is key to the efficient use of stochastic methods on problems with complex nonlinearities, such as those associated with the turbulence model equations in compressible flow and for CFD schemes requiring solution of a Riemann problem. Both methods are applied to compressible flow in a quasi-one-dimensional nozzle. The stochastic collocation method is roughly an order of magnitude faster than the fully Galerkin Polynomial Chaos method on the inviscid problem.

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

Sound Emission of Rotor Induced Deformations of Generator Casings

NASA Technical Reports Server (NTRS)

Polifke, W.; Mueller, B.; Yee, H. C.; Mansour, Nagi (Technical Monitor)

2001-01-01

The casing of large electrical generators can be deformed slightly by the rotor's magnetic field. The sound emission produced by these periodic deformations, which could possibly exceed guaranteed noise emission limits, is analysed analytically and numerically. From the deformation of the casing, the normal velocity of the generator's surface is computed. Taking into account the corresponding symmetry, an analytical solution for the acoustic pressure outside the generator is round in terms of the Hankel function of second order. The normal velocity or the generator surface provides the required boundary condition for the acoustic pressure and determines the magnitude of pressure oscillations. For the numerical simulation, the nonlinear 2D Euler equations are formulated In a perturbation form for low Mach number Computational Aeroacoustics (CAA). The spatial derivatives are discretized by the classical sixth-order central interior scheme and a third-order boundary scheme. Spurious high frequency oscillations are damped by a characteristic-based artificial compression method (ACM) filter. The time derivatives are approximated by the classical 4th-order Runge-Kutta method. The numerical results are In excellent agreement with the analytical solution.

Hybrid heating systems optimization of residential environment to have thermal comfort conditions by numerical simulation.

PubMed

Jahantigh, Nabi; Keshavarz, Ali; Mirzaei, Masoud

2015-01-01

The aim of this study is to determine optimum hybrid heating systems parameters, such as temperature, surface area of a radiant heater and vent area to have thermal comfort conditions. DOE, Factorial design method is used to determine the optimum values for input parameters. A 3D model of a virtual standing thermal manikin with real dimensions is considered in this study. Continuity, momentum, energy, species equations for turbulent flow and physiological equation for thermal comfort are numerically solved to study heat, moisture and flow field. K - ɛRNG Model is used for turbulence modeling and DO method is used for radiation effects. Numerical results have a good agreement with the experimental data reported in the literature. The effect of various combinations of inlet parameters on thermal comfort is considered. According to Pareto graph, some of these combinations that have significant effect on the thermal comfort require no more energy can be used as useful tools. A better symmetrical velocity distribution around the manikin is also presented in the hybrid system.

Anisotropic failure and size effects in periodic honeycomb materials: A gradient-elasticity approach

NASA Astrophysics Data System (ADS)

Réthoré, Julien; Dang, Thi Bach Tuyet; Kaltenbrunner, Christine

2017-02-01

This paper proposes a fracture mechanics model for the analysis of crack propagation in periodic honeycomb materials. The model is based on gradient-elasticity which enables us to account for the effect of the material structure at the macroscopic scale. For simulating the propagation of cracks along an arbitrary path, the numerical implementation is elaborated based on an extended finite element method with the required level of continuity. The two main features captured by the model are directionality and size effect. The numerical predictions are consistent with experimental results on honeycomb materials but also with results reported in the literature for microstructurally short cracks in metals.

Computation of shear viscosity of colloidal suspensions by SRD-MD

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

Laganapan, A. M. K.; Videcoq, A., E-mail: arnaud.videcoq@unilim.fr; Bienia, M.

2015-04-14

The behaviour of sheared colloidal suspensions with full hydrodynamic interactions (HIs) is numerically studied. To this end, we use the hybrid stochastic rotation dynamics-molecular dynamics (SRD-MD) method. The shear viscosity of colloidal suspensions is computed for different volume fractions, both for dilute and concentrated cases. We verify that HIs help in the collisions and the streaming of colloidal particles, thereby increasing the overall shear viscosity of the suspension. Our results show a good agreement with known experimental, theoretical, and numerical studies. This work demonstrates the ability of SRD-MD to successfully simulate transport coefficients that require correct modelling of HIs.

Neuronal Correlation Parameter and the Idea of Thermodynamic Entropy of an N-Body Gravitationally Bounded System.

PubMed

Haranas, Ioannis; Gkigkitzis, Ioannis; Kotsireas, Ilias; Austerlitz, Carlos

2017-01-01

Understanding how the brain encodes information and performs computation requires statistical and functional analysis. Given the complexity of the human brain, simple methods that facilitate the interpretation of statistical correlations among different brain regions can be very useful. In this report we introduce a numerical correlation measure that may serve the interpretation of correlational neuronal data, and may assist in the evaluation of different brain states. The description of the dynamical brain system, through a global numerical measure may indicate the presence of an action principle which may facilitate a application of physics principles in the study of the human brain and cognition.

On the Buckling of Imperfect Anisotropic Shells with Elastic Edge Supports Under Combined Loading Part I:. Pt. 1; Theory and Numerical Analysis

NASA Technical Reports Server (NTRS)

Arbocz, Johann; Hol, J. M. A. M.; deVries, J.

1998-01-01

A rigorous solution is presented for the case of stiffened anisotropic cylindrical shells with general imperfections under combined loading, where the edge supports are provided by symmetrical or unsymmetrical elastic rings. The circumferential dependence is eliminated by a truncated Fourier series. The resulting nonlinear 2-point boundary value problem is solved numerically via the "Parallel Shooting Method". The changing deformation patterns resulting from the different degrees of interaction between the given initial imperfections and the specified end rings are displayed. Recommendations are made as to the minimum ring stiffnesses required for optimal load carrying configurations.

A numerical solution for the diffusion equation in hydrogeologic systems

USGS Publications Warehouse

Ishii, A.L.; Healy, R.W.; Striegl, Robert G.

1989-01-01

The documentation of a computer code for the numerical solution of the linear diffusion equation in one or two dimensions in Cartesian or cylindrical coordinates is presented. Applications of the program include molecular diffusion, heat conduction, and fluid flow in confined systems. The flow media may be anisotropic and heterogeneous. The model is formulated by replacing the continuous linear diffusion equation by discrete finite-difference approximations at each node in a block-centered grid. The resulting matrix equation is solved by the method of preconditioned conjugate gradients. The conjugate gradient method does not require the estimation of iteration parameters and is guaranteed convergent in the absence of rounding error. The matrixes are preconditioned to decrease the steps to convergence. The model allows the specification of any number of boundary conditions for any number of stress periods, and the output of a summary table for selected nodes showing flux and the concentration of the flux quantity for each time step. The model is written in a modular format for ease of modification. The model was verified by comparison of numerical and analytical solutions for cases of molecular diffusion, two-dimensional heat transfer, and axisymmetric radial saturated fluid flow. Application of the model to a hypothetical two-dimensional field situation of gas diffusion in the unsaturated zone is demonstrated. The input and output files are included as a check on program installation. The definition of variables, input requirements, flow chart, and program listing are included in the attachments. (USGS)

Moho Modeling Using FFT Technique

NASA Astrophysics Data System (ADS)

Chen, Wenjin; Tenzer, Robert

2017-04-01

To improve the numerical efficiency, the Fast Fourier Transform (FFT) technique was facilitated in Parker-Oldenburg's method for a regional gravimetric Moho recovery, which assumes the Earth's planar approximation. In this study, we extend this definition for global applications while assuming a spherical approximation of the Earth. In particular, we utilize the FFT technique for a global Moho recovery, which is practically realized in two numerical steps. The gravimetric forward modeling is first applied, based on methods for a spherical harmonic analysis and synthesis of the global gravity and lithospheric structure models, to compute the refined gravity field, which comprises mainly the gravitational signature of the Moho geometry. The gravimetric inverse problem is then solved iteratively in order to determine the Moho depth. The application of FFT technique to both numerical steps reduces the computation time to a fraction of that required without applying this fast algorithm. The developed numerical producers are used to estimate the Moho depth globally, and the gravimetric result is validated using the global (CRUST1.0) and regional (ESC) seismic Moho models. The comparison reveals a relatively good agreement between the gravimetric and seismic models, with the RMS of differences (of 4-5 km) at the level of expected uncertainties of used input datasets, while without the presence of significant systematic bias.

High-order conservative finite difference GLM-MHD schemes for cell-centered MHD

NASA Astrophysics Data System (ADS)

Mignone, Andrea; Tzeferacos, Petros; Bodo, Gianluigi

2010-08-01

We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities. We suggest a numerical formulation based on a cell-centered approach where all of the primary flow variables are discretized at the zone center. The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. [J. Comput. Phys. 175 (2002) 645-673]. The resulting family of schemes is robust, cost-effective and straightforward to implement. Compared to previous existing approaches, it completely avoids the CPU intensive workload associated with an elliptic divergence cleaning step and the additional complexities required by staggered mesh algorithms. Extensive numerical testing demonstrate the robustness and reliability of the proposed framework for computations involving both smooth and discontinuous features.

Single- and Multiple-Objective Optimization with Differential Evolution and Neural Networks

NASA Technical Reports Server (NTRS)

Rai, Man Mohan

2006-01-01

Genetic and evolutionary algorithms have been applied to solve numerous problems in engineering design where they have been used primarily as optimization procedures. These methods have an advantage over conventional gradient-based search procedures became they are capable of finding global optima of multi-modal functions and searching design spaces with disjoint feasible regions. They are also robust in the presence of noisy data. Another desirable feature of these methods is that they can efficiently use distributed and parallel computing resources since multiple function evaluations (flow simulations in aerodynamics design) can be performed simultaneously and independently on ultiple processors. For these reasons genetic and evolutionary algorithms are being used more frequently in design optimization. Examples include airfoil and wing design and compressor and turbine airfoil design. They are also finding increasing use in multiple-objective and multidisciplinary optimization. This lecture will focus on an evolutionary method that is a relatively new member to the general class of evolutionary methods called differential evolution (DE). This method is easy to use and program and it requires relatively few user-specified constants. These constants are easily determined for a wide class of problems. Fine-tuning the constants will off course yield the solution to the optimization problem at hand more rapidly. DE can be efficiently implemented on parallel computers and can be used for continuous, discrete and mixed discrete/continuous optimization problems. It does not require the objective function to be continuous and is noise tolerant. DE and applications to single and multiple-objective optimization will be included in the presentation and lecture notes. A method for aerodynamic design optimization that is based on neural networks will also be included as a part of this lecture. The method offers advantages over traditional optimization methods. It is more flexible than other methods in dealing with design in the context of both steady and unsteady flows, partial and complete data sets, combined experimental and numerical data, inclusion of various constraints and rules of thumb, and other issues that characterize the aerodynamic design process. Neural networks provide a natural framework within which a succession of numerical solutions of increasing fidelity, incorporating more realistic flow physics, can be represented and utilized for optimization. Neural networks also offer an excellent framework for multiple-objective and multi-disciplinary design optimization. Simulation tools from various disciplines can be integrated within this framework and rapid trade-off studies involving one or many disciplines can be performed. The prospect of combining neural network based optimization methods and evolutionary algorithms to obtain a hybrid method with the best properties of both methods will be included in this presentation. Achieving solution diversity and accurate convergence to the exact Pareto front in multiple objective optimization usually requires a significant computational effort with evolutionary algorithms. In this lecture we will also explore the possibility of using neural networks to obtain estimates of the Pareto optimal front using non-dominated solutions generated by DE as training data. Neural network estimators have the potential advantage of reducing the number of function evaluations required to obtain solution accuracy and diversity, thus reducing cost to design.

Generalized multiscale finite-element method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

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

Gao, Kai; Fu, Shubin; Gibson, Richard L.

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale mediummore » property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.« less

Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

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

Gao, Kai, E-mail: kaigao87@gmail.com; Fu, Shubin, E-mail: shubinfu89@gmail.com; Gibson, Richard L., E-mail: gibson@tamu.edu

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale mediummore » property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.« less

Generalized multiscale finite-element method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

DOE PAGES

Gao, Kai; Fu, Shubin; Gibson, Richard L.; ...

2015-04-14

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale mediummore » property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.« less

Numerical and experimental investigation of turbine blade film cooling

NASA Astrophysics Data System (ADS)

Berkache, Amar; Dizene, Rabah

2017-12-01

The blades in a gas turbine engine are exposed to extreme temperature levels that exceed the melting temperature of the material. Therefore, efficient cooling is a requirement for high performance of the gas turbine engine. The present study investigates film cooling by means of 3D numerical simulations using a commercial code: Fluent. Three numerical models, namely k-ɛ, RSM and SST turbulence models; are applied and then prediction results are compared to experimental measurements conducted by PIV technique. The experimental model realized in the ENSEMA laboratory uses a flat plate with several rows of staggered holes. The performance of the injected flow into the mainstream is analyzed. The comparison shows that the RANS closure models improve the over-predictions of center-line film cooling velocities that is caused by the limitations of the RANS method due to its isotropy eddy diffusivity.

77 FR 1969 - Self-Regulatory Organizations; NYSE Arca, Inc.; Notice of Filing and Immediate Effectiveness of...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-01-12

... Numerical Thresholds With Percentage Thresholds for the Investor Tiers' Volume Requirements January 6, 2012... replace numerical thresholds with percentage thresholds for the Investor Tiers' volume requirements. The...: Replacing Numerical Thresholds With Percentage Thresholds Effective June 1, 2011, NYSE Arca introduced two...

Dissertation Defense Computational Fluid Dynamics Uncertainty Analysis for Payload Fairing Spacecraft Environmental Control Systems

NASA Technical Reports Server (NTRS)

Groves, Curtis Edward

2014-01-01

Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This paper describes an approach to quantify the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft without the use of test data. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional "validation by test only" mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions. Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computational Fluid Dynamics can be used to verify these requirements; however, the model must be validated by test data. This research includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available and open source solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT, STARCCM+, and OPENFOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid Dynamics model using the methodology found in "Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations". This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions. The method accounts for all uncertainty terms from both numerical and input variables. Objective three is to compile a table of uncertainty parameters that could be used to estimate the error in a Computational Fluid Dynamics model of the Environmental Control System /spacecraft system. Previous studies have looked at the uncertainty in a Computational Fluid Dynamics model for a single output variable at a single point, for example the re-attachment length of a backward facing step. For the flow regime being analyzed (turbulent, three-dimensional, incompressible), the error at a single point can propagate into the solution both via flow physics and numerical methods. Calculating the uncertainty in using Computational Fluid Dynamics to accurately predict airflow speeds around encapsulated spacecraft in is imperative to the success of future missions.

Dissertation Defense: Computational Fluid Dynamics Uncertainty Analysis for Payload Fairing Spacecraft Environmental Control Systems

NASA Technical Reports Server (NTRS)

Groves, Curtis Edward

2014-01-01

Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This paper describes an approach to quantify the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft without the use of test data. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional validation by test only mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions.Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computational Fluid Dynamics can be used to verify these requirements; however, the model must be validated by test data. This research includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available and open source solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT, STARCCM+, and OPENFOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid Dynamics model using the methodology found in Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations. This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions. The method accounts for all uncertainty terms from both numerical and input variables. Objective three is to compile a table of uncertainty parameters that could be used to estimate the error in a Computational Fluid Dynamics model of the Environmental Control System spacecraft system.Previous studies have looked at the uncertainty in a Computational Fluid Dynamics model for a single output variable at a single point, for example the re-attachment length of a backward facing step. For the flow regime being analyzed (turbulent, three-dimensional, incompressible), the error at a single point can propagate into the solution both via flow physics and numerical methods. Calculating the uncertainty in using Computational Fluid Dynamics to accurately predict airflow speeds around encapsulated spacecraft in is imperative to the success of future missions.

Computational Fluid Dynamics Uncertainty Analysis for Payload Fairing Spacecraft Environmental Control Systems

NASA Technical Reports Server (NTRS)

Groves, Curtis E.

2013-01-01

Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This proposal describes an approach to validate the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft. The research described here is absolutely cutting edge. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional"validation by test only'' mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions. Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computationaf Fluid Dynamics can be used to veritY these requirements; however, the model must be validated by test data. The proposed research project includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT and OPEN FOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid . . . Dynamics model using the methodology found in "Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations". This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions. The method accounts for all uncertainty terms from both numerical and input variables. Objective three is to compile a table of uncertainty parameters that could be used to estimate the error in a Computational Fluid Dynamics model of the Environmental Control System /spacecraft system. Previous studies have looked at the uncertainty in a Computational Fluid Dynamics model for a single output variable at a single point, for example the re-attachment length of a backward facing step. To date, the author is the only person to look at the uncertainty in the entire computational domain. For the flow regime being analyzed (turbulent, threedimensional, incompressible), the error at a single point can propagate into the solution both via flow physics and numerical methods. Calculating the uncertainty in using Computational Fluid Dynamics to accurately predict airflow speeds around encapsulated spacecraft in is imperative to the success of future missions.

MCore: A High-Order Finite-Volume Dynamical Core for Atmospheric General Circulation Models

NASA Astrophysics Data System (ADS)

Ullrich, P.; Jablonowski, C.

2011-12-01

The desire for increasingly accurate predictions of the atmosphere has driven numerical models to smaller and smaller resolutions, while simultaneously exponentially driving up the cost of existing numerical models. Even with the modern rapid advancement of computational performance, it is estimated that it will take more than twenty years before existing models approach the scales needed to resolve atmospheric convection. However, smarter numerical methods may allow us to glimpse the types of results we would expect from these fine-scale simulations while only requiring a fraction of the computational cost. The next generation of atmospheric models will likely need to rely on both high-order accuracy and adaptive mesh refinement in order to properly capture features of interest. We present our ongoing research on developing a set of ``smart'' numerical methods for simulating the global non-hydrostatic fluid equations which govern atmospheric motions. We have harnessed a high-order finite-volume based approach in developing an atmospheric dynamical core on the cubed-sphere. This type of method is desirable for applications involving adaptive grids, since it has been shown that spuriously reflected wave modes are intrinsically damped out under this approach. The model further makes use of an implicit-explicit Runge-Kutta-Rosenbrock (IMEX-RKR) time integrator for accurate and efficient coupling of the horizontal and vertical model components. We survey the algorithmic development of the model and present results from idealized dynamical core test cases, as well as give a glimpse at future work with our model.

Methods for Prediction of High-Speed Reacting Flows in Aerospace Propulsion

NASA Technical Reports Server (NTRS)

Drummond, J. Philip

2014-01-01

Research to develop high-speed airbreathing aerospace propulsion systems was underway in the late 1950s. A major part of the effort involved the supersonic combustion ramjet, or scramjet, engine. Work had also begun to develop computational techniques for solving the equations governing the flow through a scramjet engine. However, scramjet technology and the computational methods to assist in its evolution would remain apart for another decade. The principal barrier was that the computational methods needed for engine evolution lacked the computer technology required for solving the discrete equations resulting from the numerical methods. Even today, computer resources remain a major pacing item in overcoming this barrier. Significant advances have been made over the past 35 years, however, in modeling the supersonic chemically reacting flow in a scramjet combustor. To see how scramjet development and the required computational tools finally merged, we briefly trace the evolution of the technology in both areas.

Modeling and Numerical Challenges in Eulerian-Lagrangian Computations of Shock-driven Multiphase Flows

NASA Astrophysics Data System (ADS)

Diggs, Angela; Balachandar, Sivaramakrishnan

2015-06-01

The present work addresses the numerical methods required for particle-gas and particle-particle interactions in Eulerian-Lagrangian simulations of multiphase flow. Local volume fraction as seen by each particle is the quantity of foremost importance in modeling and evaluating such interactions. We consider a general multiphase flow with a distribution of particles inside a fluid flow discretized on an Eulerian grid. Particle volume fraction is needed both as a Lagrangian quantity associated with each particle and also as an Eulerian quantity associated with the flow. In Eulerian Projection (EP) methods, the volume fraction is first obtained within each cell as an Eulerian quantity and then interpolated to each particle. In Lagrangian Projection (LP) methods, the particle volume fraction is obtained at each particle and then projected onto the Eulerian grid. Traditionally, EP methods are used in multiphase flow, but sub-grid resolution can be obtained through use of LP methods. By evaluating the total error and its components we compare the performance of EP and LP methods. The standard von Neumann error analysis technique has been adapted for rigorous evaluation of rate of convergence. The methods presented can be extended to obtain accurate field representations of other Lagrangian quantities. Most importantly, we will show that such careful attention to numerical methodologies is needed in order to capture complex shock interaction with a bed of particles. Supported by U.S. Department of Defense SMART Program and the U.S. Department of Energy PSAAP-II program under Contract No. DE-NA0002378.

Implicit methods for efficient musculoskeletal simulation and optimal control

PubMed Central

van den Bogert, Antonie J.; Blana, Dimitra; Heinrich, Dieter

2011-01-01

The ordinary differential equations for musculoskeletal dynamics are often numerically stiff and highly nonlinear. Consequently, simulations require small time steps, and optimal control problems are slow to solve and have poor convergence. In this paper, we present an implicit formulation of musculoskeletal dynamics, which leads to new numerical methods for simulation and optimal control, with the expectation that we can mitigate some of these problems. A first order Rosenbrock method was developed for solving forward dynamic problems using the implicit formulation. It was used to perform real-time dynamic simulation of a complex shoulder arm system with extreme dynamic stiffness. Simulations had an RMS error of only 0.11 degrees in joint angles when running at real-time speed. For optimal control of musculoskeletal systems, a direct collocation method was developed for implicitly formulated models. The method was applied to predict gait with a prosthetic foot and ankle. Solutions were obtained in well under one hour of computation time and demonstrated how patients may adapt their gait to compensate for limitations of a specific prosthetic limb design. The optimal control method was also applied to a state estimation problem in sports biomechanics, where forces during skiing were estimated from noisy and incomplete kinematic data. Using a full musculoskeletal dynamics model for state estimation had the additional advantage that forward dynamic simulations, could be done with the same implicitly formulated model to simulate injuries and perturbation responses. While these methods are powerful and allow solution of previously intractable problems, there are still considerable numerical challenges, especially related to the convergence of gradient-based solvers. PMID:22102983

Applications of numerical methods to simulate the movement of contaminants in groundwater.

PubMed Central

Sun, N Z

1989-01-01

This paper reviews mathematical models and numerical methods that have been extensively used to simulate the movement of contaminants through the subsurface. The major emphasis is placed on the numerical methods of advection-dominated transport problems and inverse problems. Several mathematical models that are commonly used in field problems are listed. A variety of numerical solutions for three-dimensional models are introduced, including the multiple cell balance method that can be considered a variation of the finite element method. The multiple cell balance method is easy to understand and convenient for solving field problems. When the advection transport dominates the dispersion transport, two kinds of numerical difficulties, overshoot and numerical dispersion, are always involved in solving standard, finite difference methods and finite element methods. To overcome these numerical difficulties, various numerical techniques are developed, such as upstream weighting methods and moving point methods. A complete review of these methods is given and we also mention the problems of parameter identification, reliability analysis, and optimal-experiment design that are absolutely necessary for constructing a practical model. PMID:2695327

An advanced probabilistic structural analysis method for implicit performance functions

NASA Technical Reports Server (NTRS)

Wu, Y.-T.; Millwater, H. R.; Cruse, T. A.

1989-01-01

In probabilistic structural analysis, the performance or response functions usually are implicitly defined and must be solved by numerical analysis methods such as finite element methods. In such cases, the most commonly used probabilistic analysis tool is the mean-based, second-moment method which provides only the first two statistical moments. This paper presents a generalized advanced mean value (AMV) method which is capable of establishing the distributions to provide additional information for reliability design. The method requires slightly more computations than the second-moment method but is highly efficient relative to the other alternative methods. In particular, the examples show that the AMV method can be used to solve problems involving non-monotonic functions that result in truncated distributions.

Extrapolation of rotating sound fields.

PubMed

Carley, Michael

2018-03-01

A method is presented for the computation of the acoustic field around a tonal circular source, such as a rotor or propeller, based on an exact formulation which is valid in the near and far fields. The only input data required are the pressure field sampled on a cylindrical surface surrounding the source, with no requirement for acoustic velocity or pressure gradient information. The formulation is approximated with exponentially small errors and appears to require input data at a theoretically minimal number of points. The approach is tested numerically, with and without added noise, and demonstrates excellent performance, especially when compared to extrapolation using a far-field assumption.

A Series of MATLAB Learning Modules to Enhance Numerical Competency in Applied Marine Sciences

NASA Astrophysics Data System (ADS)

Fischer, A. M.; Lucieer, V.; Burke, C.

2016-12-01

Enhanced numerical competency to navigate the massive data landscapes are critical skills students need to effectively explore, analyse and visualize complex patterns in high-dimensional data for addressing the complexity of many of the world's problems. This is especially the case for interdisciplinary, undergraduate applied marine science programs, where students are required to demonstrate competency in methods and ideas across multiple disciplines. In response to this challenge, we have developed a series of repository-based data exploration, analysis and visualization modules in MATLAB for integration across various attending and online classes within the University of Tasmania. The primary focus of these modules is to teach students to collect, aggregate and interpret data from large on-line marine scientific data repositories to, 1) gain technical skills in discovering, accessing, managing and visualising large, numerous data sources, 2) interpret, analyse and design approaches to visualise these data, and 3) to address, through numerical approaches, complex, real-world problems, that the traditional scientific methods cannot address. All modules, implemented through a MATLAB live script, include a short recorded lecture to introduce the topic, a handout that gives an overview of the activities, an instructor's manual with a detailed methodology and discussion points, a student assessment (quiz and level-specific challenge task), and a survey. The marine science themes addressed through these modules include biodiversity, habitat mapping, algal blooms and sea surface temperature change and utilize a series of marine science and oceanographic data portals. Through these modules students, with minimal experience in MATLAB or numerical methods are introduced to array indexing, concatenation, sorting, and reshaping, principal component analysis, spectral analysis and unsupervised classification within the context of oceanographic processes, marine geology and marine community ecology.

Recovery Discontinuous Galerkin Jacobian-free Newton-Krylov Method for all-speed flows

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

HyeongKae Park; Robert Nourgaliev; Vincent Mousseau

2008-07-01

There is an increasing interest to develop the next generation simulation tools for the advanced nuclear energy systems. These tools will utilize the state-of-art numerical algorithms and computer science technology in order to maximize the predictive capability, support advanced reactor designs, reduce uncertainty and increase safety margins. In analyzing nuclear energy systems, we are interested in compressible low-Mach number, high heat flux flows with a wide range of Re, Ra, and Pr numbers. Under these conditions, the focus is placed on turbulent heat transfer, in contrast to other industries whose main interest is in capturing turbulent mixing. Our objective ismore » to develop singlepoint turbulence closure models for large-scale engineering CFD code, using Direct Numerical Simulation (DNS) or Large Eddy Simulation (LES) tools, requireing very accurate and efficient numerical algorithms. The focus of this work is placed on fully-implicit, high-order spatiotemporal discretization based on the discontinuous Galerkin method solving the conservative form of the compressible Navier-Stokes equations. The method utilizes a local reconstruction procedure derived from weak formulation of the problem, which is inspired by the recovery diffusion flux algorithm of van Leer and Nomura [?] and by the piecewise parabolic reconstruction [?] in the finite volume method. The developed methodology is integrated into the Jacobianfree Newton-Krylov framework [?] to allow a fully-implicit solution of the problem.« less

A Hyperbolic Solver for Black Hole Initial Data in Numerical Relativity

NASA Astrophysics Data System (ADS)

Babiuc, Maria

2016-03-01

Numerical relativity is essential to the efforts of detecting gravitational waves emitted at the inspiral and merger of binary black holes. The first requirement for the generation of reliable gravitational wave templates is an accurate method of constructing initial data (ID). The standard approach is to solve the constraint equations for general relativity by formulating them as an elliptic system. A shortcoming of the ID constructed this way is an initial burst of spurious unphysical radiation (junk radiation). Recently, Racz and Winicour formulated the constraints as a hyperbolic problem, requiring boundary conditions only on a large sphere surrounding the system, where the physical behavior of the gravitational field is well understood. We investigate the applicability of this new approach, by developing a new 4th order numerical code that implements the fully nonlinear constraints equations on a two dimensional stereographic foliation, and evolves them radially inward using a Runge-Kutta integrator. The tensorial quantities are written as spin-weighted fields and the angular derivatives are replaced with ``eth'' operators. We present here results for the simulation of nonlinear perturbations to Schwarzschild ID in Kerr-Schild coordinates. The code shows stability and convergence at both large and small radii. Our long-term goal is to develop this new approach into a numerical scheme for generating ID for binary black holes and to analyze its performance in eliminating the junk radiation.

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

DOE PAGES

Grayver, Alexander V.; Kolev, Tzanio V.

2015-11-01

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

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

Grayver, Alexander V.; Kolev, Tzanio V.

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

Rotatable Small Permanent Magnet Array for Ultra-Low Field Nuclear Magnetic Resonance Instrumentation: A Concept Study

PubMed Central

Vegh, Viktor; Reutens, David C.

2016-01-01

Object We studied the feasibility of generating the variable magnetic fields required for ultra-low field nuclear magnetic resonance relaxometry with dynamically adjustable permanent magnets. Our motivation was to substitute traditional electromagnets by distributed permanent magnets, increasing system portability. Materials and Methods The finite element method (COMSOL®) was employed for the numerical study of a small permanent magnet array to calculate achievable magnetic field strength, homogeneity, switching time and magnetic forces. A manually operated prototype was simulated and constructed to validate the numerical approach and to verify the generated magnetic field. Results A concentric small permanent magnet array can be used to generate strong sample pre-polarisation and variable measurement fields for ultra-low field relaxometry via simple prescribed magnet rotations. Using the array, it is possible to achieve a pre-polarisation field strength above 100 mT and variable measurement fields ranging from 20–50 μT with 200 ppm absolute field homogeneity within a field-of-view of 5 x 5 x 5 cubic centimetres. Conclusions A dynamic small permanent magnet array can generate multiple highly homogeneous magnetic fields required in ultra-low field nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) instruments. This design can significantly reduce the volume and energy requirements of traditional systems based on electromagnets, improving portability considerably. PMID:27271886

A class of renormalised meshless Laplacians for boundary value problems

NASA Astrophysics Data System (ADS)

Basic, Josip; Degiuli, Nastia; Ban, Dario

2018-02-01

A meshless approach to approximating spatial derivatives on scattered point arrangements is presented in this paper. Three various derivations of approximate discrete Laplace operator formulations are produced using the Taylor series expansion and renormalised least-squares correction of the first spatial derivatives. Numerical analyses are performed for the introduced Laplacian formulations, and their convergence rate and computational efficiency are examined. The tests are conducted on regular and highly irregular scattered point arrangements. The results are compared to those obtained by the smoothed particle hydrodynamics method and the finite differences method on a regular grid. Finally, the strong form of various Poisson and diffusion equations with Dirichlet or Robin boundary conditions are solved in two and three dimensions by making use of the introduced operators in order to examine their stability and accuracy for boundary value problems. The introduced Laplacian operators perform well for highly irregular point distribution and offer adequate accuracy for mesh and mesh-free numerical methods that require frequent movement of the grid or point cloud.