NASA Astrophysics Data System (ADS)
Takahashi, Takashi; Matunaga, Saburo
In order to analyze dynamics of space systems, such as cluster satellite systems and the capturing process of damaged satellites, it is necessary to consider such space systems as reconfigurable multibody systems. In this paper, we discuss the numerical computation of the dynamics of the ground experiment system to simulate the capturing and berthing process of a satellite by a dual-manipulator on the flat floor as an example. We have previously discussed the efficient dynamics algorithm for reconfigurable multibody system with topological changes. However, the contact dynamics, which is one of the most difficult issues on our study, remains to be discussed. We introduce two types of the linear complementarity problem (LCP) concerned with contact dynamics. The difference between two types of the LCP is whether impacts can be considered. Dynamics systems with impacts and friction are non-conservation systems, moreover the LCP is not always solvable. Therefore we must check if the solutions of the numerical computation are correct, or how accurate those are. In this paper, we derive the method of numerical computation with guaranteed accuracy of the LCP for contact dynamics.
Towards a wave-extraction method for numerical relativity. II. The quasi-Kinnersley frame
Nerozzi, Andrea; Beetle, Christopher; Bruni, Marco; Burko, Lior M.; Pollney, Denis
2005-07-15
The Newman-Penrose formalism may be used in numerical relativity to extract coordinate-invariant information about gravitational radiation emitted in strong-field dynamical scenarios. The main challenge in doing so is to identify a null tetrad appropriately adapted to the simulated geometry such that Newman-Penrose quantities computed relative to it have an invariant physical meaning. In black hole perturbation theory, the Teukolsky formalism uses such adapted tetrads, those which differ only perturbatively from the background Kinnersley tetrad. At late times, numerical simulations of astrophysical processes producing isolated black holes ought to admit descriptions in the Teukolsky formalism. However, adapted tetrads in this context must be identified using only the numerically computed metric, since no background Kerr geometry is known a priori. To do this, this paper introduces the notion of a quasi-Kinnersley frame. This frame, when space-time is perturbatively close to Kerr, approximates the background Kinnersley frame. However, it remains calculable much more generally, in space-times nonperturbatively different from Kerr. We give an explicit solution for the tetrad transformation which is required in order to find this frame in a general space-time.
Baciero, A. Zurro, B.; Martínez, M.
2014-11-15
The isotope effect is an important topic that is relevant for future D-T fusion reactors, where the use of deuterium, rather than hydrogen, may lean to improved plasma confinement. An evaluation of the ratio of hydrogen/deuterium is needed for isotope effect studies in current isotopic experiments. Here, the spectral range around H{sub α} and D{sub α} lines, obtained with an intensified multi-channel detector mounted to a 1-m focal length spectrometer, is analyzed using a fit function that includes several Gaussian components. The isotopic ratio evolution for a single operational day of the TJ-II stellarator is presented. The role of injected hydrogen by Neutral Beam Injection heating is also studied.
Numerical methods for molecular dynamics
Skeel, R.D.
1991-01-01
This report summarizes our research progress to date on the use of multigrid methods for three-dimensional elliptic partial differential equations, with particular emphasis on application to the Poisson-Boltzmann equation of molecular biophysics. This research is motivated by the need for fast and accurate numerical solution techniques for three-dimensional problems arising in physics and engineering. In many applications these problems must be solved repeatedly, and the extremely large number of discrete unknowns required to accurately approximate solutions to partial differential equations in three-dimensional regions necessitates the use of efficient solution methods. This situation makes clear the importance of developing methods which are of optimal order (or nearly so), meaning that the number of operations required to solve the discrete problem is on the order of the number of discrete unknowns. Multigrid methods are generally regarded as being in this class of methods, and are in fact provably optimal order for an increasingly large class of problems. The fundamental goal of this research is to develop a fast and accurate numerical technique, based on multi-level principles, for the solutions of the Poisson-Boltzmann equation of molecular biophysics and similar equations occurring in other applications. An outline of the report is as follows. We first present some background material, followed by a survey of the literature on the use of multigrid methods for solving problems similar to the Poisson-Boltzmann equation. A short description of the software we have developed so far is then given, and numerical results are discussed. Finally, our research plans for the coming year are presented.
Numerical methods for multibody systems
NASA Technical Reports Server (NTRS)
Glowinski, Roland; Nasser, Mahmoud G.
1994-01-01
This article gives a brief summary of some results obtained by Nasser on modeling and simulation of inequality problems in multibody dynamics. In particular, the augmented Lagrangian method discussed here is applied to a constrained motion problem with impulsive inequality constraints. A fundamental characteristic of the multibody dynamics problem is the lack of global convexity of its Lagrangian. The problem is transformed into a convex analysis problem by localization (piecewise linearization), where the augmented Lagrangian has been successfully used. A model test problem is considered and a set of numerical experiments is presented.
Evolution of Planetesimals. II. Numerical Simulations
NASA Astrophysics Data System (ADS)
Aarseth, S. J.; Lin, D. N. C.; Palmer, P. L.
1993-01-01
We continue our investigation of the dynamical evolution and coagulation process of planetesimals With a numerical N-body scheme, we simulate gravitational scattering and physical collisions among a system of planetesimals. The results of these simulations confirm our earlier analytical results that dynamical equilibrium is attained with a velocity dispersion comparable to the surface escape velocity of those planetesimals which contribute most of the system mass. In such an equilibrium, the rate of energy transfer from the systematic shear to dispersive motion, induced by gravitational scattering, is balanced by the rate of energy dissipation resulting from physical collisions. We also confirm that dynamical friction can lead to energy equipartition between an abundant population of low-mass field planetesimals and a few collisionally induced mergers with larger masses. These effects produce mass segregation in phase space and runaway coagulation. Collisions also lead to coagulation and evolution of the mass spectrum. The mergers of two field planetesimals can provide sufficient mass differential with other planetesimals for dynamical friction to induce energy equipartition and mass segregation. For small velocity dispersions, the more massive planetesimals produce relatively large gravitational focusing factors. Consequently, the growth time scale decreases with mass and runaway coagulation is initiated. Our numerical simulations show that, provided there is sufficient supply of low-mass planetesimals, runaway coagulation can lead to the formation of protoplanetary cores with masses comparable to a significant fraction of an Earth mass. We estimate that, at 1 AU, the characteristic time scale for the initial stages of planetesimal growth is ˜104 yr and ˜105 yr for the growth to protoplanetary cores. At Jupiter's present distance, these time scales are an order of magnitude longer.
NASA Technical Reports Server (NTRS)
Bement, Laurence J.; Schimmel, Morry L.
1990-01-01
To determine functional performance of initiating devices, the NASA's Langley Research Center's novel ignitability research on percussion primers has been expanded in 1989 to include measurements of function time, the evaluation of six primer lots (five types), and the determination of the effects of the military cold-temperature requirement of -65 F and primer output closure disks. This test method, a major improvement over the prior primer output test methods, fully met all objectives, while showing a significant amount of ignition variability.
Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics
Klein, R I; Stone, J M
2007-11-20
We describe numerical methods for solving the equations of radiation magnetohydrodynamics (MHD) for astrophysical fluid flow. Such methods are essential for the investigation of the time-dependent and multidimensional dynamics of a variety of astrophysical systems, although our particular interest is motivated by problems in star formation. Over the past few years, the authors have been members of two parallel code development efforts, and this review reflects that organization. In particular, we discuss numerical methods for MHD as implemented in the Athena code, and numerical methods for radiation hydrodynamics as implemented in the Orion code. We discuss the challenges introduced by the use of adaptive mesh refinement in both codes, as well as the most promising directions for future developments.
a Numerical Method for Turbulent Combustion Problems
NASA Astrophysics Data System (ADS)
Song, Yu.
This dissertation presents a random numerical method which combines a random vortex method and a random choice method. With the assumption of incompressibility, the equations governing the fluid motion can be uncoupled from the equations governing the chemical reaction. A hybrid random vortex method is used for solving Navier -Stokes equation which governs the fluid motion. Combustion process is governed by reaction-diffusion system for the conservation of energy and the various chemical species participating in reaction. A random choice method is used for the modeling reaction-diffusion equations. The random choice method is tested and the numerical solutions are compared with the results by either the other numerical methods or exact solutions, good improvement and agreement have been obtained. For physical problem in two or more space dimensions, extension of the random choice method requires splitting the source terms into an x-sweep followed by a y-sweep. The splitting of the source term is also examined for an equation with an exact solution. The combustion model is applied to the problem of combustion in a circular cylinder with cylinder heated or kept cold. The flame profiles are obtained and effect of the turbulent is observed. The method is also applied to the ignition of a Bunsen burner. The correct modeling of mixing layer at the edge of the burner is found important in this application. Flame propagation profiles are obtained and have good agreement with experiments.
A numerical method of detecting singularity
NASA Technical Reports Server (NTRS)
Laporte, M.; Vignes, J.
1978-01-01
A numerical method is reported which determines a value C for the degree of conditioning of a matrix. This value is C = 0 for a singular matrix and has progressively larger values for matrices which are increasingly well-conditioned. This value is C sub = C max sub max (C defined by the precision of the computer) when the matrix is perfectly well conditioned.
Analytical and numerical methods; advanced computer concepts
Lax, P D
1991-03-01
This past year, two projects have been completed and a new is under way. First, in joint work with R. Kohn, we developed a numerical algorithm to study the blowup of solutions to equations with certain similarity transformations. In the second project, the adaptive mesh refinement code of Berger and Colella for shock hydrodynamic calculations has been parallelized and numerical studies using two different shared memory machines have been done. My current effort is towards the development of Cartesian mesh methods to solve pdes with complicated geometries. Most of the coming year will be spent on this project, which is joint work with Prof. Randy Leveque at the University of Washington in Seattle.
EPACT II: project and methods.
Juillerat, Pascal; Froehlich, Florian; Felley, Christian; Pittet, Valérie; Mottet, Christian; Gonvers, Jean-Jacques; Michetti, Pierre; Vader, John-Paul
2007-01-01
Building on the first European Panel on the Appropriateness of Crohn's Disease Treatment (EPACT I) which was held in Lausanne at the beginning of March 2004, a new panel will be convened in Switzerland (EPACT II, November to December 2007) to update this work. A combined evidence- and panel-based method (RAND) will be applied to assess the appropriateness of therapy for Crohn's disease (CD). In preparation for the meeting of experts, reviews of evidence-based literature were prepared for major clinical presentations of CD. During the meeting, an international multidis- ciplinary panel that includes gastroenterologists, surgeons and general practitioners weigh the strength of evidence and apply their clinical experience when assessing the appropriateness of therapy for 569 specific indications (clinical scenarios). This chapter describes in detail the process of updating the literature review and the systematic approach of the RAND Appropriateness Method used during the expert panel meeting. PMID:18239398
Numerical Methods in Polarized Line Formation Theory
NASA Astrophysics Data System (ADS)
Nagendra, K. N.; Sampoorna, M.
2009-06-01
We review some numerical methods and provide benchmark solutions for the polarized line formation theory with partial redistribution (PRD) in the presence of magnetic fields. The transfer equation remains non-axisymmetric when written in the `Stokes vector basis'. It is relatively easier to develop numerical methods to solve the transfer equation for axisymmetric radiation fields. Therefore for non-axisymmetric problems it would be necessary to expand the azimuthal dependence of the scattering redistribution matrices in a Fourier series. The transfer equation in this so called `reduced form' becomes axisymmetric in the Fourier domain in which it is solved, and the reduced intensity is then transformed into the Stokes vector basis in real space. The advantage is that the reduced problem lends itself to be solved by appropriately organized PALI (Polarized Approximate Lambda Iteration) methods. We first dwell upon a frequency by frequency method (PALI7) that uses non-domain based PRD for the Hanle scattering problem, and then compare it with a core-wing method (PALI6) that uses a domain based PRD. The PALI methods use operator perturbation and involve construction of a suitable procedure to evaluate an `iterated source vector correction'. Another important component of PALI methods is the `Formal Solver' (for example Feautrier, short characteristic, DELOPAR etc.). The PALI methods are extremely fast on a computer and require very small memory. Finally, we present a simple perturbation method to solve the Hanle-Zeeman line formation problem in arbitrary strength magnetic fields.
Numerical methods: Analytical benchmarking in transport theory
Ganapol, B.D. )
1988-01-01
Numerical methods applied to reactor technology have reached a high degree of maturity. Certainly one- and two-dimensional neutron transport calculations have become routine, with several programs available on personal computer and the most widely used programs adapted to workstation and minicomputer computational environments. With the introduction of massive parallelism and as experience with multitasking increases, even more improvement in the development of transport algorithms can be expected. Benchmarking an algorithm is usually not a very pleasant experience for the code developer. Proper algorithmic verification by benchmarking involves the following considerations: (1) conservation of particles, (2) confirmation of intuitive physical behavior, and (3) reproduction of analytical benchmark results. By using today's computational advantages, new basic numerical methods have been developed that allow a wider class of benchmark problems to be considered.
Hyperbolic conservation laws and numerical methods
NASA Technical Reports Server (NTRS)
Leveque, Randall J.
1990-01-01
The mathematical structure of hyperbolic systems and the scalar equation case of conservation laws are discussed. Linear, nonlinear systems and the Riemann problem for the Euler equations are also studied. The numerical methods for conservation laws are presented in a nonstandard manner which leads to large time steps generalizations and computations on irregular grids. The solution of conservation laws with stiff source terms is examined.
Numerical methods for molecular dynamics. Progress report
Skeel, R.D.
1991-12-31
This report summarizes our research progress to date on the use of multigrid methods for three-dimensional elliptic partial differential equations, with particular emphasis on application to the Poisson-Boltzmann equation of molecular biophysics. This research is motivated by the need for fast and accurate numerical solution techniques for three-dimensional problems arising in physics and engineering. In many applications these problems must be solved repeatedly, and the extremely large number of discrete unknowns required to accurately approximate solutions to partial differential equations in three-dimensional regions necessitates the use of efficient solution methods. This situation makes clear the importance of developing methods which are of optimal order (or nearly so), meaning that the number of operations required to solve the discrete problem is on the order of the number of discrete unknowns. Multigrid methods are generally regarded as being in this class of methods, and are in fact provably optimal order for an increasingly large class of problems. The fundamental goal of this research is to develop a fast and accurate numerical technique, based on multi-level principles, for the solutions of the Poisson-Boltzmann equation of molecular biophysics and similar equations occurring in other applications. An outline of the report is as follows. We first present some background material, followed by a survey of the literature on the use of multigrid methods for solving problems similar to the Poisson-Boltzmann equation. A short description of the software we have developed so far is then given, and numerical results are discussed. Finally, our research plans for the coming year are presented.
RELAP-7 Numerical Stabilization: Entropy Viscosity Method
R. A. Berry; M. O. Delchini; J. Ragusa
2014-06-01
The RELAP-7 code is the next generation nuclear reactor system safety analysis code being developed at the Idaho National Laboratory (INL). The code is based on the INL's modern scientific software development framework, MOOSE (Multi-Physics Object Oriented Simulation Environment). The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical integration methods, and physical models. The end result will be a reactor systems analysis capability that retains and improves upon RELAP5's capability and extends the analysis capability for all reactor system simulation scenarios. RELAP-7 utilizes a single phase and a novel seven-equation two-phase flow models as described in the RELAP-7 Theory Manual (INL/EXT-14-31366). The basic equation systems are hyperbolic, which generally require some type of stabilization (or artificial viscosity) to capture nonlinear discontinuities and to suppress advection-caused oscillations. This report documents one of the available options for this stabilization in RELAP-7 -- a new and novel approach known as the entropy viscosity method. Because the code is an ongoing development effort in which the physical sub models, numerics, and coding are evolving, so too must the specific details of the entropy viscosity stabilization method. Here the fundamentals of the method in their current state are presented.
Numerical methods for engine-airframe integration
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 of 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.
Numerical analysis method for linear induction machines.
NASA Technical Reports Server (NTRS)
Elliott, D. G.
1972-01-01
A numerical analysis method has been developed for linear induction machines such as liquid metal MHD pumps and generators and linear motors. Arbitrary phase currents or voltages can be specified and the moving conductor can have arbitrary velocity and conductivity variations from point to point. The moving conductor is divided into a mesh and coefficients are calculated for the voltage induced at each mesh point by unit current at every other mesh point. Combining the coefficients with the mesh resistances yields a set of simultaneous equations which are solved for the unknown currents.
Numerical methods for finding stationary gravitational solutions
NASA Astrophysics Data System (ADS)
Dias, Óscar J. C.; Santos, Jorge E.; Way, Benson
2016-07-01
The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical foundations and give a practical guide for the numerical solution of gravitational boundary value problems. We present these methods by way of example: resolving asymptotically flat black rings, singly spinning lumpy black holes in anti-de Sitter (AdS), and the Gregory-Laflamme zero modes of small rotating black holes in AdS{}5× {S}5. We also include several tools and tricks that have been useful throughout the literature.
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.
Preliminary numerical study of Thailand Plasma Focus II (TPF-II) design
NASA Astrophysics Data System (ADS)
Tamman, Arlee; Nisoa, Mudtorlep; Onjun, Thawatchai
2014-08-01
In this work, we use the Lee model to predict the plasma parameters, such as plasma temperature and pinch duration, in the 3.37 kJ DPF device, called “Thailand Plasma Focus-II (TPF-II).” This numerical result is then used to optimize the electrode parameters for the maximum production rate of 18F. The crossing point of pinch duration and pinch temperature is considered to obtain the appropriate electrode length, anode radius and gas gap between anode and cathode. The gas gap between both electrodes is indicated in ratio between cathode radius and anode radius, c. The results show that the best values of c, anode radius and electrode length are 1.48, 1.2 cm and 26.1 cm, respectively, in which the plasma pinch temperature, peak current and pinch duration of 0.76 keV, 207 kA and 8.725 ns can be obtained.
Numerical methods for problems in computational aeroacoustics
NASA Astrophysics Data System (ADS)
Mead, Jodi Lorraine
1998-12-01
A goal of computational aeroacoustics is the accurate calculation of noise from a jet in the far field. This work concerns the numerical aspects of accurately calculating acoustic waves over large distances and long time. More specifically, the stability, efficiency, accuracy, dispersion and dissipation in spatial discretizations, time stepping schemes, and absorbing boundaries for the direct solution of wave propagation problems are determined. Efficient finite difference methods developed by Tam and Webb, which minimize dispersion and dissipation, are commonly used for the spatial and temporal discretization. Alternatively, high order pseudospectral methods can be made more efficient by using the grid transformation introduced by Kosloff and Tal-Ezer. Work in this dissertation confirms that the grid transformation introduced by Kosloff and Tal-Ezer is not spectrally accurate because, in the limit, the grid transformation forces zero derivatives at the boundaries. If a small number of grid points are used, it is shown that approximations with the Chebyshev pseudospectral method with the Kosloff and Tal-Ezer grid transformation are as accurate as with the Chebyshev pseudospectral method. This result is based on the analysis of the phase and amplitude errors of these methods, and their use for the solution of a benchmark problem in computational aeroacoustics. For the grid transformed Chebyshev method with a small number of grid points it is, however, more appropriate to compare its accuracy with that of high- order finite difference methods. This comparison, for an order of accuracy 10-3 for a benchmark problem in computational aeroacoustics, is performed for the grid transformed Chebyshev method and the fourth order finite difference method of Tam. Solutions with the finite difference method are as accurate. and the finite difference method is more efficient than, the Chebyshev pseudospectral method with the grid transformation. The efficiency of the Chebyshev
Numerical manifold method based on the method of weighted residuals
NASA Astrophysics Data System (ADS)
Li, S.; Cheng, Y.; Wu, Y.-F.
2005-05-01
Usually, the governing equations of the numerical manifold method (NMM) are derived from the minimum potential energy principle. For many applied problems it is difficult to derive in general outset the functional forms of the governing equations. This obviously strongly restricts the implementation of the minimum potential energy principle or other variational principles in NMM. In fact, the governing equations of NMM can be derived from a more general method of weighted residuals. By choosing suitable weight functions, the derivation of the governing equations of the NMM from the weighted residual method leads to the same result as that derived from the minimum potential energy principle. This is demonstrated in the paper by deriving the governing equations of the NMM for linear elasticity problems, and also for Laplace's equation for which the governing equations of the NMM cannot be derived from the minimum potential energy principle. The performance of the method is illustrated by three numerical examples.
Spectral multigrid methods for elliptic equations II
NASA Technical Reports Server (NTRS)
Zang, T. A.; Wong, Y. S.; Hussaini, M. Y.
1984-01-01
A detailed description of spectral multigrid methods is provided. This includes the interpolation and coarse-grid operators for both periodic and Dirichlet problems. The spectral methods for periodic problems use Fourier series and those for Dirichlet problems are based upon Chebyshev polynomials. An improved preconditioning for Dirichlet problems is given. Numerical examples and practical advice are included.
Numerical Relativity, Black Hole Mergers, and Gravitational Waves: Part II
NASA Technical Reports Server (NTRS)
Centrella, Joan
2012-01-01
This series of 3 lectures will present recent developments in numerical relativity, and their applications to simulating black hole mergers and computing the resulting gravitational waveforms. In this second lecture, we focus on simulations of black hole binary mergers. We hig hlight the instabilities that plagued the codes for many years, the r ecent breakthroughs that led to the first accurate simulations, and the current state of the art.
Numerical matrix method for quantum periodic potentials
NASA Astrophysics Data System (ADS)
Le Vot, Felipe; Meléndez, Juan J.; Yuste, Santos B.
2016-06-01
A numerical matrix methodology is applied to quantum problems with periodic potentials. The procedure consists essentially in replacing the true potential by an alternative one, restricted by an infinite square well, and in expressing the wave functions as finite superpositions of eigenfunctions of the infinite well. A matrix eigenvalue equation then yields the energy levels of the periodic potential within an acceptable accuracy. The methodology has been successfully used to deal with problems based on the well-known Kronig-Penney (KP) model. Besides the original model, these problems are a dimerized KP solid, a KP solid containing a surface, and a KP solid under an external field. A short list of additional problems that can be solved with this procedure is presented.
Numerical methods in Markov chain modeling
NASA Technical Reports Server (NTRS)
Philippe, Bernard; Saad, Youcef; Stewart, William J.
1989-01-01
Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.
Interpolation Method Needed for Numerical Uncertainty
NASA Technical Reports Server (NTRS)
Groves, Curtis E.; Ilie, Marcel; Schallhorn, Paul A.
2014-01-01
Using Computational Fluid Dynamics (CFD) to predict a flow field is an approximation to the exact problem and uncertainties exist. There is a method to approximate the errors in CFD via Richardson's Extrapolation. This method is based off of progressive grid refinement. To estimate the errors, the analyst must interpolate between at least three grids. This paper describes a study to find an appropriate interpolation scheme that can be used in Richardson's extrapolation or other uncertainty method to approximate errors.
Numerical analysis of the orthogonal descent method
Shokov, V.A.; Shchepakin, M.B.
1994-11-01
The author of the orthogonal descent method has been testing it since 1977. The results of these tests have only strengthened the need for further analysis and development of orthogonal descent algorithms for various classes of convex programming problems. Systematic testing of orthogonal descent algorithms and comparison of test results with other nondifferentiable optimization methods was conducted at TsEMI RAN in 1991-1992 using the results.
Generalized propagation of light through optical systems. II. Numerical implications.
Tessmer, Manuel; Gross, Herbert
2015-12-01
We present an algorithm implemented in a MATLAB toolbox that is able to compute the wave propagation of coherent visible light through macroscopic lenses. The mathematical operations that complete the status at the end of the first paper of this sequence, where only limited configurations of the propagation direction were allowed toward arbitrarily directed input beam computations, are provided. With their help, high numerical aperture (NA) field tracing is made possible that is based on fast Fourier routines and is Maxwell exact in the limit of macroscopic structures and large curvature radii, including reflection and transmission. Whereas the curvature-dependent terms in the Helmholtz equation are under analytical control through the first perturbation order in the curvature, they are only included in the propagation distance in the current investigation for the sake of reasonable time consumption. We give a number of examples that demonstrate the strengths of our approach, describe essential differences from other approaches that were not obvious when Paper 1 was written, and list a number of drawbacks and possible simplifications to overcome them.
Generalized propagation of light through optical systems. II. Numerical implications.
Tessmer, Manuel; Gross, Herbert
2015-12-01
We present an algorithm implemented in a MATLAB toolbox that is able to compute the wave propagation of coherent visible light through macroscopic lenses. The mathematical operations that complete the status at the end of the first paper of this sequence, where only limited configurations of the propagation direction were allowed toward arbitrarily directed input beam computations, are provided. With their help, high numerical aperture (NA) field tracing is made possible that is based on fast Fourier routines and is Maxwell exact in the limit of macroscopic structures and large curvature radii, including reflection and transmission. Whereas the curvature-dependent terms in the Helmholtz equation are under analytical control through the first perturbation order in the curvature, they are only included in the propagation distance in the current investigation for the sake of reasonable time consumption. We give a number of examples that demonstrate the strengths of our approach, describe essential differences from other approaches that were not obvious when Paper 1 was written, and list a number of drawbacks and possible simplifications to overcome them. PMID:26831382
Numerical simulation of the boat growth method
NASA Astrophysics Data System (ADS)
Oda, K.; Saito, T.; Nishihama, J.; Ishihara, T.
1989-09-01
This paper presents a three-dimensional mathematical model for thermal convection in molten metals, which is applicable to the heat transfer phenomena in a boat-shaped crucibles. The governing equations are solved using an extended version, developed by Saito et al. (1986), of the Amsden and Harlow (1968) simplified marker and cell method. It is shown that the following parameters must be incorporated for an accurate simulation of melt growth: (1) the radiative heat transfer in the furnace, (2) the complex crucible configuration, (3) the melt flow, and (4) the solid-liquid interface shape. The velocity and temperature distribution calculated from this model are compared with the results of previous studies.
Flight test and numerical simulation of transonic flow around YAV-8B Harrier II wing
NASA Technical Reports Server (NTRS)
Gea, Lie-Mine; Chyu, Wei J.; Stortz, Michael W.; Roberts, Andrew C.; Chow, Chuen-Yen
1991-01-01
A computational fluid dynamics (CFD) method is used to study the aerodynamics of the YAV-8B Harrier II wing in the transonic region. A numerical procedure is developed to compute the flow field around the complicated wing-pylon-fairing geometry. The surface definition of the wing and pylons were obtained from direct measurement using theodolite triangulation. A thin-layer Navier-Stokes code with the Chimera technique is used to compute flow solutions. The computed pressure distributions at several span stations are compared with flight test data and show good agreement. Computed results are correlated with flight test data that show the flow is severely separated in the vicinity of the wing-pylon junction. Analysis shows that shock waves are induced by pylon swaybrace fairings, that the flow separation is much stronger at the outboard pylon and that the separation is caused mainly by the crossflow passing the geometry of wing-pylon junction.
Coordinated Optimization of Visual Cortical Maps (II) Numerical Studies
Reichl, Lars; Heide, Dominik; Löwel, Siegrid; Crowley, Justin C.; Kaschube, Matthias; Wolf, Fred
2012-01-01
In the juvenile brain, the synaptic architecture of the visual cortex remains in a state of flux for months after the natural onset of vision and the initial emergence of feature selectivity in visual cortical neurons. It is an attractive hypothesis that visual cortical architecture is shaped during this extended period of juvenile plasticity by the coordinated optimization of multiple visual cortical maps such as orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we introduced a class of analytically tractable coordinated optimization models and solved representative examples, in which a spatially complex organization of the OP map is induced by interactions between the maps. We found that these solutions near symmetry breaking threshold predict a highly ordered map layout. Here we examine the time course of the convergence towards attractor states and optima of these models. In particular, we determine the timescales on which map optimization takes place and how these timescales can be compared to those of visual cortical development and plasticity. We also assess whether our models exhibit biologically more realistic, spatially irregular solutions at a finite distance from threshold, when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. We show that, although maps typically undergo substantial rearrangement, no other solutions than pinwheel crystals and stripes dominate in the emerging layouts. Pinwheel crystallization takes place on a rather short timescale and can also occur for detuned wavelengths of different maps. Our numerical results thus support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the architecture of the visual cortex. We discuss several alternative scenarios that may improve the agreement between model solutions and biological
Numerical methods for analyzing electromagnetic scattering
NASA Technical Reports Server (NTRS)
Lee, S. W.; Lo, Y. T.; Chuang, S. L.; Lee, C. S.
1985-01-01
Attenuation properties of the normal modes in an overmoded waveguide coated with a lossy material were analyzed. It is found that the low-order modes, can be significantly attenuated even with a thin layer of coating if the coating material is not too lossy. A thinner layer of coating is required for large attenuation of the low-order modes if the coating material is magnetic rather than dielectric. The Radar Cross Section (RCS) from an uncoated circular guide terminated by a perfect electric conductor was calculated and compared with available experimental data. It is confirmed that the interior irradiation contributes to the RCS. The equivalent-current method based on the geometrical theory of diffraction (GTD) was chosen for the calculation of the contribution from the rim diffraction. The RCS reduction from a coated circular guide terminated by a PEC are planned schemes for the experiments are included. The waveguide coated with a lossy magnetic material is suggested as a substitute for the corrugated waveguide.
Methods for preparation of cyclopentadienyliron (II) arenes
Keipert, Steven J.
1991-01-01
Two improved methods for preparation of compounds with the structure shown in equation X [(Cp)--Fe--(Ar)].sup.+.sub.b X.sup.b- (X) where Cp is an eta.sup.5 complexed, substituted or unsubstituted, cyclopentadienyl or indenyl anion, Ar is an eta.sup.6 complexed substituted or unsubstituted, pi-arene ligand anad X is a b-valent anion where b is an integer between 1 and 3. The two methods, which differ in the source of the cyclopentadienyl anion - Lewis acid complex, utilize a Lewis acid assisted ligand transfer reaction. The cyclopentadienyl anion ligand, assisted by a Lewis acid is transferred to ferrous ion in the presence of an arene. In the first method, the cyclopentadienyl anion is derived from ferrocene and ferrous chloride. In this reaction, the cyclopentadienyliron (II) arene product is derived partially from ferrocene and partially from the ferrous salt. In the second method, the cyclopentadienyl anion - Lewis acid complex is formed by direct reaction of the Lewis acid with an inorganic cyclopentadienide salt. The cyclopentadienyliron (II) arene product of this reaction is derived entirely from the ferrous salt. Cyclopentadienyliron (II) arene cations are of great interest due to their utility as photoactivatable catalysts for a variety of polymerization reactions.
Numerical Weather Predictions Evaluation Using Spatial Verification Methods
NASA Astrophysics Data System (ADS)
Tegoulias, I.; Pytharoulis, I.; Kotsopoulos, S.; Kartsios, S.; Bampzelis, D.; Karacostas, T.
2014-12-01
During the last years high-resolution numerical weather prediction simulations have been used to examine meteorological events with increased convective activity. Traditional verification methods do not provide the desired level of information to evaluate those high-resolution simulations. To assess those limitations new spatial verification methods have been proposed. In the present study an attempt is made to estimate the ability of the WRF model (WRF -ARW ver3.5.1) to reproduce selected days with high convective activity during the year 2010 using those feature-based verification methods. Three model domains, covering Europe, the Mediterranean Sea and northern Africa (d01), the wider area of Greece (d02) and central Greece - Thessaly region (d03) are used at horizontal grid-spacings of 15km, 5km and 1km respectively. By alternating microphysics (Ferrier, WSM6, Goddard), boundary layer (YSU, MYJ) and cumulus convection (Kain--Fritsch, BMJ) schemes, a set of twelve model setups is obtained. The results of those simulations are evaluated against data obtained using a C-Band (5cm) radar located at the centre of the innermost domain. Spatial characteristics are well captured but with a variable time lag between simulation results and radar data. Acknowledgements: This research is cofinanced by the European Union (European Regional Development Fund) and Greek national funds, through the action "COOPERATION 2011: Partnerships of Production and Research Institutions in Focused Research and Technology Sectors" (contract number 11SYN_8_1088 - DAPHNE) in the framework of the operational programme "Competitiveness and Entrepreneurship" and Regions in Transition (OPC II, NSRF 2007--2013).
NASA Astrophysics Data System (ADS)
Tremblin, P.; Minier, V.; Schneider, N.; Audit, E.; Hill, T.; Didelon, P.; Peretto, N.; Arzoumanian, D.; Motte, F.; Zavagno, A.; Bontemps, S.; Anderson, L. D.; André, Ph.; Bernard, J. P.; Csengeri, T.; Di Francesco, J.; Elia, D.; Hennemann, M.; Könyves, V.; Marston, A. P.; Nguyen Luong, Q.; Rivera-Ingraham, A.; Roussel, H.; Sousbie, T.; Spinoglio, L.; White, G. J.; Williams, J.
2013-12-01
Context. Herschel far-infrared imaging observations have revealed the density structure of the interface between H ii regions and molecular clouds in great detail. In particular, pillars and globules are present in many high-mass star-forming regions, such as the Eagle nebula (M 16) and the Rosette molecular cloud, and understanding their origin will help characterize triggered star formation. Aims: The formation mechanisms of these structures are still being debated. The initial morphology of the molecular cloud and its turbulent state are key parameters since they generate deformations and curvatures of the shell during the expansion of the H ii region. Recent numerical simulations have shown how pillars can arise from the collapse of the shell in on itself and how globules can be formed from the interplay of the turbulent molecular cloud and the ionization from massive stars. The goal here is to test this scenario through recent observations of two massive star-forming regions, M 16 and the Rosette molecular cloud. Methods: First, the column density structure of the interface between molecular clouds and associated H ii regions was characterized using column density maps obtained from far-infrared imaging of the Herschel HOBYS key programme. Then, the DisPerSe algorithm was used on these maps to detect the compressed layers around the ionized gas and pillars in different evolutionary states. Column density profiles were constructed. Finally, their velocity structure was investigated using CO data, and all observational signatures were tested against some distinct diagnostics established from simulations. Results: The column density profiles have revealed the importance of compression at the edge of the ionized gas. The velocity properties of the structures, i.e. pillars and globules, are very close to what we predict from the numerical simulations. We have identified a good candidate of a nascent pillar in the Rosette molecular cloud that presents the velocity
Numerical solution of integral-algebraic equations for multistep methods
NASA Astrophysics Data System (ADS)
Budnikova, O. S.; Bulatov, M. V.
2012-05-01
Systems of Volterra linear integral equations with identically singular matrices in the principal part (called integral-algebraic equations) are examined. Multistep methods for the numerical solution of a selected class of such systems are proposed and justified.
Asymptotic-induced numerical methods for conservation laws
NASA Technical Reports Server (NTRS)
Garbey, Marc; Scroggs, Jeffrey S.
1990-01-01
Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.
EFFECTS OF DIFFERENT NUMERICAL INTERFACE METHODS ON HYDRODYNAMICS INSTABILITY
FRANCOIS, MARIANNE M.; DENDY, EDWARD D.; LOWRIE, ROBERT B.; LIVESCU, DANIEL; STEINKAMP, MICHAEL J.
2007-01-11
The authors compare the effects of different numerical schemes for the advection and material interface treatments on the single-mode Rayleigh-Taylor instability, using the RAGE hydro-code. The interface growth and its surface density (interfacial area) versus time are investigated. The surface density metric shows to be better suited to characterize the difference in the flow, than the conventional interface growth metric. They have found that Van Leer's limiter combined to no interface treatment leads to the largest surface area. Finally, to quantify the difference between the numerical methods they have estimated the numerical viscosity in the linear-regime at different scales.
Parallel processing numerical method for confined vortex dynamics and applications
NASA Astrophysics Data System (ADS)
Bistrian, Diana Alina
2013-10-01
This paper explores a combined analytical and numerical technique to investigate the hydrodynamic instability of confined swirling flows, with application to vortex rope dynamics in a Francis turbine diffuser, in condition of sophisticated boundary constraints. We present a new approach based on the method of orthogonal decomposition in the Hilbert space, implemented with a spectral descriptor scheme in discrete space. A parallel implementation of the numerical scheme is conducted reducing the computational time compared to other techniques.
Numeric Modified Adomian Decomposition Method for Power System Simulations
Dimitrovski, Aleksandar D; Simunovic, Srdjan; Pannala, Sreekanth
2016-01-01
This paper investigates the applicability of numeric Wazwaz El Sayed modified Adomian Decomposition Method (WES-ADM) for time domain simulation of power systems. WESADM is a numerical method based on a modified Adomian decomposition (ADM) technique. WES-ADM is a numerical approximation method for the solution of nonlinear ordinary differential equations. The non-linear terms in the differential equations are approximated using Adomian polynomials. In this paper WES-ADM is applied to time domain simulations of multimachine power systems. WECC 3-generator, 9-bus system and IEEE 10-generator, 39-bus system have been used to test the applicability of the approach. Several fault scenarios have been tested. It has been found that the proposed approach is faster than the trapezoidal method with comparable accuracy.
Evolving excised black holes with TVD numerical methods
NASA Astrophysics Data System (ADS)
Neilsen, David
2003-04-01
Total Variation Diminishing (TVD) numerical methods have improved stability properties for nonlinear differential equations, and are widely used in computational fluid dynamics. While Einstein's equations are not genuinely nonlinear, these methods may be advantageous for solving the Einstein equations in specific instances, such as evolving fluid spacetimes and black holes with excision. Using a Frittelli-Reula formulation of the Einstein equations, I will present results of 1-D and 3-D black hole evolutions, and compare the performance of TVD methods with other numerical approaches.
Collocation Method for Numerical Solution of Coupled Nonlinear Schroedinger Equation
Ismail, M. S.
2010-09-30
The coupled nonlinear Schroedinger equation models several interesting physical phenomena presents a model equation for optical fiber with linear birefringence. In this paper we use collocation method to solve this equation, we test this method for stability and accuracy. Numerical tests using single soliton and interaction of three solitons are used to test the resulting scheme.
A numerical method for solving singular De`s
Mahaver, W.T.
1996-12-31
A numerical method is developed for solving singular differential equations using steepest descent based on weighted Sobolev gradients. The method is demonstrated on a variety of first and second order problems, including linear constrained, unconstrained, and partially constrained first order problems, a nonlinear first order problem with irregular singularity, and two second order variational problems.
Investigating Convergence Patterns for Numerical Methods Using Data Analysis
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2013-01-01
The article investigates the patterns that arise in the convergence of numerical methods, particularly those in the errors involved in successive iterations, using data analysis and curve fitting methods. In particular, the results obtained are used to convey a deeper level of understanding of the concepts of linear, quadratic, and cubic…
25 Years of Self-organized Criticality: Numerical Detection Methods
NASA Astrophysics Data System (ADS)
McAteer, R. T. James; Aschwanden, Markus J.; Dimitropoulou, Michaila; Georgoulis, Manolis K.; Pruessner, Gunnar; Morales, Laura; Ireland, Jack; Abramenko, Valentyna
2016-01-01
The detection and characterization of self-organized criticality (SOC), in both real and simulated data, has undergone many significant revisions over the past 25 years. The explosive advances in the many numerical methods available for detecting, discriminating, and ultimately testing, SOC have played a critical role in developing our understanding of how systems experience and exhibit SOC. In this article, methods of detecting SOC are reviewed; from correlations to complexity to critical quantities. A description of the basic autocorrelation method leads into a detailed analysis of application-oriented methods developed in the last 25 years. In the second half of this manuscript space-based, time-based and spatial-temporal methods are reviewed and the prevalence of power laws in nature is described, with an emphasis on event detection and characterization. The search for numerical methods to clearly and unambiguously detect SOC in data often leads us outside the comfort zone of our own disciplines—the answers to these questions are often obtained by studying the advances made in other fields of study. In addition, numerical detection methods often provide the optimum link between simulations and experiments in scientific research. We seek to explore this boundary where the rubber meets the road, to review this expanding field of research of numerical detection of SOC systems over the past 25 years, and to iterate forwards so as to provide some foresight and guidance into developing breakthroughs in this subject over the next quarter of a century.
Comparison of methods for numerical calculation of continuum damping
Bowden, G. W.; Hole, M. J.; Dennis, G. R.; Könies, A.; Gorelenkov, N. N.
2014-05-15
Continuum resonance damping is an important factor in determining the stability of certain global modes in fusion plasmas. A number of analytic and numerical approaches have been developed to compute this damping, particularly, in the case of the toroidicity-induced shear Alfvén eigenmode. This paper compares results obtained using an analytical perturbative approach with those found using resistive and complex contour numerical approaches. It is found that the perturbative method does not provide accurate agreement with reliable numerical methods for the range of parameters examined. This discrepancy exists even in the limit where damping approaches zero. When the perturbative technique is implemented using a standard finite element method, the damping estimate fails to converge with radial grid resolution. The finite elements used cannot accurately represent the eigenmode in the region of the continuum resonance, regardless of the number of radial grid points used.
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.
NASA Technical Reports Server (NTRS)
Duque, Earl P. N.; Johnson, Wayne; vanDam, C. P.; Chao, David D.; Cortes, Regina; Yee, Karen
1999-01-01
Accurate, reliable and robust numerical predictions of wind turbine rotor power remain a challenge to the wind energy industry. The literature reports various methods that compare predictions to experiments. The methods vary from Blade Element Momentum Theory (BEM), Vortex Lattice (VL), to variants of Reynolds-averaged Navier-Stokes (RaNS). The BEM and VL methods consistently show discrepancies in predicting rotor power at higher wind speeds mainly due to inadequacies with inboard stall and stall delay models. The RaNS methodologies show promise in predicting blade stall. However, inaccurate rotor vortex wake convection, boundary layer turbulence modeling and grid resolution has limited their accuracy. In addition, the inherently unsteady stalled flow conditions become computationally expensive for even the best endowed research labs. Although numerical power predictions have been compared to experiment. The availability of good wind turbine data sufficient for code validation experimental data that has been extracted from the IEA Annex XIV download site for the NREL Combined Experiment phase II and phase IV rotor. In addition, the comparisons will show data that has been further reduced into steady wind and zero yaw conditions suitable for comparisons to "steady wind" rotor power predictions. In summary, the paper will present and discuss the capabilities and limitations of the three numerical methods and make available a database of experimental data suitable to help other numerical methods practitioners validate their own work.
Prandtl's Equations: Numerical Results about Singularity Formation and a New Numerical Method
NASA Astrophysics Data System (ADS)
Puppo, Gabriella
1990-01-01
In this work, new numerical results about singularity formation for unsteady Prandtl's equations are presented. Extensive computations with a Lax Wendroff scheme for the impulsively started circular cylinder show that the gradient of the velocity becomes infinite in a finite time. The accuracy and the simplicity of the Lax Wendroff scheme allow us to couple the resolution given by second order accuracy in space with the detail of an extremely fine grid. Thus, while these computations confirm previous results about singularity formation (Van Dommelen and Shen, Cebeci, Wang), they differ in other respects. In fact the peak in the velocity gradient appears to be located upstream of the region of reversed flow and away from the zero vorticity line. Some analytic arguments are also presented to support these conclusions, independently of the computations. In the second part of this work another new numerical method to solve the unsteady Prandtl equations is proposed. This numerical scheme derives from Chorin's Vortex Sheet method. The equations are also solved with operator splitting, but, unlike Chorin's, this scheme is deterministic. This feature is achieved using a Lagrangian particle formulation for the convective step and solving the diffusion step with finite differences on an Eulerian mesh. Finally, a numerical convergence proof is presented.
Numerical Methods of Computational Electromagnetics for Complex Inhomogeneous Systems
Cai, Wei
2014-05-15
Understanding electromagnetic phenomena is the key in many scientific investigation and engineering designs such as solar cell designs, studying biological ion channels for diseases, and creating clean fusion energies, among other things. The objectives of the project are to develop high order numerical methods to simulate evanescent electromagnetic waves occurring in plasmon solar cells and biological ion-channels, where local field enhancement within random media in the former and long range electrostatic interactions in the latter are of major challenges for accurate and efficient numerical computations. We have accomplished these objectives by developing high order numerical methods for solving Maxwell equations such as high order finite element basis for discontinuous Galerkin methods, well-conditioned Nedelec edge element method, divergence free finite element basis for MHD, and fast integral equation methods for layered media. These methods can be used to model the complex local field enhancement in plasmon solar cells. On the other hand, to treat long range electrostatic interaction in ion channels, we have developed image charge based method for a hybrid model in combining atomistic electrostatics and continuum Poisson-Boltzmann electrostatics. Such a hybrid model will speed up the molecular dynamics simulation of transport in biological ion-channels.
COMPARING NUMERICAL METHODS FOR ISOTHERMAL MAGNETIZED SUPERSONIC TURBULENCE
Kritsuk, Alexei G.; Collins, David; Norman, Michael L.; Xu Hao E-mail: dccollins@lanl.gov
2011-08-10
Many astrophysical applications involve magnetized turbulent flows with shock waves. Ab initio star formation simulations require a robust representation of supersonic turbulence in molecular clouds on a wide range of scales imposing stringent demands on the quality of numerical algorithms. We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine popular astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. These applications employ a variety of numerical approaches, including both split and unsplit, finite difference and finite volume, divergence preserving and divergence cleaning, a variety of Riemann solvers, and a range of spatial reconstruction and time integration techniques. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss the convergence of various characteristics for the turbulence decay test and the impact of various components of numerical schemes on the accuracy of solutions. The nine codes gave qualitatively the same results, implying that they are all performing reasonably well and are useful for scientific applications. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the
Numerical methods for aerothermodynamic design of hypersonic space transport vehicles
NASA Astrophysics Data System (ADS)
Wanie, K. M.; Brenneis, A.; Eberle, A.; Heiss, S.
1993-04-01
The requirement of the design process of hypersonic vehicles to predict flow past entire configurations with wings, fins, flaps, and propulsion system represents one of the major challenges for aerothermodynamics. In this context computational fluid dynamics has come up as a powerful tool to support the experimental work. A couple of numerical methods developed at MBB designed to fulfill the needs of the design process are described. The governing equations and fundamental details of the solution methods are shortly reviewed. Results are given for both geometrically simple test cases and realistic hypersonic configurations. Since there is still a considerable lack of experience for hypersonic flow calculations an extensive testing and verification is essential. This verification is done by comparison of results with experimental data and other numerical methods. The results presented prove that the methods used are robust, flexible, and accurate enough to fulfill the strong needs of the design process.
A general numerical method to solve for dislocation configurations
NASA Astrophysics Data System (ADS)
Xin, X. J.; Wagoner, R. H.; Daehn, G. S.
1999-08-01
The shape of a mechanically equilibrated dislocation line is of considerable interest in the study of plastic deformation of metals and alloys. A general numerical method for finding such configurations in arbitrary stress fields has been developed. Analogous to the finite-element method (FEM), a general dislocation line is approximated by a series of straight segments (elements) bounded by nodes. The equilibrium configuration is found by minimizing the system energy with respect to nodal positions using a Newton-Raphson procedure. This approach, termed the finite-segment method (FSM), confers several advantages relative to segment-based, explicit formulations. The utility, generality, and robustness of the FSM is demonstrated by analyzing the Orowan bypass mechanism and a model of dislocation generation and equilibration at misfitting particles. Energy differences from previous analytical methods based on simple loop shapes are significant, up to 80 pct. Explicit expressions for the coordinate transformations, energies, and forces required for numerical implementation are presented.
Numerical methods in vehicle system dynamics: state of the art and current developments
NASA Astrophysics Data System (ADS)
Arnold, M.; Burgermeister, B.; Führer, C.; Hippmann, G.; Rill, G.
2011-07-01
introduced and illustrated by a well-known benchmark problem from rail vehicle simulation. Over the last few decades, the complexity of high-end applications in vehicle system dynamics has frequently given a fresh impetus for substantial improvements of numerical methods and for the development of novel methods for new problem classes. In the present paper, we address three of these challenging problems of current interest that are today still beyond the mainstream of numerical mathematics: (i) modelling and simulation of contact problems in multibody dynamics, (ii) real-time capable numerical simulation techniques in vehicle system dynamics and (iii) modelling and time integration of multidisciplinary problems in system dynamics including co-simulation techniques.
A novel numerical method for radiation exchange in granular medium
NASA Astrophysics Data System (ADS)
Dayal, Ram; Gambaryan-Roisman, Tatiana
2016-11-01
A very simple numerical method is developed to determine the inter-particle radiation heat transfer in a granular powder bed. The method is completely independent of coordinate system and does not require any domain discretization. The solution procedure does not involve any matrix inversion, thus making it suitable candidate for radiation heat transfer problems involving large number of interacting surfaces, especially granular powder beds.
Comparison of Two Numerical Methods for Computing Fractal Dimensions
NASA Astrophysics Data System (ADS)
Shiozawa, Yui; Miller, Bruce; Rouet, Jean-Louis
2012-10-01
From cosmology to economics, the examples of fractals can be found virtually everywhere. However, since few fractals permit the analytical evaluation of generalized fractal dimensions or R'enyi dimensions, the search for effective numerical methods is inevitable. In this project two promising numerical methods for obtaining generalized fractal dimensions, based on the distribution of distances within a set, are examined. They can be applied, in principle, to any set even if no closed-form expression is available. The biggest advantage of these methods is their ability to generate a spectrum of generalized dimensions almost simultaneously. It should be noted that this feature is essential to the analysis of multifractals. As a test of their effectiveness, here the methods were applied to the generalized Cantor set and the multiplicative binomial process. The generalized dimensions of both sets can be readily derived analytically, thus enabling the accuracy of the numerical methods to be verified. Here we will present a comparison of the analytical results and the predictions of the methods. We will show that, while they are effective, care must be taken in their interpretation.
Singularity Preserving Numerical Methods for Boundary Integral Equations
NASA Technical Reports Server (NTRS)
Kaneko, Hideaki (Principal Investigator)
1996-01-01
In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.
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.
Numerical Polynomial Homotopy Continuation Method and String Vacua
Mehta, Dhagash
2011-01-01
Finding vmore » acua for the four-dimensional effective theories for supergravity which descend from flux compactifications and analyzing them according to their stability is one of the central problems in string phenomenology. Except for some simple toy models, it is, however, difficult to find all the vacua analytically. Recently developed algorithmic methods based on symbolic computer algebra can be of great help in the more realistic models. However, they suffer from serious algorithmic complexities and are limited to small system sizes. In this paper, we review a numerical method called the numerical polynomial homotopy continuation (NPHC) method, first used in the areas of lattice field theories, which by construction finds all of the vacua of a given potential that is known to have only isolated solutions. The NPHC method is known to suffer from no major algorithmic complexities and is embarrassingly parallelizable , and hence its applicability goes way beyond the existing symbolic methods. We first solve a simple toy model as a warm-up example to demonstrate the NPHC method at work. We then show that all the vacua of a more complicated model of a compactified M theory model, which has an S U ( 3 ) structure, can be obtained by using a desktop machine in just about an hour, a feat which was reported to be prohibitively difficult by the existing symbolic methods. Finally, we compare the various technicalities between the two methods.« less
Numerical analysis of Weyl's method for integrating boundary layer equations
NASA Technical Reports Server (NTRS)
Najfeld, I.
1982-01-01
A fast method for accurate numerical integration of Blasius equation is proposed. It is based on the limit interchange in Weyl's fixed point method formulated as an iterated limit process. Each inner limit represents convergence to a discrete solution. It is shown that the error in a discrete solution admits asymptotic expansion in even powers of step size. An extrapolation process is set up to operate on a sequence of discrete solutions to reach the outer limit. Finally, this method is extended to related boundary layer equations.
Computational methods for aerodynamic design using numerical optimization
NASA Technical Reports Server (NTRS)
Peeters, M. F.
1983-01-01
Five methods to increase the computational efficiency of aerodynamic design using numerical optimization, by reducing the computer time required to perform gradient calculations, are examined. The most promising method consists of drastically reducing the size of the computational domain on which aerodynamic calculations are made during gradient calculations. Since a gradient calculation requires the solution of the flow about an airfoil whose geometry was slightly perturbed from a base airfoil, the flow about the base airfoil is used to determine boundary conditions on the reduced computational domain. This method worked well in subcritical flow.
Projected discrete ordinates methods for numerical transport problems
Larsen, E.W.
1985-01-01
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.
Fast and stable numerical method for neuronal modelling
NASA Astrophysics Data System (ADS)
Hashemi, Soheil; Abdolali, Ali
2016-11-01
Excitable cell modelling is of a prime interest in predicting and targeting neural activity. Two main limits in solving related equations are speed and stability of numerical method. Since there is a tradeoff between accuracy and speed, most previously presented methods for solving partial differential equations (PDE) are focused on one side. More speed means more accurate simulations and therefore better device designing. By considering the variables in finite differenced equation in proper time and calculating the unknowns in the specific sequence, a fast, stable and accurate method is introduced in this paper for solving neural partial differential equations. Propagation of action potential in giant axon is studied by proposed method and traditional methods. Speed, consistency and stability of the methods are compared and discussed. The proposed method is as fast as forward methods and as stable as backward methods. Forward methods are known as fastest methods and backward methods are stable in any circumstances. Complex structures can be simulated by proposed method due to speed and stability of the method.
Efficient and accurate numerical methods for the Klein-Gordon-Schroedinger equations
Bao, Weizhu . E-mail: bao@math.nus.edu.sg; Yang, Li . E-mail: yangli@nus.edu.sg
2007-08-10
In this paper, we present efficient, unconditionally stable and accurate numerical methods for approximations of the Klein-Gordon-Schroedinger (KGS) equations with/without damping terms. The key features of our methods are based on: (i) the application of a time-splitting spectral discretization for a Schroedinger-type equation in KGS (ii) the utilization of Fourier pseudospectral discretization for spatial derivatives in the Klein-Gordon equation in KGS (iii) the adoption of solving the ordinary differential equations (ODEs) in phase space analytically under appropriate chosen transmission conditions between different time intervals or applying Crank-Nicolson/leap-frog for linear/nonlinear terms for time derivatives. The numerical methods are either explicit or implicit but can be solved explicitly, unconditionally stable, and of spectral accuracy in space and second-order accuracy in time. Moreover, they are time reversible and time transverse invariant when there is no damping terms in KGS, conserve (or keep the same decay rate of) the wave energy as that in KGS without (or with a linear) damping term, keep the same dynamics of the mean value of the meson field, and give exact results for the plane-wave solution. Extensive numerical tests are presented to confirm the above properties of our numerical methods for KGS. Finally, the methods are applied to study solitary-wave collisions in one dimension (1D), as well as dynamics of a 2D problem in KGS.
Numerical simulation of boundary layers. Part 1: Weak formulation and numerical method
NASA Technical Reports Server (NTRS)
Spalart, P. R.
1986-01-01
A numerical method designed to solve the time-dependent, three-dimensional, incompressible Navier-Stokes equations in boundary layers is presented. The fluid domain is the half-space over a flat plate, and periodic conditions are applied in the horizontal directions. The discretization is spectral. The basis functions are divergence-free and a weak formulation of the momentum equation is used, which eliminates the pressure term. An exponential mapping and Jacobi polynomials are used in the semi-infinite direction, with the irrotational component receiving special treatment. Issues related to the accuracy, stability and efficiency of the method are discussed. Very fast convergence is demonstrated on some model problems with smooth solutions. The method has also been shown to accurately resolve the fine scales of transitional and turbulent boundary layers.
Fast numerical treatment of nonlinear wave equations by spectral methods
Skjaeraasen, Olaf; Robinson, P. A.; Newman, D. L.
2011-02-15
A method is presented that accelerates spectral methods for numerical solution of a broad class of nonlinear partial differential wave equations that are first order in time and that arise in plasma wave theory. The approach involves exact analytical treatment of the linear part of the wave evolution including growth and damping as well as dispersion. After introducing the method for general scalar and vector equations, we discuss and illustrate it in more detail in the context of the coupling of high- and low-frequency plasma wave modes, as modeled by the electrostatic and electromagnetic Zakharov equations in multiple dimensions. For computational efficiency, the method uses eigenvector decomposition, which is particularly advantageous when the wave damping is mode-dependent and anisotropic in wavenumber space. In this context, it is shown that the method can significantly speed up numerical integration relative to standard spectral or finite difference methods by allowing much longer time steps, especially in the limit in which the nonlinear Schroedinger equation applies.
Numerical Continuation Methods for Intrusive Uncertainty Quantification Studies
Safta, Cosmin; Najm, Habib N.; Phipps, Eric Todd
2014-09-01
Rigorous modeling of engineering systems relies on efficient propagation of uncertainty from input parameters to model outputs. In recent years, there has been substantial development of probabilistic polynomial chaos (PC) Uncertainty Quantification (UQ) methods, enabling studies in expensive computational models. One approach, termed ”intrusive”, involving reformulation of the governing equations, has been found to have superior computational performance compared to non-intrusive sampling-based methods in relevant large-scale problems, particularly in the context of emerging architectures. However, the utility of intrusive methods has been severely limited due to detrimental numerical instabilities associated with strong nonlinear physics. Previous methods for stabilizing these constructions tend to add unacceptably high computational costs, particularly in problems with many uncertain parameters. In order to address these challenges, we propose to adapt and improve numerical continuation methods for the robust time integration of intrusive PC system dynamics. We propose adaptive methods, starting with a small uncertainty for which the model has stable behavior and gradually moving to larger uncertainty where the instabilities are rampant, in a manner that provides a suitable solution.
Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus
NASA Astrophysics Data System (ADS)
Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.
2015-05-01
We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.
Integrated numerical methods for hypersonic aircraft cooling systems analysis
NASA Technical Reports Server (NTRS)
Petley, Dennis H.; Jones, Stuart C.; Dziedzic, William M.
1992-01-01
Numerical methods have been developed for the analysis of hypersonic aircraft cooling systems. A general purpose finite difference thermal analysis code is used to determine areas which must be cooled. Complex cooling networks of series and parallel flow can be analyzed using a finite difference computer program. Both internal fluid flow and heat transfer are analyzed, because increased heat flow causes a decrease in the flow of the coolant. The steady state solution is a successive point iterative method. The transient analysis uses implicit forward-backward differencing. Several examples of the use of the program in studies of hypersonic aircraft and rockets are provided.
Numerical simulation of thermal discharge based on FVM method
NASA Astrophysics Data System (ADS)
Yu, Yunli; Wang, Deguan; Wang, Zhigang; Lai, Xijun
2006-01-01
A two-dimensional numerical model is proposed to simulate the thermal discharge from a power plant in Jiangsu Province. The equations in the model consist of two-dimensional non-steady shallow water equations and thermal waste transport equations. Finite volume method (FVM) is used to discretize the shallow water equations, and flux difference splitting (FDS) scheme is applied. The calculated area with the same temperature increment shows the effect of thermal discharge on sea water. A comparison between simulated results and the experimental data shows good agreement. It indicates that this method can give high precision in the heat transfer simulation in coastal areas.
Teaching Thermal Hydraulics & Numerical Methods: An Introductory Control Volume Primer
Lucas, D.S.
2004-10-03
This paper covers the basics of the implementation of the control volume method in the context of the Homogeneous Equilibrium Model (HEM)(T/H) code using the conservation equations of mass, momentum, and energy. This primer uses the advection equation as a template. The discussion will cover the basic equations of the control volume portion of the course in the primer, which includes the advection equation, numerical methods, along with the implementation of the various equations via FORTRAN into computer programs and the final result for a three equation HEM code and its validation.
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.
Numerical methods for the Poisson-Fermi equation in electrolytes
NASA Astrophysics Data System (ADS)
Liu, Jinn-Liang
2013-08-01
The Poisson-Fermi equation proposed by Bazant, Storey, and Kornyshev [Phys. Rev. Lett. 106 (2011) 046102] for ionic liquids is applied to and numerically studied for electrolytes and biological ion channels in three-dimensional space. This is a fourth-order nonlinear PDE that deals with both steric and correlation effects of all ions and solvent molecules involved in a model system. The Fermi distribution follows from classical lattice models of configurational entropy of finite size ions and solvent molecules and hence prevents the long and outstanding problem of unphysical divergence predicted by the Gouy-Chapman model at large potentials due to the Boltzmann distribution of point charges. The equation reduces to Poisson-Boltzmann if the correlation length vanishes. A simplified matched interface and boundary method exhibiting optimal convergence is first developed for this equation by using a gramicidin A channel model that illustrates challenging issues associated with the geometric singularities of molecular surfaces of channel proteins in realistic 3D simulations. Various numerical methods then follow to tackle a range of numerical problems concerning the fourth-order term, nonlinearity, stability, efficiency, and effectiveness. The most significant feature of the Poisson-Fermi equation, namely, its inclusion of steric and correlation effects, is demonstrated by showing good agreement with Monte Carlo simulation data for a charged wall model and an L type calcium channel model.
Numerical integration of population models satisfying conservation laws: NSFD methods.
Mickens, Ronald E
2007-10-01
Population models arising in ecology, epidemiology and mathematical biology may involve a conservation law, i.e. the total population is constant. In addition to these cases, other situations may occur for which the total population, asymptotically in time, approach a constant value. Since it is rarely the situation that the equations of motion can be analytically solved to obtain exact solutions, it follows that numerical techniques are needed to provide solutions. However, numerical procedures are only valid if they can reproduce fundamental properties of the differential equations modeling the phenomena of interest. We show that for population models, involving a dynamical conservation law the use of nonstandard finite difference (NSFD) methods allows the construction of discretization schemes such that they are dynamically consistent (DC) with the original differential equations. The paper will briefly discuss the NSFD methodology, the concept of DC, and illustrate their application to specific problems for population models.
HYDRA-II: A hydrothermal analysis computer code: Volume 1, Equations and numerics
McCann, R.A.
1987-04-01
HYDRA-II is a hydrothermal computer code capable of three-dimensional analysis of coupled conduction, convection, and thermal radiation problems. This code is especially appropriate for simulating the steady-state performance of spent fuel storage systems. The code has been evaluated for this application for the US Department of Energy's Commercial Spent Fuel Management Program. HYDRA-II provides a finite difference solution in Cartesian coordinates to the equations governing the conservation of mass, momentum, and energy. A cylindrical coordinate system may also be used to enclose the Cartesian coordinate system. This exterior coordinate system is useful for modeling cylindrical cask bodies. The difference equations for conservation of momentum are enhanced by the incorporation of directional porosities and permeabilities that aid in modeling solid structures whose dimensions may be smaller than the computational mesh. The equation for conservation of energy permits of modeling of orthotropic physical properties and film resistances. Several automated procedures are available to model radiation transfer within enclosures and from fuel rod to fuel rod. The documentation of HYDRA-II is presented in three separate volumes. This volume, Volume I - Equations and Numerics, describes the basic differential equations, illustrates how the difference equations are formulated, and gives the solution procedures employed. Volume II - User's Manual contains code flow charts, discusses the code structure, provides detailed instructions for preparing an input file, and illustrates the operation of the code by means of a model problem. The final volume, Volume III - Verification/Validation Assessments, presents results of numerical simulations of single- and multiassembly storage systems and comparisons with experimental data. 4 refs.
Numerical Analyses on Transient Thermal Process of Gas - Cooled Current Leads in BEPC II
NASA Astrophysics Data System (ADS)
Zhang, X. B.; Yao, Z. L.; Wang, L.; Jia, L. X.
2004-06-01
A pair of high current leads will be used for the superconducting detector solenoid magnet and six pairs of low current leads will be used for the superconducting interaction quadruple magnets in the Beijing Electron-Positron Collider Upgrade (BEPC II). This paper reports the numerical analyses on the thermal processes in the current leads, including the power charging process and overloaded current case as well as the transient characteristic of the leads once the helium cooling is interrupted. The design parameters of the current leads are studied for the stable and unstable conditions.
ERIC Educational Resources Information Center
Henle, James M.
This pamphlet consists of 17 brief chapters, each containing a discussion of a numeration system and a set of problems on the use of that system. The numeration systems used include Egyptian fractions, ordinary continued fractions and variants of that method, and systems using positive and negative bases. The book is informal and addressed to…
NASA Astrophysics Data System (ADS)
Bravo, Agustín; Barham, Richard; Ruiz, Mariano; López, Juan Manuel; De Arcas, Guillermo; Alonso, Jesus
2012-12-01
In part I, the feasibility of using three-dimensional (3D) finite elements (FEs) to model the acoustic behaviour of the IEC 60318-1 artificial ear was studied and the numerical approach compared with classical lumped elements modelling. It was shown that by using a more complex acoustic model that took account of thermo-viscous effects, geometric shapes and dimensions, it was possible to develop a realistic model. This model then had clear advantages in comparison with the models based on equivalent circuits using lumped parameters. In fact results from FE modelling produce a better understanding about the physical phenomena produced inside ear simulator couplers, facilitating spatial and temporal visualization of the sound fields produced. The objective of this study (part II) is to extend the investigation by validating the numerical calculations against measurements on an ear simulator conforming to IEC 60318-1. For this purpose, an appropriate commercially available device is taken and a complete 3D FE model developed for it. The numerical model is based on key dimensional data obtained with a non-destructive x-ray inspection technique. Measurements of the acoustic transfer impedance have been carried out on the same device at a national measurement institute using the method embodied in IEC 60318-1. Having accounted for the actual device dimensions, the thermo-viscous effects inside narrow slots and holes and environmental conditions, the results of the numerical modelling were found to be in good agreement with the measured values.
NASA Astrophysics Data System (ADS)
Feng, Xueshang; Wu, S. T.; Wei, Fengsi; Fan, Quanlin
2003-04-01
It has been believed that three-dimensional, numerical, magnetohydrodynamic (MHD) modelling must play a crucial role in a seamless forecasting system. This system refers to space weather originating on the sun; propagation of disturbances through the solar wind and interplanetary magnetic field (IMF), and thence, transmission into the magnetosphere, ionosphere, and thermosphere. This role comes as no surprise to numerical modelers that participate in the numerical modelling of atmospheric environments as well as the meteorological conditions at Earth. Space scientists have paid great attention to operational numerical space weather prediction models. To this purpose practical progress has been made in the past years. Here first is reviewed the progress of the numerical methods in solar wind modelling. Then, based on our discussion, a new numerical scheme of total variation diminishing (TVD) type for magnetohydrodynamic equations in spherical coordinates is proposed by taking into account convergence, stability and resolution. This new MHD model is established by solving the fluid equations of MHD system with a modified Lax-Friedrichs scheme and the magnetic induction equations with MacCormack II scheme for the purpose of developing a combined scheme of quick convergence as well as of TVD property. To verify the validation of the scheme, the propagation of one-dimensional MHD fast and slow shock problem is discussed with the numerical results conforming to the existing results obtained by the piece-wise parabolic method (PPM). Finally, some conclusions are made.
Advanced numerical methods in mesh generation and mesh adaptation
Lipnikov, Konstantine; Danilov, A; Vassilevski, Y; Agonzal, A
2010-01-01
Numerical solution of partial differential equations requires appropriate meshes, efficient solvers and robust and reliable error estimates. Generation of high-quality meshes for complex engineering models is a non-trivial task. This task is made more difficult when the mesh has to be adapted to a problem solution. This article is focused on a synergistic approach to the mesh generation and mesh adaptation, where best properties of various mesh generation methods are combined to build efficiently simplicial meshes. First, the advancing front technique (AFT) is combined with the incremental Delaunay triangulation (DT) to build an initial mesh. Second, the metric-based mesh adaptation (MBA) method is employed to improve quality of the generated mesh and/or to adapt it to a problem solution. We demonstrate with numerical experiments that combination of all three methods is required for robust meshing of complex engineering models. The key to successful mesh generation is the high-quality of the triangles in the initial front. We use a black-box technique to improve surface meshes exported from an unattainable CAD system. The initial surface mesh is refined into a shape-regular triangulation which approximates the boundary with the same accuracy as the CAD mesh. The DT method adds robustness to the AFT. The resulting mesh is topologically correct but may contain a few slivers. The MBA uses seven local operations to modify the mesh topology. It improves significantly the mesh quality. The MBA method is also used to adapt the mesh to a problem solution to minimize computational resources required for solving the problem. The MBA has a solid theoretical background. In the first two experiments, we consider the convection-diffusion and elasticity problems. We demonstrate the optimal reduction rate of the discretization error on a sequence of adaptive strongly anisotropic meshes. The key element of the MBA method is construction of a tensor metric from hierarchical edge
The numerical methods for the fluid flow of UCMCWS
Zhang Wenfu; Li Hui; Zhu Shuquan; Wang Zuna
1997-12-31
As an alternative for diesel oil for internal combustion engines, the fluid flow state of Ultra Clean Micronized Coal-Water Slurry (UCMCWS) in mini pipe and nozzle of a diesel engine must be known. In the laboratory three kinds of UCMCWS have been made with coal containing less than 0.8% ash, viscosity less than 600 mPa.s and concentration between 50% and 56%. Because the UCMCWS is a non-Newtonian fluid, there are no analytical resolution for pipe flow, especially in inlet and outlet sections. In this case using the numerical methods to research the flow state of UCMCWS is a useful method. Using the method of finite element, the flow state of UCMCWS in inlet and outlet sections (similar to a nozzle) have been studied. The distribution of velocity at different pressures of UCMCWS in outlet and inlet sections have been obtained. The result of the numerical methods is the efficient base for the pipe and nozzle design.
Numerical Analysis of a Finite Element/Volume Penalty Method
NASA Astrophysics Data System (ADS)
Maury, Bertrand
The penalty method makes it possible to incorporate a large class of constraints in general purpose Finite Element solvers like freeFEM++. We present here some contributions to the numerical analysis of this method. We propose an abstract framework for this approach, together with some general error estimates based on the discretization parameter ɛ and the space discretization parameter h. As this work is motivated by the possibility to handle constraints like rigid motion for fluid-particle flows, we shall pay a special attention to a model problem of this kind, where the constraint is prescribed over a subdomain. We show how the abstract estimate can be applied to this situation, in the case where a non-body-fitted mesh is used. In addition, we describe how this method provides an approximation of the Lagrange multiplier associated to the constraint.
Numerical methods for high-dimensional probability density function equations
NASA Astrophysics Data System (ADS)
Cho, H.; Venturi, D.; Karniadakis, G. E.
2016-01-01
In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker-Planck and Dostupov-Pugachev equations), random wave theory (Malakhov-Saichev equations) and coarse-grained stochastic systems (Mori-Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.
Calculation of free-fall trajectories using numerical optimization methods.
NASA Technical Reports Server (NTRS)
Hull, D. G.; Fowler, W. T.; Gottlieb, R. G.
1972-01-01
An important problem in space flight is the calculation of trajectories for nonthrusting vehicles between fixed points in a given time. A new procedure based on Hamilton's principle for solving such two-point boundary-value problems is presented. It employs numerical optimization methods to perform the extremization required by Hamilton's principle. This procedure is applied to the calculation of an Earth-Moon trajectory. The results show that the initial guesses required to obtain an iteration procedure which converges are not critical and that convergence can be obtained to any predetermined degree of accuracy.
Saetta, Anna V.; Vitaliani, Renato V
2005-05-01
The mathematical-numerical method developed by the authors to predict the corrosion initiation time of reinforced concrete structures due to carbonation process, recalled in Part I of this work, is here applied to some real cases. The final aim is to develop and test a practical method for determining the durability characteristics of existing buildings liable to carbonation, as well as estimating the corrosion initiation time of a building at the design stage. Two industrial sheds with different ages and located in different areas have been analyzed performing both experimental tests and numerical analyses. Finally, a case of carbonation-induced failure in a prestressed r.c. beam is presented.
Vivit, D.V.; Jenne, E.A.
1985-01-01
Dissolved sulfide (-II) and dissolved iron (II, III) were determined in geothermal well water samples collected at Cerro Prieto, Mexico. Most samples consisted of liquid and gas (two phases) at the instant of collection; and a subset of samples, referred to as ' flashed ' samples, consisted of pressurized steam samples which were allowed to condense. Sulfide was determined by sulfide specific ion electrode; Fe(II) and Fe(III) plus Fe(II) were determined spectrophotometrically. The precision and accuracy of the methods were evaluated for these high-silica waters with replicate analyses, spike recoveries, and an alternate method. Direct current (d.c.) argon plasma emission spectrometry was the alternate method used for Fe(III)-plus-Fe(II) analyses. Mean dissolved iron concentrations ranged from 20.2 to 834 micrograms/L (ug/L) as Fe(II) and 26.8 to 904 ug/L as Fe(III) plus Fe(II). Mean sulfide concentrations ranged from about 0.01 to 5.3 mg/L (S-II) Generally, higher S(-II) values and larger Fe(II)/Fe(III) ratios were found in the two-phase samples. These findings suggest that the ' flashed ' samples are at a less reduced state than the two-phase samples. (Author 's abstract)
ERIC Educational Resources Information Center
Smith, Authella; And Others
Documentation of the Coursewriter II Function FCALC is provided. The function is designed for use on the IBM 1500 instructional system and has three major applications: 1) comparison of a numeric expression in buffer 5 with a numeric expression in buffer 0; 2) comparison of an algebraic expression in buffer 5 with an algebraic expression in buffer…
A Collocation Method for Numerical Solutions of Coupled Burgers' Equations
NASA Astrophysics Data System (ADS)
Mittal, R. C.; Tripathi, A.
2014-09-01
In this paper, we propose a collocation-based numerical scheme to obtain approximate solutions of coupled Burgers' equations. The scheme employs collocation of modified cubic B-spline functions. We have used modified cubic B-spline functions for unknown dependent variables u, v, and their derivatives w.r.t. space variable x. Collocation forms of the partial differential equations result in systems of first-order ordinary differential equations (ODEs). In this scheme, we did not use any transformation or linearization method to handle nonlinearity. The obtained system of ODEs has been solved by strong stability preserving the Runge-Kutta method. The proposed scheme needs less storage space and execution time. The test problems considered in the literature have been discussed to demonstrate the strength and utility of the proposed scheme. The computed numerical solutions are in good agreement with the exact solutions and competent with those available in earlier studies. The scheme is simple as well as easy to implement. The scheme provides approximate solutions not only at the grid points, but also at any point in the solution range.
Teaching Thermal Hydraulics & Numerical Methods: An Introductory Control Volume Primer
D. S. Lucas
2004-10-01
A graduate level course for Thermal Hydraulics (T/H) was taught through Idaho State University in the spring of 2004. A numerical approach was taken for the content of this course since the students were employed at the Idaho National Laboratory and had been users of T/H codes. The majority of the students had expressed an interest in learning about the Courant Limit, mass error, semi-implicit and implicit numerical integration schemes in the context of a computer code. Since no introductory text was found the author developed notes taught from his own research and courses taught for Westinghouse on the subject. The course started with a primer on control volume methods and the construction of a Homogeneous Equilibrium Model (HEM) (T/H) code. The primer was valuable for giving the students the basics behind such codes and their evolution to more complex codes for Thermal Hydraulics and Computational Fluid Dynamics (CFD). The course covered additional material including the Finite Element Method and non-equilibrium (T/H). The control volume primer and the construction of a three-equation (mass, momentum and energy) HEM code are the subject of this paper . The Fortran version of the code covered in this paper is elementary compared to its descendants. The steam tables used are less accurate than the available commercial version written in C Coupled to a Graphical User Interface (GUI). The Fortran version and input files can be downloaded at www.microfusionlab.com.
Shear mixing in stellar radiative zones. II. Robustness of numerical simulations
NASA Astrophysics Data System (ADS)
Prat, V.; Guilet, J.; Viallet, M.; Müller, E.
2016-07-01
Context. Recent numerical simulations suggest that the model by Zahn (1992, A&A, 265, 115) for the turbulent mixing of chemical elements due to differential rotation in stellar radiative zones is valid. Aims: We investigate the robustness of this result with respect to the numerical configuration and Reynolds number of the flow. Methods: We compare results from simulations performed with two different numerical codes, including one that uses the shearing-box formalism. We also extensively study the dependence of the turbulent diffusion coefficient on the turbulent Reynolds number. Results: The two numerical codes used in this study give consistent results. The turbulent diffusion coefficient is independent of the size of the numerical domain if at least three large turbulent structures fit in the box. Generally, the turbulent diffusion coefficient depends on the turbulent Reynolds number. However, our simulations suggest that an asymptotic regime is obtained when the turbulent Reynolds number is larger than 103. Conclusions: Shear mixing in the regime of small Péclet numbers can be investigated numerically both with shearing-box simulations and simulations using explicit forcing. Our results suggest that Zahn's model is valid at large turbulent Reynolds numbers.
A numerical method for solving the Vlasov equation
NASA Technical Reports Server (NTRS)
Satofuka, N.
1982-01-01
A numerical procedure is derived for the solution of the Vlasov-Poisson system of equations in two phase-space variables. Derivatives with respect to the phase-space variables are approximated by a weighted sum of the values of the distribution function at property chosen neighboring points. The resulting set of ordinary differential equations is then solved by using an appropriate time intergration scheme. The accuracy of the proposed method is tested with some simple model problems. The results for the free streaming case, linear Landau damping, and nonlinear Landau damping are investigated and compared with those of the splitting scheme. The proposed method is found to be very accurate and efficient.
Numerical solution of fractionally damped beam by homotopy perturbation method
NASA Astrophysics Data System (ADS)
Behera, Diptiranjan; Chakraverty, Snehashish
2013-06-01
This paper investigates the numerical solution of a viscoelastic continuous beam whose damping behaviours are defined in term of fractional derivatives of arbitrary order. The Homotopy Perturbation Method (HPM) is used to obtain the dynamic response. Unit step function response is considered for the analysis. The obtained results are depicted in various plots. From the results obtained it is interesting to note that by increasing the order of the fractional derivative the beam suffers less oscillation. Similar observations have also been made by keeping the order of the fractional derivative constant and varying the damping ratios. Comparisons are made with the analytic solutions obtained by Zu-feng and Xiao-yan [Appl. Math. Mech. 28, 219 (2007)] to show the effectiveness and validation of this method.
Multigrid methods for numerical simulation of laminar diffusion flames
NASA Technical Reports Server (NTRS)
Liu, C.; Liu, Z.; Mccormick, S.
1993-01-01
This paper documents the result of a computational study of multigrid methods for numerical simulation of 2D diffusion flames. The focus is on a simplified combustion model, which is assumed to be a single step, infinitely fast and irreversible chemical reaction with five species (C3H8, O2, N2, CO2 and H2O). A fully-implicit second-order hybrid scheme is developed on a staggered grid, which is stretched in the streamwise coordinate direction. A full approximation multigrid scheme (FAS) based on line distributive relaxation is developed as a fast solver for the algebraic equations arising at each time step. Convergence of the process for the simplified model problem is more than two-orders of magnitude faster than other iterative methods, and the computational results show good grid convergence, with second-order accuracy, as well as qualitatively agreement with the results of other researchers.
Numerical modeling of spray combustion with an advanced VOF method
NASA Technical Reports Server (NTRS)
Chen, Yen-Sen; Shang, Huan-Min; Shih, Ming-Hsin; Liaw, Paul
1995-01-01
This paper summarizes the technical development and validation of a multiphase computational fluid dynamics (CFD) numerical method using the volume-of-fluid (VOF) model and a Lagrangian tracking model which can be employed to analyze general multiphase flow problems with free surface mechanism. The gas-liquid interface mass, momentum and energy conservation relationships are modeled by continuum surface mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed flow regimes. The objectives of the present study are to develop and verify the fractional volume-of-fluid cell partitioning approach into a predictor-corrector algorithm and to demonstrate the effectiveness of the present approach by simulating benchmark problems including laminar impinging jets, shear coaxial jet atomization and shear coaxial spray combustion flows.
Numerical Methods and Simulations of Complex Multiphase Flows
NASA Astrophysics Data System (ADS)
Brady, Peter
Multiphase flows are an important part of many natural and technological phenomena such as ocean-air coupling (which is important for climate modeling) and the atomization of liquid fuel jets in combustion engines. The unique challenges of multiphase flow often make analytical solutions to the governing equations impossible and experimental investigations very difficult. Thus, high-fidelity numerical simulations can play a pivotal role in understanding these systems. This dissertation describes numerical methods developed for complex multiphase flows and the simulations performed using these methods. First, the issue of multiphase code verification is addressed. Code verification answers the question "Is this code solving the equations correctly?" The method of manufactured solutions (MMS) is a procedure for generating exact benchmark solutions which can test the most general capabilities of a code. The chief obstacle to applying MMS to multiphase flow lies in the discontinuous nature of the material properties at the interface. An extension of the MMS procedure to multiphase flow is presented, using an adaptive marching tetrahedron style algorithm to compute the source terms near the interface. Guidelines for the use of the MMS to help locate coding mistakes are also detailed. Three multiphase systems are then investigated: (1) the thermocapillary motion of three-dimensional and axisymmetric drops in a confined apparatus, (2) the flow of two immiscible fluids completely filling an enclosed cylinder and driven by the rotation of the bottom endwall, and (3) the atomization of a single drop subjected to a high shear turbulent flow. The systems are simulated numerically by solving the full multiphase Navier-Stokes equations coupled to the various equations of state and a level set interface tracking scheme based on the refined level set grid method. The codes have been parallelized using MPI in order to take advantage of today's very large parallel computational
Numerical methods for assessment of the ship's pollutant emissions
NASA Astrophysics Data System (ADS)
Jenaru, A.; Acomi, N.
2016-08-01
The maritime transportation sector constitutes a source of atmospheric pollution. To avoid or minimize ships pollutant emissions the first step is to assess them. Two methods of estimation of the ships’ emissions are proposed in this paper. These methods prove their utility for shipboard and shore based management personnel from the practical perspective. The methods were demonstrated for a product tanker vessel where a permanent monitoring system for the pollutant emissions has previously been fitted. The values of the polluting agents from the exhaust gas were determined for the ship from the shipyard delivery and were used as starting point. Based on these values, the paper aimed at numerical assessing of ship's emissions in order to determine the ways for avoiding environmental pollution: the analytical method of determining the concentrations of the exhaust gas components, by using computation program MathCAD, and the graphical method of determining the concentrations of the exhaust gas components, using variation diagrams of the parameters, where the results of the on board measurements were introduced, following the application of pertinent correction factors. The results should be regarded as a supporting tool during the decision making process linked to the reduction of ship's pollutant emissions.
Asymmetric MRI magnet design using a hybrid numerical method.
Zhao, H; Crozier, S; Doddrell, D M
1999-12-01
This paper describes a hybrid numerical method for the design of asymmetric magnetic resonance imaging magnet systems. The problem is formulated as a field synthesis and the desired current density on the surface of a cylinder is first calculated by solving a Fredholm equation of the first kind. Nonlinear optimization methods are then invoked to fit practical magnet coils to the desired current density. The field calculations are performed using a semi-analytical method. A new type of asymmetric magnet is proposed in this work. The asymmetric MRI magnet allows the diameter spherical imaging volume to be positioned close to one end of the magnet. The main advantages of making the magnet asymmetric include the potential to reduce the perception of claustrophobia for the patient, better access to the patient by attending physicians, and the potential for reduced peripheral nerve stimulation due to the gradient coil configuration. The results highlight that the method can be used to obtain an asymmetric MRI magnet structure and a very homogeneous magnetic field over the central imaging volume in clinical systems of approximately 1.2 m in length. Unshielded designs are the focus of this work. This method is flexible and may be applied to magnets of other geometries.
A method for improving time-stepping numerics
NASA Astrophysics Data System (ADS)
Williams, P. D.
2012-04-01
In contemporary numerical simulations of the atmosphere, evidence suggests that time-stepping errors may be a significant component of total model error, on both weather and climate time-scales. This presentation will review the available evidence, and will then suggest a simple but effective method for substantially improving the time-stepping numerics at no extra computational expense. The most common time-stepping method is the leapfrog scheme combined with the Robert-Asselin (RA) filter. This method is used in the following atmospheric models (and many more): ECHAM, MAECHAM, MM5, CAM, MESO-NH, HIRLAM, KMCM, LIMA, SPEEDY, IGCM, PUMA, COSMO, FSU-GSM, FSU-NRSM, NCEP-GFS, NCEP-RSM, NSEAM, NOGAPS, RAMS, and CCSR/NIES-AGCM. Although the RA filter controls the time-splitting instability in these models, it also introduces non-physical damping and reduces the accuracy. This presentation proposes a simple modification to the RA filter. The modification has become known as the RAW filter (Williams 2011). When used in conjunction with the leapfrog scheme, the RAW filter eliminates the non-physical damping and increases the amplitude accuracy by two orders, yielding third-order accuracy. (The phase accuracy remains second-order.) The RAW filter can easily be incorporated into existing models, typically via the insertion of just a single line of code. Better simulations are obtained at no extra computational expense. Results will be shown from recent implementations of the RAW filter in various atmospheric models, including SPEEDY and COSMO. For example, in SPEEDY, the skill of weather forecasts is found to be significantly improved. In particular, in tropical surface pressure predictions, five-day forecasts made using the RAW filter have approximately the same skill as four-day forecasts made using the RA filter (Amezcua, Kalnay & Williams 2011). These improvements are encouraging for the use of the RAW filter in other models.
Libration Orbit Mission Design: Applications of Numerical & Dynamical Methods
NASA Technical Reports Server (NTRS)
Bauer, Frank (Technical Monitor); Folta, David; Beckman, Mark
2002-01-01
Sun-Earth libration point orbits serve as excellent locations for scientific investigations. These orbits are often selected to minimize environmental disturbances and maximize observing efficiency. Trajectory design in support of libration orbits is ever more challenging as more complex missions are envisioned in the next decade. Trajectory design software must be further enabled to incorporate better understanding of the libration orbit solution space and thus improve the efficiency and expand the capabilities of current approaches. The Goddard Space Flight Center (GSFC) is currently supporting multiple libration missions. This end-to-end support consists of mission operations, trajectory design, and control. It also includes algorithm and software development. The recently launched Microwave Anisotropy Probe (MAP) and upcoming James Webb Space Telescope (JWST) and Constellation-X missions are examples of the use of improved numerical methods for attaining constrained orbital parameters and controlling their dynamical evolution at the collinear libration points. This paper presents a history of libration point missions, a brief description of the numerical and dynamical design techniques including software used, and a sample of future GSFC mission designs.
Unsaturated Shear Strength and Numerical Analysis Methods for Unsaturated Soils
NASA Astrophysics Data System (ADS)
Kim, D.; Kim, G.; Kim, D.; Baek, H.; Kang, S.
2011-12-01
The angles of shearing resistance(φb) and internal friction(φ') appear to be identical in low suction range, but the angle of shearing resistance shows non-linearity as suction increases. In most numerical analysis however, a fixed value for the angle of shearing resistance is applied even in low suction range for practical reasons, often leading to a false conclusion. In this study, a numerical analysis has been undertaken employing the estimated shear strength curve of unsaturated soils from the residual water content of SWCC proposed by Vanapalli et al.(1996). The result was also compared with that from a fixed value of φb. It is suggested that, in case it is difficult to measure the unsaturated shear strength curve through the triaxial soil tests, the estimated shear strength curve using the residual water content can be a useful alternative. This result was applied for analyzing the slope stablity of unsaturated soils. The effects of a continuous rainfall on slope stability were analyzed using a commercial program "SLOPE/W", with the coupled infiltration analysis program "SEEP/W" from the GEO-SLOPE International Ltd. The results show that, prior to the infiltration by the intensive rainfall, the safety factors using the estimated shear strength curve were substantially higher than that from the fixed value of φb at all time points. After the intensive infiltration, both methods showed a similar behavior.
Space-time adaptive numerical methods for geophysical applications.
Castro, C E; Käser, M; Toro, E F
2009-11-28
In this paper we present high-order formulations of the finite volume and discontinuous Galerkin finite-element methods for wave propagation problems with a space-time adaptation technique using unstructured meshes in order to reduce computational cost without reducing accuracy. Both methods can be derived in a similar mathematical framework and are identical in their first-order version. In their extension to higher order accuracy in space and time, both methods use spatial polynomials of higher degree inside each element, a high-order solution of the generalized Riemann problem and a high-order time integration method based on the Taylor series expansion. The static adaptation strategy uses locally refined high-resolution meshes in areas with low wave speeds to improve the approximation quality. Furthermore, the time step length is chosen locally adaptive such that the solution is evolved explicitly in time by an optimal time step determined by a local stability criterion. After validating the numerical approach, both schemes are applied to geophysical wave propagation problems such as tsunami waves and seismic waves comparing the new approach with the classical global time-stepping technique. The problem of mesh partitioning for large-scale applications on multi-processor architectures is discussed and a new mesh partition approach is proposed and tested to further reduce computational cost. PMID:19840984
Numerical method of characteristics for one-dimensional blood flow
NASA Astrophysics Data System (ADS)
Acosta, Sebastian; Puelz, Charles; Rivière, Béatrice; Penny, Daniel J.; Rusin, Craig G.
2015-08-01
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant.
A mathematical model and numerical method for thermoelectric DNA sequencing
NASA Astrophysics Data System (ADS)
Shi, Liwei; Guilbeau, Eric J.; Nestorova, Gergana; Dai, Weizhong
2014-05-01
Single nucleotide polymorphisms (SNPs) are single base pair variations within the genome that are important indicators of genetic predisposition towards specific diseases. This study explores the feasibility of SNP detection using a thermoelectric sequencing method that measures the heat released when DNA polymerase inserts a deoxyribonucleoside triphosphate into a DNA strand. We propose a three-dimensional mathematical model that governs the DNA sequencing device with a reaction zone that contains DNA template/primer complex immobilized to the surface of the lower channel wall. The model is then solved numerically. Concentrations of reactants and the temperature distribution are obtained. Results indicate that when the nucleoside is complementary to the next base in the DNA template, polymerization occurs lengthening the complementary polymer and releasing thermal energy with a measurable temperature change, implying that the thermoelectric conceptual device for sequencing DNA may be feasible for identifying specific genes in individuals.
Numerical optimization method for packing regular convex polygons
NASA Astrophysics Data System (ADS)
Galiev, Sh. I.; Lisafina, M. S.
2016-08-01
An algorithm is presented for the approximate solution of the problem of packing regular convex polygons in a given closed bounded domain G so as to maximize the total area of the packed figures. On G a grid is constructed whose nodes generate a finite set W on G, and the centers of the figures to be packed can be placed only at some points of W. The problem of packing these figures with centers in W is reduced to a 0-1 linear programming problem. A two-stage algorithm for solving the resulting problems is proposed. The algorithm finds packings of the indicated figures in an arbitrary closed bounded domain on the plane. Numerical results are presented that demonstrate the effectiveness of the method.
Advanced Numerical Methods and Software Approaches for Semiconductor Device Simulation
Carey, Graham F.; Pardhanani, A. L.; Bova, S. W.
2000-01-01
In this article we concisely present several modern strategies that are applicable to driftdominated carrier transport in higher-order deterministic models such as the driftdiffusion, hydrodynamic, and quantum hydrodynamic systems. The approaches include extensions of “upwind” and artificial dissipation schemes, generalization of the traditional Scharfetter – Gummel approach, Petrov – Galerkin and streamline-upwind Petrov Galerkin (SUPG), “entropy” variables, transformations, least-squares mixed methods and other stabilized Galerkin schemes such as Galerkin least squares and discontinuous Galerkin schemes. The treatment is representative rather than an exhaustive review and several schemes are mentioned only briefly with appropriate reference to the literature. Some of themore » methods have been applied to the semiconductor device problem while others are still in the early stages of development for this class of applications. We have included numerical examples from our recent research tests with some of the methods. A second aspect of the work deals with algorithms that employ unstructured grids in conjunction with adaptive refinement strategies. The full benefits of such approaches have not yet been developed in this application area and we emphasize the need for further work on analysis, data structures and software to support adaptivity. Finally, we briefly consider some aspects of software frameworks. These include dial-an-operator approaches such as that used in the industrial simulator PROPHET, and object-oriented software support such as those in the SANDIA National Laboratory framework SIERRA.« less
a Numerical Method for Stability Analysis of Pinned Flexible Mechanisms
NASA Astrophysics Data System (ADS)
Beale, D. G.; Lee, S. W.
1996-05-01
A technique is presented to investigate the stability of mechanisms with pin-jointed flexible members. The method relies on a special floating frame from which elastic link co-ordinates are defined. Energies are easily developed for use in a Lagrange equation formulation, leading to a set of non-linear and mixed ordinary differential-algebraic equations of motion with constraints. Stability and bifurcation analysis is handled using a numerical procedure (generalized co-ordinate partitioning) that avoids the tedious and difficult task of analytically reducing the system of equations to a number equalling the system degrees of freedom. The proposed method was then applied to (1) a slider-crank mechanism with a flexible connecting rod and crank of constant rotational speed, and (2) a four-bar linkage with a flexible coupler with a constant speed crank. In both cases, a single pinned-pinned beam bending mode is employed to develop resonance curves and stability boundaries in the crank length-crank speed parameter plane. Flip and fold bifurcations are common occurrences in both mechanisms. The accuracy of the proposed method was also verified by comparison with previous experimental results [1].
Introduction to finite-difference methods for numerical fluid dynamics
Scannapieco, E.; Harlow, F.H.
1995-09-01
This work is intended to be a beginner`s exercise book for the study of basic finite-difference techniques in computational fluid dynamics. It is written for a student level ranging from high-school senior to university senior. Equations are derived from basic principles using algebra. Some discussion of partial-differential equations is included, but knowledge of calculus is not essential. The student is expected, however, to have some familiarity with the FORTRAN computer language, as the syntax of the computer codes themselves is not discussed. Topics examined in this work include: one-dimensional heat flow, one-dimensional compressible fluid flow, two-dimensional compressible fluid flow, and two-dimensional incompressible fluid flow with additions of the equations of heat flow and the {Kappa}-{epsilon} model for turbulence transport. Emphasis is placed on numerical instabilities and methods by which they can be avoided, techniques that can be used to evaluate the accuracy of finite-difference approximations, and the writing of the finite-difference codes themselves. Concepts introduced in this work include: flux and conservation, implicit and explicit methods, Lagrangian and Eulerian methods, shocks and rarefactions, donor-cell and cell-centered advective fluxes, compressible and incompressible fluids, the Boussinesq approximation for heat flow, Cartesian tensor notation, the Boussinesq approximation for the Reynolds stress tensor, and the modeling of transport equations. A glossary is provided which defines these and other terms.
Advanced numerical methods and software approaches for semiconductor device simulation
CAREY,GRAHAM F.; PARDHANANI,A.L.; BOVA,STEVEN W.
2000-03-23
In this article the authors concisely present several modern strategies that are applicable to drift-dominated carrier transport in higher-order deterministic models such as the drift-diffusion, hydrodynamic, and quantum hydrodynamic systems. The approaches include extensions of upwind and artificial dissipation schemes, generalization of the traditional Scharfetter-Gummel approach, Petrov-Galerkin and streamline-upwind Petrov Galerkin (SUPG), entropy variables, transformations, least-squares mixed methods and other stabilized Galerkin schemes such as Galerkin least squares and discontinuous Galerkin schemes. The treatment is representative rather than an exhaustive review and several schemes are mentioned only briefly with appropriate reference to the literature. Some of the methods have been applied to the semiconductor device problem while others are still in the early stages of development for this class of applications. They have included numerical examples from the recent research tests with some of the methods. A second aspect of the work deals with algorithms that employ unstructured grids in conjunction with adaptive refinement strategies. The full benefits of such approaches have not yet been developed in this application area and they emphasize the need for further work on analysis, data structures and software to support adaptivity. Finally, they briefly consider some aspects of software frameworks. These include dial-an-operator approaches such as that used in the industrial simulator PROPHET, and object-oriented software support such as those in the SANDIA National Laboratory framework SIERRA.
Numerical Improvement of The Three-dimensional Boundary Element Method
NASA Astrophysics Data System (ADS)
Ortiz-Aleman, C.; Gil-Zepeda, A.; SÃ¡nchez-Sesma, F. J.; Luzon-Martinez, F.
2001-12-01
Boundary element methods have been applied to calculate the seismic response of various types of geological structures. Dimensionality reduction and a relatively easy fulfillment of radiation conditions at infinity are recognized advantages over domain approaches. Indirect Boundary Element Method (IBEM) formulations give rise to large systems of equations, and the considerable amount of operations required for solving them suggest the possibility of getting some benefit from exploitation of sparsity patterns. In this article, a brief study on the structure of the linear systems derived from the IBEM method is carried out. Applicability of a matrix static condensation algorithm to the inversion of the IBEM coefficient matrix is explored, in order to optimize the numerical burden of such method. Seismic response of a 3-D alluvial valley of irregular shape, as originally proposed by Sánchez-Sesma and Luzon (1995), was computed and comparisons on time consumption and memory allocation are established. An alternative way to deal with those linear systems is the use of threshold criteria for the truncation of the coefficient matrix, which implies the solution of sparse approximations instead of the original full IBEM systems (Ortiz-Aleman et al., 1998). Performance of this optimized approach is evaluated on its application to the case of a three-dimensional alluvial basin with irregular shape. Transfer functions were calculated for the frequency range from 0 to 1.25 Hz. Inversion of linear systems by using this algorithm lead to significant saving on computer time and memory allocation relative to the original IBEM formulation. Results represent an extension in the range of application of the IBEM method.
NASA Astrophysics Data System (ADS)
Lambert, J.; Josselin, E.; Ryde, N.; Faure, A.
2015-08-01
Context. The solution of the nonlocal thermodynamical equilibrium (non-LTE) radiative transfer equation usually relies on stationary iterative methods, which may falsely converge in some cases. Furthermore, these methods are often unable to handle large-scale systems, such as molecular spectra emerging from, for example, cool stellar atmospheres. Aims: Our objective is to develop a new method, which aims to circumvent these problems, using nonstationary numerical techniques and taking advantage of parallel computers. Methods: The technique we develop may be seen as a generalization of the coupled escape probability method. It solves the statistical equilibrium equations in all layers of a discretized model simultaneously. The numerical scheme adopted is based on the generalized minimum residual method. Results: The code has already been applied to the special case of the water spectrum in a red supergiant stellar atmosphere. This demonstrates the fast convergence of this method, and opens the way to a wide variety of astrophysical problems.
Numerical Methods for Forward and Inverse Problems in Discontinuous Media
Chartier, Timothy P.
2011-03-08
The research emphasis under this grant's funding is in the area of algebraic multigrid methods. The research has two main branches: 1) exploring interdisciplinary applications in which algebraic multigrid can make an impact and 2) extending the scope of algebraic multigrid methods with algorithmic improvements that are based in strong analysis.The work in interdisciplinary applications falls primarily in the field of biomedical imaging. Work under this grant demonstrated the effectiveness and robustness of multigrid for solving linear systems that result from highly heterogeneous finite element method models of the human head. The results in this work also give promise to medical advances possible with software that may be developed. Research to extend the scope of algebraic multigrid has been focused in several areas. In collaboration with researchers at the University of Colorado, Lawrence Livermore National Laboratory, and Los Alamos National Laboratory, the PI developed an adaptive multigrid with subcycling via complementary grids. This method has very cheap computing costs per iterate and is showing promise as a preconditioner for conjugate gradient. Recent work with Los Alamos National Laboratory concentrates on developing algorithms that take advantage of the recent advances in adaptive multigrid research. The results of the various efforts in this research could ultimately have direct use and impact to researchers for a wide variety of applications, including, astrophysics, neuroscience, contaminant transport in porous media, bi-domain heart modeling, modeling of tumor growth, and flow in heterogeneous porous media. This work has already led to basic advances in computational mathematics and numerical linear algebra and will continue to do so into the future.
Numerical methods for determining interstitial oxygen in silicon
Stevenson, J.O.; Medernach, J.W.
1995-01-01
The interstitial oxygen (O{sub i}) concentration in Czochralski silicon and the subsequent SiO{sub x} precipitation are important parameters for integrated circuit fabrication. Uncontrolled SiO{sub x} precipitation during processing can create detrimental mechanical and electrical effects that contribute to poor performance. An inability to consistently and accurately measure the initial O{sub i} concentration in heavily doped silicon has led to contradictory results regarding the effects of dopant type and concentration on SiO{sub x} precipitation. The authors have developed a software package for reliably determining and comparing O{sub i} in heavily doped silicon. The SiFTIR{copyright} code implements three independent oxygen analysis methods in a single integrated package. Routine oxygen measurements are desirable over a wide range of silicon resistivities, but there has been confusion concerning which of the three numerical methods is most suitable for the low resistivity portion of the continuum. A major strength of the software is an ability to rapidly produce results for all three methods using only a single Fourier Transform Infrared Spectroscopy (FTIR) spectrum as input. This ability to perform three analyses on a single data set allows a detailed comparison of the three methods across the entire range of resistivities in question. Integrated circuit manufacturers could use the enabling technology provided by SiFTIR{copyright} to monitor O{sub i} content. Early detection of O{sub i} using this diagnostic could be beneficial in controlling SiO{sub x} precipitation during integrated circuit processing.
Simplified method for numerical modeling of fiber lasers.
Shtyrina, O V; Yarutkina, I A; Fedoruk, M P
2014-12-29
A simplified numerical approach to modeling of dissipative dispersion-managed fiber lasers is examined. We present a new numerical iteration algorithm for finding the periodic solutions of the system of nonlinear ordinary differential equations describing the intra-cavity dynamics of the dissipative soliton characteristics in dispersion-managed fiber lasers. We demonstrate that results obtained using simplified model are in good agreement with full numerical modeling based on the corresponding partial differential equations.
Extracting S-matrix poles for resonances from numerical scattering data: Type-II Padé reconstruction
NASA Astrophysics Data System (ADS)
Sokolovski, D.; Akhmatskaya, E.; Sen, S. K.
2011-02-01
residues of resonance poles from numerical scattering data supplied by the user. The data can then be used for quantitative analysis of interference patterns observed in elastic, inelastic and reactive integral and differential cross sections. Solution method: The S-matrix element is analytically continued in the complex plane of either energy or angular momentum with the help of Padé approximation of type II. Resonance (complex energy or Regge) poles are identified and their residues evaluated. Unusual features: Use of multiple precision MPFUN package (Bailey (1993) [45]). (Distributed with the PADE II code.) Running time: From several seconds to several minutes depending on the precision level chosen and the number of iterations performed.
Micarta Propellers II : Method of Construction
NASA Technical Reports Server (NTRS)
Caldwell, F W; Clay, N S
1924-01-01
The methods used in manufacturing Micarta propellers differ considerably from those employed with wood propellers on account of the hardness of the materials. The propellers must be formed accurately to size in a mold and afterwards balanced without the customary trimming of the material from the tips. Described here are the pressing and molding processes, filing, boring, balancing, and curing.
Numerical methods for portfolio selection with bounded constraints
NASA Astrophysics Data System (ADS)
Yin, G.; Jin, Hanqing; Jin, Zhuo
2009-11-01
This work develops an approximation procedure for portfolio selection with bounded constraints. Based on the Markov chain approximation techniques, numerical procedures are constructed for the utility optimization task. Under simple conditions, the convergence of the approximation sequences to the wealth process and the optimal utility function is established. Numerical examples are provided to illustrate the performance of the algorithms.
Trigonometrically fitted two step hybrid method for the numerical integration of second order IVPs
NASA Astrophysics Data System (ADS)
Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E.
2016-06-01
In this work we consider the numerical integration of second order ODEs where the first derivative is missing. We construct trigonometrically fitted two step hybrid methods. We apply the new methods on the numerical integration of several test problems.
Kamalian, Morteza; Prilepsky, Jaroslaw E; Le, Son Thai; Turitsyn, Sergei K
2016-08-01
In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption. PMID:27505799
Full Wave Simulation of Integrated Circuits Using Hybrid Numerical Methods
NASA Astrophysics Data System (ADS)
Tan, Jilin
Transmission lines play an important role in digital electronics, and in microwave and millimeter-wave circuits. Analysis, modeling, and design of transmission lines are critical to the development of the circuitry in the chip, subsystem, and system levels. In the past several decays, at the EM modeling level, the quasi-static approximation has been widely used due to its great simplicity. As the clock rates increase, the inter-connect effects such as signal delay, distortion, dispersion, reflection, and crosstalk, limit the performance of microwave systems. Meanwhile, the quasi-static approach loses its validity for some complex system structures. Since the successful system design of the PCB, MCM, and the chip packaging, rely very much on the computer aided EM level modeling and simulation, many new methods have been developed, such as the full wave approach, to guarantee the successful design. Many difficulties exist in the rigorous EM level analysis. Some of these include the difficulties in describing the behavior of the conductors with finite thickness and finite conductivity, the field singularity, and the arbitrary multilayered multi-transmission lines structures. This dissertation concentrates on the full wave study of the multi-conductor transmission lines with finite conductivity and finite thickness buried in an arbitrary lossy multilayered environment. Two general approaches have been developed. The first one is the integral equation method in which the dyadic Green's function for arbitrary layered media has been correctly formulated and has been tested both analytically and numerically. By applying this method, the double layered high dielectric permitivitty problem and the heavy dielectrical lossy problem in multilayered media in the CMOS circuit design have been solved. The second approach is the edge element method. In this study, the correct functional for the two dimensional propagation problem has been successfully constructed in a rigorous way
Active Problem Solving and Applied Research Methods in a Graduate Course on Numerical Methods
ERIC Educational Resources Information Center
Maase, Eric L.; High, Karen A.
2008-01-01
"Chemical Engineering Modeling" is a first-semester graduate course traditionally taught in a lecture format at Oklahoma State University. The course as taught by the author for the past seven years focuses on numerical and mathematical methods as necessary skills for incoming graduate students. Recent changes to the course have included Visual…
Examination of DFT and TDDFT Methods II
NASA Astrophysics Data System (ADS)
Wang, Yi-Gui
2009-09-01
We investigated the isomerization energies for C8 alkanes (n-octane and 2,2,3,3-tetra-methyl butane) and 1-X-propenes (X = CH3, F, Cl, Br) and the excited states for tropolone. The recently implemented TDDFT gradients enabled us to optimize the adiabatic excited-state structures and to obtain wave function files for excited-state electron density analyses with 25 functionals. The dispersion interactions had been found to be important for predicting the isomerization energies for n-octane and 2,2,3,3-tetra-methyl butane and for cis- and trans-1-X-propenes (X = CH3, F, Cl, Br). B3LYP failed to predict the isomerization energies for the first case but succeeded for the latter. We noticed that the integrated electron density and the merging contour values in the electron density difference plots were related to the isomerization energies; the DFT functionals (LSDA, BHandH, VSXC, and M052X) that could correctly account for the dispersion forces produced a greater electron density response for 2,2,3,3-tetramethyl butane than n-octane. Although the faster proton transfer reaction rate in the Ã1B2 excited state relative to the X˜1A1 ground state of tropolone could be reproduced only by M052X, the three newly designed functionals (BMK, CAM-B3LYP, and M052X) apparently performed better than other DFT functionals. The C-C' bond lengths of the Cs symmetry excited state were possibly underestimated by DFT methods; the underestimation of C-C' bond lengths contributed to the high proton transfer barriers in the Ã1B2 excited state of tropolone.
NUMERICAL METHODS FOR THE SIMULATION OF HIGH INTENSITY HADRON SYNCHROTRONS.
LUCCIO, A.; D'IMPERIO, N.; MALITSKY, N.
2005-09-12
Numerical algorithms for PIC simulation of beam dynamics in a high intensity synchrotron on a parallel computer are presented. We introduce numerical solvers of the Laplace-Poisson equation in the presence of walls, and algorithms to compute tunes and twiss functions in the presence of space charge forces. The working code for the simulation here presented is SIMBAD, that can be run as stand alone or as part of the UAL (Unified Accelerator Libraries) package.
Alfvén wave collisions, the fundamental building block of plasma turbulence. II. Numerical solution
Nielson, K. D.; Howes, G. G.; Dorland, W.
2013-07-15
This paper presents the numerical verification of an asymptotic analytical solution for the nonlinear interaction between counterpropagating Alfvén waves, the fundamental building block of astrophysical plasma turbulence. The analytical solution, derived in the weak turbulence limit using the equations of incompressible MHD, is compared to a nonlinear gyrokinetic simulation of an Alfvén wave collision. The agreement between these methods signifies that the incompressible solution satisfactorily describes the essential dynamics of the nonlinear energy transfer, even under the weakly collisional plasma conditions relevant to many astrophysical environments.
Numerical modeling of beam-environment interactions in the PEP-II B-Factory
Ng, C.K.; Ko, K.; Li, Z.; Lin, X.E.
1996-11-01
The PEP-II B-Factory is designed to operate at high currents with many bunches (1658) to achieve the luminosity required for physics studies. Interactions of a beam with its environment in a storage ring raise various issues of concern for accelerator physics, mechanical design and device performance. First, for accelerator physics, wakefields generated by interactions of a beam with beamline components, if not properly controlled, will drive single-bunch and coupled-bunch instabilities. The total broad-band impedance of the ring cannot exceed a budget limited by single-bunch effects. The growth rate of a coupled-bunch mode contributed from narrow-band impedance should be smaller than the damping rate due to synchrotron radiation; otherwise, suppression by feedback control will be necessary. Second, the energy loss by a beam at a beamline component in the form of higher-order-mode (HOM) power leads to additional heating on the component, and to TE mode radiation through openings on vacuum chamber walls. Last, calculations of transfer and beam impedances of pickup and kicker devices are essential for improving their performance and for identifying trapped modes. To address these issues quantitatively requires numerical simulations of each beamline component which include the realistic geometry and the relevant physics involved in the particular beam-environment interactions.
SAMSAN- MODERN NUMERICAL METHODS FOR CLASSICAL SAMPLED SYSTEM ANALYSIS
NASA Technical Reports Server (NTRS)
Frisch, H. P.
1994-01-01
SAMSAN was developed to aid the control system analyst by providing a self consistent set of computer algorithms that support large order control system design and evaluation studies, with an emphasis placed on sampled system analysis. Control system analysts have access to a vast array of published algorithms to solve an equally large spectrum of controls related computational problems. The analyst usually spends considerable time and effort bringing these published algorithms to an integrated operational status and often finds them less general than desired. SAMSAN reduces the burden on the analyst by providing a set of algorithms that have been well tested and documented, and that can be readily integrated for solving control system problems. Algorithm selection for SAMSAN has been biased toward numerical accuracy for large order systems with computational speed and portability being considered important but not paramount. In addition to containing relevant subroutines from EISPAK for eigen-analysis and from LINPAK for the solution of linear systems and related problems, SAMSAN contains the following not so generally available capabilities: 1) Reduction of a real non-symmetric matrix to block diagonal form via a real similarity transformation matrix which is well conditioned with respect to inversion, 2) Solution of the generalized eigenvalue problem with balancing and grading, 3) Computation of all zeros of the determinant of a matrix of polynomials, 4) Matrix exponentiation and the evaluation of integrals involving the matrix exponential, with option to first block diagonalize, 5) Root locus and frequency response for single variable transfer functions in the S, Z, and W domains, 6) Several methods of computing zeros for linear systems, and 7) The ability to generate documentation "on demand". All matrix operations in the SAMSAN algorithms assume non-symmetric matrices with real double precision elements. There is no fixed size limit on any matrix in any
Numerical Analysis on the Vortex Pattern and Flux Particle Dispersion in KR Method Using MPS Method
NASA Astrophysics Data System (ADS)
Hirata, N.; Xu, Y.; Anzai, K.
2015-06-01
The mechanically-stirring vessel is widely used in many fields, such as chemical reactor, bioreactor, and metallurgy, etc. The type of vortex mode that formed during impeller stirring has great effect on stirring efficiency, chemical reacting rate and air entrapment. Many efforts have been made to numerically simulate the fluid flow in the stirring vessel with classical Eulerian method. However, it is difficult to directly investigate the vortex mode and flux particle dispersion. Therefore, moving particle semi-implicit (MPS) method, which is based on Lagrangian method, is applied to simulate the fluid flow in a KR method in this practice. Top height and bottom heights of vortex surface in a steady state under several rotation speed was taken as key parameters to compare the results of numerical and published results. Flux particle dispersion behaviour under a rotation speed range from 80 to 480 rpm was also compared with the past study. The result shows that the numerical calculation has high consistency with experimental results. It is confirmed that the calculation using MPS method well reflected the vortex mode and flux particle dispersion in a mechanically-stirring vessel.
Adaptive Numerical Dissipation Controls for High Order Methods
NASA Technical Reports Server (NTRS)
Yee, Helen C.; Sjogreen, B.; Sandham, N. D.; Mansour, Nagi (Technical Monitor)
2001-01-01
A numerical scheme for direct numerical simulation of shock-turbulence interactions of high speed compressible flows would ideally not be significantly more expensive than the standard fourth or sixth-order compact or non-compact central differencing scheme. It should be possible to resolve all scales down to scales of order of the Kolmogorov scales of turbulence accurately and efficiently, while at the same time being able to capture steep gradients occurring at much smaller scales efficiently. The goal of this lecture is to review the progress and new development of the low dissipative high order shock-capturing schemes proposed by Yee et al. Comparison on the efficiency and accuracy of this class of schemes with spectral and the fifth-order WENO (weighted essentially nonoscillatory) scheme will be presented. A new approach to dynamically sense the appropriate amount of numerical dissipation to be added at each grid point using non-orthogonal wavelets will be discussed.
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
A numerical method for solving partial differential algebraic equations
NASA Astrophysics Data System (ADS)
Diep, Nguyen Khac; Chistyakov, V. F.
2013-06-01
Linear systems of partial differential equations with constant coefficient matrices are considered. The matrices multiplying the derivatives of the sought vector function are assumed to be singular. The structure of solutions to such systems is examined. The numerical solution of initialboundary value problems for such equations by applying implicit difference schemes is discussed.
NASA Astrophysics Data System (ADS)
Jacques, S.; De Baere, I.; Van Paepegem, W.
2015-12-01
The reliability of composite structures depends, among other damage mechanisms, on their ability to withstand delaminations. In order to have a better understanding of the cohesive zone method technique for delamination simulations, a complete analysis of the multiple parameters influencing the results is necessary. In this paper the work is concentrated on the cohesive zone method using cohesive elements. First a summary of the theory of the cohesive zone method is given. A numerical investigation on the multiple parameters influencing the numerical simulation of the mode I and mode II delamination tests has been performed. The parameters such as the stabilization method, the output frequency, the friction and the computational efficiency have been taken into account. The results will be compared to an analytical solution obtained by linear elastic fracture mechanics. Additionally the numerical simulation results will be compared to the experimental results of a glass-fibre reinforced composite material for the mode I Double Cantilever Beam (DCB) and to a carbon fibre 5-harness satin weave reinforced polyphenylene sulphide composite for the mode I DCB and mode II End Notched Flexure (ENF).
Cvetkovic, Aleksandar M; Milasinovic, Danko Z; Peulic, Aleksandar S; Mijailovic, Nikola V; Filipovic, Nenad D; Zdravkovic, Nebojsa D
2014-11-01
The main goal of this study was to numerically quantify risk of duodenal stump blowout after Billroth II (BII) gastric resection. Our hypothesis was that the geometry of the reconstructed tract after BII resection is one of the key factors that can lead to duodenal dehiscence. We used computational fluid dynamics (CFD) with finite element (FE) simulations of various models of BII reconstructed gastrointestinal (GI) tract, as well as non-perfused, ex vivo, porcine experimental models. As main geometrical parameters for FE postoperative models we have used duodenal stump length and inclination between gastric remnant and duodenal stump. Virtual gastric resection was performed on each of 3D FE models based on multislice Computer Tomography (CT) DICOM. According to our computer simulation the difference between maximal duodenal stump pressures for models with most and least preferable geometry of reconstructed GI tract is about 30%. We compared the resulting postoperative duodenal pressure from computer simulations with duodenal stump dehiscence pressure from the experiment. Pressure at duodenal stump after BII resection obtained by computer simulation is 4-5 times lower than the dehiscence pressure according to our experiment on isolated bowel segment. Our conclusion is that if the surgery is performed technically correct, geometry variations of the reconstructed GI tract by themselves are not sufficient to cause duodenal stump blowout. Pressure that develops in the duodenal stump after BII resection using omega loop, only in the conjunction with other risk factors can cause duodenal dehiscence. Increased duodenal pressure after BII resection is risk factor. Hence we recommend the routine use of Roux en Y anastomosis as a safer solution in terms of resulting intraluminal pressure. However, if the surgeon decides to perform BII reconstruction, results obtained with this methodology can be valuable. PMID:25201585
An Improved Numerical Integration Method for Springback Predictions
NASA Astrophysics Data System (ADS)
Ibrahim, R.; Smith, L. M.; Golovashchenko, Sergey F.
2011-08-01
In this investigation, the focus is on the springback of steel sheets in V-die air bending. A full replication to a numerical integration algorithm presented rigorously in [1] to predict the springback in air bending was performed and confirmed successfully. Algorithm alteration and extensions were proposed here. The altered approach used in solving the moment equation numerically resulted in springback values much closer to the trend presented by the experimental data, Although investigation here extended to use a more realistic work-hardening model, the differences in the springback values obtained by both hardening models were almost negligible. The algorithm was extended to be applied on thin sheets down to 0.8 mm. Results show that this extension is possible as verified by FEA and other published experiments on TRIP steel sheets.
Methods, Software and Tools for Three Numerical Applications. Final report
E. R. Jessup
2000-03-01
This is a report of the results of the authors work supported by DOE contract DE-FG03-97ER25325. They proposed to study three numerical problems. They are: (1) the extension of the PMESC parallel programming library; (2) the development of algorithms and software for certain generalized eigenvalue and singular value (SVD) problems, and (3) the application of techniques of linear algebra to an information retrieval technique known as latent semantic indexing (LSI).
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.
Finite strip method combined with other numerical methods for the analysis of plates
NASA Astrophysics Data System (ADS)
Cheung, M. S.; Li, Wenchang
1992-09-01
Finite plate strips are combined with finite elements or boundary elements in the analysis of rectangular plates with some minor irregularities such as openings, skew edges, etc. The plate is divided into regular and irregular regions. The regular region is analyzed by the finite strip method while the irregular one is analyzed by the finite element or boundary element method. A special transition element and strip are developed in order to connect the both regions. Numerical examples will show the accuracy and efficiency of this combined analysis.
Spectral methods in general relativity and large Randall-Sundrum II black holes
Abdolrahimi, Shohreh; Cattoën, Céline; Page, Don N.; Yaghoobpour-Tari, Shima E-mail: celine.cattoen-gilbert@canterbury.ac.nz E-mail: yaghoobp@ualberta.ca
2013-06-01
Using a novel numerical spectral method, we have found solutions for large static Randall-Sundrum II (RSII) black holes by perturbing a numerical AdS{sub 5}-CFT{sub 4} solution to the Einstein equation with a negative cosmological constant Λ that is asymptotically conformal to the Schwarzschild metric. We used a numerical spectral method independent of the Ricci-DeTurck-flow method used by Figueras, Lucietti, and Wiseman for a similar numerical solution. We have compared our black-hole solution to the one Figueras and Wiseman have derived by perturbing their numerical AdS{sub 5}-CFT{sub 4} solution, showing that our solution agrees closely with theirs. We have obtained a closed-form approximation to the metric of the black hole on the brane. We have also deduced the new results that to first order in 1/(−ΛM{sup 2}), the Hawking temperature and entropy of an RSII static black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about 4.7/(−Λ)
NASA Technical Reports Server (NTRS)
Chamberlain, D. M.; Elliot, J. L.
1997-01-01
We present a method for speeding up numerical calculations of a light curve for a stellar occultation by a planetary atmosphere with an arbitrary atmospheric model that has spherical symmetry. This improved speed makes least-squares fitting for model parameters practical. Our method takes as input several sets of values for the first two radial derivatives of the refractivity at different values of model parameters, and interpolates to obtain the light curve at intermediate values of one or more model parameters. It was developed for small occulting bodies such as Pluto and Triton, but is applicable to planets of all sizes. We also present the results of a series of tests showing that our method calculates light curves that are correct to an accuracy of 10(exp -4) of the unocculted stellar flux. The test benchmarks are (i) an atmosphere with a l/r dependence of temperature, which yields an analytic solution for the light curve, (ii) an atmosphere that produces an exponential refraction angle, and (iii) a small-planet isothermal model. With our method, least-squares fits to noiseless data also converge to values of parameters with fractional errors of no more than 10(exp -4), with the largest errors occurring in small planets. These errors are well below the precision of the best stellar occultation data available. Fits to noisy data had formal errors consistent with the level of synthetic noise added to the light curve. We conclude: (i) one should interpolate refractivity derivatives and then form light curves from the interpolated values, rather than interpolating the light curves themselves; (ii) for the most accuracy, one must specify the atmospheric model for radii many scale heights above half light; and (iii) for atmospheres with smoothly varying refractivity with altitude, light curves can be sampled as coarsely as two points per scale height.
Numerical methods for a general class of porous medium equations
Rose, M. E.
1980-03-01
The partial differential equation par. deltau/par. deltat + par. delta(f(u))/par. deltax = par. delta(g(u)par. deltau/par. deltax)/par. deltax, where g(u) is a non-negative diffusion coefficient that may vanish for one or more values of u, was used to model fluid flow through a porous medium. Error estimates for a numerical procedure to approximate the solution are derived. A revised version of this report will appear in Computers and Mathematics with Applications.
Magnetohydrodynamic (MHD) modelling of solar active phenomena via numerical methods
NASA Technical Reports Server (NTRS)
Wu, S. T.
1988-01-01
Numerical ideal MHD models for the study of solar active phenomena are summarized. Particular attention is given to the following physical phenomena: (1) local heating of a coronal loop in an isothermal and stratified atmosphere, and (2) the coronal dynamic responses due to magnetic field movement. The results suggest that local heating of a magnetic loop will lead to the enhancement of the density of the neighboring loops through MHD wave compression. It is noted that field lines can be pinched off and may form a self-contained magnetized plasma blob that may move outward into interplanetary space.
A Numerical Simulation of Cosmic Ray Modulation Near the Heliopause. II. Some Physical Insights
NASA Astrophysics Data System (ADS)
Luo, Xi; Potgieter, Marius S.; Zhang, Ming; Pogorelov, Nikolai V.; Feng, Xueshang; du Toit Strauss, R.
2016-08-01
Cosmic ray (CR) transport near the heliopause (HP) is studied using a hybrid transport model, with the parameters constrained by observations from the Voyager 1 spacecraft. We simulate the CR radial flux along different directions in the heliosphere. There is no well-defined thin layer between the solar wind region and the interstellar region along the tail and polar directions of the heliosphere. By analyzing the radial flux curve along the direction of Voyager 2, together with its trajectory information, the crossing time of the HP by Voyager 2 is predicted to be in 2017.14. We simulate the CR radial flux for different energy values along the direction of Voyager 1. We find that there is only a modest modulation region of about 10 au wide beyond the HP, so that Voyager 1 observing the Local Interstellar Spectra is justified in numerical modeling. We analyze the heliospheric exit information of pseudo-particles in our stochastic numerical (time-backward) method, conjecturing that they represent the behavior of CR particles, and we find that pseudo-particles that have been traced from the nose region exit in the tail region. This implies that many CR particles diffuse directly from the heliospheric tail region to the nose region near the HP. In addition, when pseudo-particles were traced from the Local Interstellar Medium (LISM), it is found that their exit location (entrance for real particles) from the simulation domain is along the prescribed Interstellar Magnetic Field direction. This indicates that parallel diffusion dominates CR particle transport in the LISM.
Projection methods for the numerical solution of Markov chain models
NASA Technical Reports Server (NTRS)
Saad, Youcef
1989-01-01
Projection methods for computing stationary probability distributions for Markov chain models are presented. A general projection method is a method which seeks an approximation from a subspace of small dimension to the original problem. Thus, the original matrix problem of size N is approximated by one of dimension m, typically much smaller than N. A particularly successful class of methods based on this principle is that of Krylov subspace methods which utilize subspaces of the form span(v,av,...,A(exp m-1)v). These methods are effective in solving linear systems and eigenvalue problems (Lanczos, Arnoldi,...) as well as nonlinear equations. They can be combined with more traditional iterative methods such as successive overrelaxation, symmetric successive overrelaxation, or with incomplete factorization methods to enhance convergence.
Biphasic indentation of articular cartilage--II. A numerical algorithm and an experimental study.
Mow, V C; Gibbs, M C; Lai, W M; Zhu, W B; Athanasiou, K A
1989-01-01
Part I (Mak et al., 1987, J. Biomechanics 20, 703-714) presented the theoretical solutions for the biphasic indentation of articular cartilage under creep and stress-relaxation conditions. In this study, using the creep solution, we developed an efficient numerical algorithm to compute all three material coefficients of cartilage in situ on the joint surface from the indentation creep experiment. With this method we determined the average values of the aggregate modulus. Poisson's ratio and permeability for young bovine femoral condylar cartilage in situ to be HA = 0.90 MPa, vs = 0.39 and k = 0.44 x 10(-15) m4/Ns respectively, and those for patellar groove cartilage to be HA = 0.47 MPa, vs = 0.24, k = 1.42 x 10(-15) m4/Ns. One surprising finding from this study is that the in situ Poisson's ratio of cartilage (0.13-0.45) may be much less than those determined from measurements performed on excised osteochondral plugs (0.40-0.49) reported in the literature. We also found the permeability of patellar groove cartilage to be several times higher than femoral condyle cartilage. These findings may have important implications on understanding the functional behavior of cartilage in situ and on methods used to determine the elastic moduli of cartilage using the indentation experiments.
Ab initio theory of superconductivity in a magnetic field. II. Numerical solution
NASA Astrophysics Data System (ADS)
Linscheid, A.; Sanna, A.; Gross, E. K. U.
2015-07-01
We numerically investigate the spin density functional theory for superconductors (SpinSCDFT) and the approximated exchange-correlation functional, derived and presented in the preceding Paper I [A. Linscheid et al., Phys. Rev. B 92, 024505 (2015), 10.1103/PhysRevB.92.024505]. As a test system, we employ a free-electron gas featuring an exchange splitting, a phononic pairing field, and a Coulomb repulsion. SpinSCDFT results are compared with Sarma, the Bardeen-Cooper-Schrieffer theory, and with an Eliashberg type of approach. We find that the spectrum of the superconducting Kohn-Sham SpinSCDFT system is not in agreement with the true quasiparticle structure. Therefore, starting from the Dyson equation, we derive a scheme that allows to compute the many-body excitations of the superconductor and represents the extension to superconductivity of the G0W0 method in band-structure theory. This superconducting G0W0 method vastly improves the predicted spectra.
Nguyen, Tam H.; Song, Junho; Paulino, Glaucio H.
2008-02-15
Probabilistic fracture analyses are performed for investigating uncertain fracture response of Functionally Graded Material (FGM) structures. The First-Order-Reliability-Method (FORM) is implemented into an existing Finite Element code for FGM (FE-FGM), which was previously developed at the University of Illinois at Urbana-Champaign. The computational simulation will be used in order to estimate the probability of crack initiation with uncertainties in the material properties only. The two-step probability analysis method proposed in the companion paper is illustrated by a numerical example of a composite strip with an edge crack. First, the reliability index of a crack initiation event is estimated as we vary the mean and standard deviation of the slope and the location of the inflection point of the spatial profile of Young's modulus. Secondly, the reliability index is estimated as we vary the standard deviation and the correlation length of the random field that characterize the random spatial fluctuation of Young's modulus. Also investigated is the relative importance of the uncertainties in the toughness compared to those in Young's modulus.
A numerical model of non-equilibrium thermal plasmas. II. Governing equations
Li HePing; Zhang XiaoNing; Xia Weidong
2013-03-15
Governing equations and the corresponding physical properties of the plasmas are both prerequisites for studying the fundamental processes in a non-equilibrium thermal plasma system numerically. In this paper, a kinetic derivation of the governing equations used for describing the complicated thermo-electro-magneto-hydrodynamic-chemical coupling effects in non-equilibrium thermal plasmas is presented. This derivation, which is achieved using the Chapman-Enskog method, is completely consistent with the theory of the transport properties reported in the previous paper by the same authors. It is shown, based on this self-consistent theory, that the definitions of the specific heat at constant pressure and the reactive thermal conductivity of two-temperature plasmas are not necessary. The governing equations can be reduced to their counterparts under local thermodynamic equilibrium (LTE) and local chemical equilibrium (LCE) conditions. The general method for the determination of the boundary conditions of the solved variables is also discussed briefly. The two papers establish a self-consistent physical-mathematical model that describes the complicated physical and chemical processes in a thermal plasma system for the cases both in LTE or LCE conditions and under non-equilibrium conditions.
Numerical conformal mapping methods for exterior and doubly connected regions
DeLillo, T.K.; Pfaltzgraff, J.A.
1996-12-31
Methods are presented and analyzed for approximating the conformal map from the exterior of the disk to the exterior a smooth, simple closed curve and from an annulus to a bounded, doubly connected region with smooth boundaries. The methods are Newton-like methods for computing the boundary correspondences and conformal moduli similar to Fornberg`s method for the interior of the disk. We show that the linear systems are discretizations of the identity plus a compact operator and, hence, that the conjugate gradient method converges superlinearly.
An introduction to nonlinear programming. IV - Numerical methods for constrained minimization
NASA Technical Reports Server (NTRS)
Sorenson, H. W.; Koble, H. M.
1976-01-01
An overview is presented of the numerical solution of constrained minimization problems. Attention is given to both primal and indirect (linear programs and unconstrained minimizations) methods of solution.
Numerical methods for simulating blood flow at macro, micro, and multi scales.
Imai, Yohsuke; Omori, Toshihiro; Shimogonya, Yuji; Yamaguchi, Takami; Ishikawa, Takuji
2016-07-26
In the past decade, numerical methods for the computational biomechanics of blood flow have progressed to overcome difficulties in diverse applications from cellular to organ scales. Such numerical methods may be classified by the type of computational mesh used for the fluid domain, into fixed mesh methods, moving mesh (boundary-fitted mesh) methods, and mesh-free methods. The type of computational mesh used is closely related to the characteristics of each method. We herein provide an overview of numerical methods recently used to simulate blood flow at macro and micro scales, with a focus on computational meshes. We also discuss recent progress in the multi-scale modeling of blood flow.
Analysis of free turbulent shear flows by numerical methods
NASA Technical Reports Server (NTRS)
Korst, H. H.; Chow, W. L.; Hurt, R. F.; White, R. A.; Addy, A. L.
1973-01-01
Studies are described in which the effort was essentially directed to classes of problems where the phenomenologically interpreted effective transport coefficients could be absorbed by, and subsequently extracted from (by comparison with experimental data), appropriate coordinate transformations. The transformed system of differential equations could then be solved without further specifications or assumptions by numerical integration procedures. An attempt was made to delineate different regimes for which specific eddy viscosity models could be formulated. In particular, this would account for the carryover of turbulence from attached boundary layers, the transitory adjustment, and the asymptotic behavior of initially disturbed mixing regions. Such models were subsequently used in seeking solutions for the prescribed two-dimensional test cases, yielding a better insight into overall aspects of the exchange mechanisms.
Feasibility study of the numerical integration of shell equations using the field method
NASA Technical Reports Server (NTRS)
Cohen, G. A.
1973-01-01
The field method is developed for arbitrary open branch domains subjected to general linear boundary conditions. Although closed branches are within the scope of the method, they are not treated here. The numerical feasibility of the method has been demonstrated by implementing it in a computer program for the linear static analysis of open branch shells of revolution under asymmetric loads. For such problems the field method eliminates the well-known numerical problem of long subintervals associated with the rapid growth of extraneous solutions. Also, the method appears to execute significantly faster than other numerical integration methods.
Using MACSYMA to drive numerical methods to computer radiation integrals
Clark, B.A.
1986-01-01
Because the emission of thermal radiation is characterized by the Planck emission spectrum, a multigroup solution of the thermal-radiation transport equation demands the calculation of definite integrals of the Planck spectrum. In the past, many approximate methods have been used with varying degrees of accuracy and efficiency. This paper describes how a symbolic algebra package, in this case MACSYMA is used to develop new methods for accurately and efficiently evaluating multigroup Planck integrals. The advantage of using a symbolic algebra package is that the job of developing the new methods is accomplished more efficiently.
Relativistic magnetohydrodynamics in dynamical spacetimes: Numerical methods and tests
Duez, Matthew D.; Liu, Yuk Tung; Shapiro, Stuart L.; Stephens, Branson C.
2005-07-15
Many problems at the forefront of theoretical astrophysics require the treatment of magnetized fluids in dynamical, strongly curved spacetimes. Such problems include the origin of gamma-ray bursts, magnetic braking of differential rotation in nascent neutron stars arising from stellar core collapse or binary neutron star merger, the formation of jets and magnetized disks around newborn black holes, etc. To model these phenomena, all of which involve both general relativity (GR) and magnetohydrodynamics (MHD), we have developed a GRMHD code capable of evolving MHD fluids in dynamical spacetimes. Our code solves the Einstein-Maxwell-MHD system of coupled equations in axisymmetry and in full 3+1 dimensions. We evolve the metric by integrating the Baumgarte-Shapiro-Shibata-Nakamura equations, and use a conservative, shock-capturing scheme to evolve the MHD equations. Our code gives accurate results in standard MHD code-test problems, including magnetized shocks and magnetized Bondi flow. To test our code's ability to evolve the MHD equations in a dynamical spacetime, we study the perturbations of a homogeneous, magnetized fluid excited by a gravitational plane wave, and we find good agreement between the analytic and numerical solutions.
Numerical Stability and Convergence of Approximate Methods for Conservation Laws
NASA Astrophysics Data System (ADS)
Galkin, V. A.
We present the new approach to background of approximate methods convergence based on functional solutions theory for conservation laws. The applications to physical kinetics, gas and fluid dynamics are considered.
A numerical method for eigenvalue problems in modeling liquid crystals
Baglama, J.; Farrell, P.A.; Reichel, L.; Ruttan, A.; Calvetti, D.
1996-12-31
Equilibrium configurations of liquid crystals in finite containments are minimizers of the thermodynamic free energy of the system. It is important to be able to track the equilibrium configurations as the temperature of the liquid crystals decreases. The path of the minimal energy configuration at bifurcation points can be computed from the null space of a large sparse symmetric matrix. We describe a new variant of the implicitly restarted Lanczos method that is well suited for the computation of extreme eigenvalues of a large sparse symmetric matrix, and we use this method to determine the desired null space. Our implicitly restarted Lanczos method determines adoptively a polynomial filter by using Leja shifts, and does not require factorization of the matrix. The storage requirement of the method is small, and this makes it attractive to use for the present application.
Cox, T.J.; Runkel, R.L.
2008-01-01
Past applications of one-dimensional advection, dispersion, and transient storage zone models have almost exclusively relied on a central differencing, Eulerian numerical approximation to the nonconservative form of the fundamental equation. However, there are scenarios where this approach generates unacceptable error. A new numerical scheme for this type of modeling is presented here that is based on tracking Lagrangian control volumes across a fixed (Eulerian) grid. Numerical tests are used to provide a direct comparison of the new scheme versus nonconservative Eulerian numerical methods, in terms of both accuracy and mass conservation. Key characteristics of systems for which the Lagrangian scheme performs better than the Eulerian scheme include: nonuniform flow fields, steep gradient plume fronts, and pulse and steady point source loadings in advection-dominated systems. A new analytical derivation is presented that provides insight into the loss of mass conservation in the nonconservative Eulerian scheme. This derivation shows that loss of mass conservation in the vicinity of spatial flow changes is directly proportional to the lateral inflow rate and the change in stream concentration due to the inflow. While the nonconservative Eulerian scheme has clearly worked well for past published applications, it is important for users to be aware of the scheme's limitations. ?? 2008 ASCE.
Improved numerical methods for turbulent viscous recirculating flows
NASA Technical Reports Server (NTRS)
Turan, A.; Vandoormaal, J. P.
1988-01-01
The performance of discrete methods for the prediction of fluid flows can be enhanced by improving the convergence rate of solvers and by increasing the accuracy of the discrete representation of the equations of motion. This report evaluates the gains in solver performance that are available when various acceleration methods are applied. Various discretizations are also examined and two are recommended because of their accuracy and robustness. Insertion of the improved discretization and solver accelerator into a TEACH mode, that has been widely applied to combustor flows, illustrates the substantial gains to be achieved.
Numerical solution of 2D-vector tomography problem using the method of approximate inverse
NASA Astrophysics Data System (ADS)
Svetov, Ivan; Maltseva, Svetlana; Polyakova, Anna
2016-08-01
We propose a numerical solution of reconstruction problem of a two-dimensional vector field in a unit disk from the known values of the longitudinal and transverse ray transforms. The algorithm is based on the method of approximate inverse. Numerical simulations confirm that the proposed method yields good results of reconstruction of vector fields.
Numerical experiments with a parallel conjugate gradient method
Oppe, T.C.; Kincaid, D.R.
1987-04-01
A parallel version of the conjugate gradient method introduced by Seager is implemented using various Cray multitasking tools. The parallel algorithm is used to solve a model partial differential equation on the unit square for various mesh sizes. Speed-up factors are given, and the effects of bank conflicts are noted. 8 refs., 10 figs.
Evaluating numerical ODE/DAE methods, algorithms and software
NASA Astrophysics Data System (ADS)
Soderlind, Gustaf; Wang, Lina
2006-01-01
Until recently, the testing of ODE/DAE software has been limited to simple comparisons and benchmarking. The process of developing software from a mathematically specified method is complex: it entails constructing control structures and objectives, selecting iterative methods and termination criteria, choosing norms and many more decisions. Most software constructors have taken a heuristic approach to these design choices, and as a consequence two different implementations of the same method may show significant differences in performance. Yet it is common to try to deduce from software comparisons that one method is better than another. Such conclusions are not warranted, however, unless the testing is carried out under true ceteris paribus conditions. Moreover, testing is an empirical science and as such requires a formal test protocol; without it conclusions are questionable, invalid or even false.We argue that ODE/DAE software can be constructed and analyzed by proven, "standard" scientific techniques instead of heuristics. The goals are computational stability, reproducibility, and improved software quality. We also focus on different error criteria and norms, and discuss modifications to DASPK and RADAU5. Finally, some basic principles of a test protocol are outlined and applied to testing these codes on a variety of problems.
A survey of numerical methods for shock physics applications
Hertel, E.S. Jr.
1997-10-01
Hydrocodes or more accurately, shock physics analysis packages, have been widely used in the US Department of Energy (DOE) laboratories and elsewhere around the world for over 30 years. Initial applications included weapons effects studies where the pressure levels were high enough to disregard the material strength, hence the term hydrocode. Over the last 30 years, Sandia has worked extensively to develop and apply advanced hydrocodes to armor/anti-armor interactions, warhead design, high explosive initiation, and nuclear weapon safety issues. The needs of the DOE have changed over the last 30 years, especially over the last decade. A much stronger emphasis is currently placed on the details of material deformation and high explosive initiation phenomena. The hydrocodes of 30 years ago have now evolved into sophisticated analysis tools that can replace testing in some situations and complement it in all situations. A brief history of the development of hydrocodes in the US will be given. The author also discusses and compares the four principal methods in use today for the solution of the conservation equations of mass, momentum, and energy for shock physics applications. The techniques discussed are the Eulerian methods currently employed by the Sandia multi-dimensional shock physics analysis package known as CTH; the element based Lagrangian method currently used by codes like DYNA; the element free Lagrangian method (also known as smooth particle hydrodynamics) used by codes like the Los Alamos code SPHINX; and the Arbitrary Lagrangian Eulerian methods used by codes like the Lawrence Livermore code CALE or the Sandia code ALEGRA.
A novel method for preparation of cobalt(II) and lead(II) carbonates
NASA Astrophysics Data System (ADS)
Refat, M. S.; Teleb, S. M.; Sadeek, S. A.
2004-10-01
Cobalt(II) carbonate, CoCO 3·4H 2O and lead(II) carbonate, PbCO 3·2H 2O were synthesis by a new simple method during the reaction of aqueous solutions of CoX 2 (X = Cl -, NO 3- and CH 3COO -) and PbX 2 (X = NO 3- or CH 3COO -), respectively, with urea at ˜85 °C for 2 h. The infrared spectra of the reaction products clearly indicates the absence of the bands due to coordinated urea, but show the characteristic bands of ionic carbonate. A general mechanisms describing the formation of cobalt and lead carbonates are suggested.
Sound graphs: a numerical data analysis method for the blind.
Mansur, D L; Blattner, M M; Joy, K I
1985-06-01
A system for the creation of computer-generated sound patterns of two-dimensional line graphs is described. The objectives of the system are to provide the blind with a means of understanding line graphs in the holistic manner used by those with sight. A continuously varying pitch is used to represent motion in the x direction. To test the feasibility of using sound to represent graphs, a prototype system was developed and human factors experimenters were performed. Fourteen subjects were used to compare the tactile-graph methods normally used by the blind to these new sound graphs. It was discovered that mathematical concepts such as symmetry, monotonicity, and the slopes of lines could be determined quickly using sound. Even better performance may be expected with additional training. The flexibility, speed, cost-effectiveness, and greater measure of independence provided the blind or sight-impaired using these methods was demonstrated. PMID:2932516
Extremal polynomials and methods of optimization of numerical algorithms
Lebedev, V I
2004-10-31
Chebyshev-Markov-Bernstein-Szegoe polynomials C{sub n}(x) extremal on [-1,1] with weight functions w(x)=(1+x){sup {alpha}}(1- x){sup {beta}}/{radical}(S{sub l}(x)) where {alpha},{beta}=0,1/2 and S{sub l}(x)={pi}{sub k=1}{sup m}(1-c{sub k}T{sub l{sub k}}(x))>0 are considered. A universal formula for their representation in trigonometric form is presented. Optimal distributions of the nodes of the weighted interpolation and explicit quadrature formulae of Gauss, Markov, Lobatto, and Rado types are obtained for integrals with weight p(x)=w{sup 2}(x)(1-x{sup 2}){sup -1/2}. The parameters of optimal Chebyshev iterative methods reducing the error optimally by comparison with the initial error defined in another norm are determined. For each stage of the Fedorenko-Bakhvalov method iteration parameters are determined which take account of the results of the previous calculations. Chebyshev filters with weight are constructed. Iterative methods of the solution of equations containing compact operators are studied.
Numerical simulation of fluid-structure interactions with stabilized finite element method
NASA Astrophysics Data System (ADS)
Sváček, Petr
2016-03-01
This paper is interested to the interactions of the incompressible flow with a flexibly supported airfoil. The bending and the torsion modes are considered. The problem is mathematically described. The numerical method is based on the finite element method. A combination of the streamline-upwind/Petrov-Galerkin and pressure stabilizing/Petrov-Galerkin method is used for the stabilization of the finite element method. The numerical results for a three-dimensional problem of flow over an airfoil are shown.
Design of braided composite tubes by numerical analysis method
Hamada, Hiroyuki; Fujita, Akihiro; Maekawa, Zenichiro; Nakai, Asami; Yokoyama, Atsushi
1995-11-01
Conventional composite laminates have very poor strength through thickness and as a result are limited in their application for structural parts with complex shape. In this paper, the design for braided composite tube was proposed. The concept of analysis model which involved from micro model to macro model was presented. This method was applied to predict bending rigidity and initial fracture stress under bending load of the braided tube. The proposed analytical procedure can be included as a unit in CAE system for braided composites.
NASA Astrophysics Data System (ADS)
Lamas, Luís N.; Leitão, Noemí S.; Esteves, Carlos; Plasencia, Nadir
2014-05-01
The underground structures of the Venda Nova II reversible hydroelectric power scheme present features that make it an interesting case study. Worthy of mention are the inclination and length of the unlined pressure tunnel, the high water head and the great depth of the powerhouse cavern. In projects of this type, the main effect of the internal water pressure in the pressure tunnel is the establishment of seepage from the tunnel into the rock mass, which can reach the adits and the powerhouse cavern. This seepage is influenced by several factors, such as the geometry of the underground openings, the rock mass properties—namely, the joints characteristics—and the stress state resulting from the excavation and from the internal water pressure. This article presents the main features of the underground structures of the Venda Nova II scheme and a detailed description of the observed behaviour during the first infilling of the pressure tunnel. A three-dimensional multi-laminated numerical model of the rock mass hydromechanical behaviour was developed to help understand the observed behaviour. The model assumptions in regard to the geometry of the openings, the jointing pattern, the rock mass hydraulic and mechanical behaviour, as well as the hydromechanical interaction, are described. Results obtained with the numerical model are presented and compared with the observed behaviour. Finally, the validity and importance of the numerical tools for the interpretation of the rock mass hydromechanical behaviour is discussed.
Two Different Methods for Numerical Solution of the Modified Burgers' Equation
Karakoç, Seydi Battal Gazi; Başhan, Ali; Geyikli, Turabi
2014-01-01
A numerical solution of the modified Burgers' equation (MBE) is obtained by using quartic B-spline subdomain finite element method (SFEM) over which the nonlinear term is locally linearized and using quartic B-spline differential quadrature (QBDQM) method. The accuracy and efficiency of the methods are discussed by computing L 2 and L ∞ error norms. Comparisons are made with those of some earlier papers. The obtained numerical results show that the methods are effective numerical schemes to solve the MBE. A linear stability analysis, based on the von Neumann scheme, shows the SFEM is unconditionally stable. A rate of convergence analysis is also given for the DQM. PMID:25162064
Fast Numerical Methods for the Design of Layered Photonic Structures with Rough Interfaces
NASA Technical Reports Server (NTRS)
Komarevskiy, Nikolay; Braginsky, Leonid; Shklover, Valery; Hafner, Christian; Lawson, John
2011-01-01
Modified boundary conditions (MBC) and a multilayer approach (MA) are proposed as fast and efficient numerical methods for the design of 1D photonic structures with rough interfaces. These methods are applicable for the structures, composed of materials with arbitrary permittivity tensor. MBC and MA are numerically validated on different types of interface roughness and permittivities of the constituent materials. The proposed methods can be combined with the 4x4 scattering matrix method as a field solver and an evolutionary strategy as an optimizer. The resulted optimization procedure is fast, accurate, numerically stable and can be used to design structures for various applications.
Numerical computation of sapphire crystal growth using heat exchanger method
NASA Astrophysics Data System (ADS)
Lu, Chung-Wei; Chen, Jyh-Chen
2001-05-01
The finite element software FIDAP is employed to study the temperature and velocity distribution and the interface shape during a large sapphire crystal growth process using a heat exchanger method (HEM). In the present study, the energy input to the crucible by the radiation and convection inside the furnace and the energy output through the heat exchanger is modeled by the convection boundary conditions. The effects of the various growth parameters are studied. It is found that the contact angle is obtuse before the solid-melt interface touches the sidewall of the crucible. Therefore, hot spots always appear in this process. The maximum convexity decreases significantly when the cooling-zone radius (RC) increases. The maximum convexity also decreases significantly as the combined convection coefficient inside the furnace (hI) decreases.
Transforming Mean and Osculating Elements Using Numerical Methods
NASA Technical Reports Server (NTRS)
Ely, Todd A.
2010-01-01
Mean element propagation of perturbed two body orbits has as its mathematical basis averaging theory of nonlinear dynamical systems. Averaged mean elements define the long-term evolution characteristics of an orbit. Using averaging theory, a near identity transformation can be found that transforms the mean elements back to the osculating elements that contain short period terms in addition to the secular and long period mean elements. The ability to perform the conversion is necessary so that orbit design conducted in mean elements can be converted back into osculating results. In the present work, this near identity transformation is found using the Fast Fourier Transform. An efficient method is found that is capable of recovering the osculating elements to first order
IMPROVED NUMERICAL METHODS FOR MODELING RIVER-AQUIFER INTERACTION.
Tidwell, Vincent Carroll; Sue Tillery; Phillip King
2008-09-01
A new option for Local Time-Stepping (LTS) was developed to use in conjunction with the multiple-refined-area grid capability of the U.S. Geological Survey's (USGS) groundwater modeling program, MODFLOW-LGR (MF-LGR). The LTS option allows each local, refined-area grid to simulate multiple stress periods within each stress period of a coarser, regional grid. This option is an alternative to the current method of MF-LGR whereby the refined grids are required to have the same stress period and time-step structure as the coarse grid. The MF-LGR method for simulating multiple-refined grids essentially defines each grid as a complete model, then for each coarse grid time-step, iteratively runs each model until the head and flux changes at the interfacing boundaries of the models are less than some specified tolerances. Use of the LTS option is illustrated in two hypothetical test cases consisting of a dual well pumping system and a hydraulically connected stream-aquifer system, and one field application. Each of the hypothetical test cases was simulated with multiple scenarios including an LTS scenario, which combined a monthly stress period for a coarse grid model with a daily stress period for a refined grid model. The other scenarios simulated various combinations of grid spacing and temporal refinement using standard MODFLOW model constructs. The field application simulated an irrigated corridor along the Lower Rio Grande River in New Mexico, with refinement of a small agricultural area in the irrigated corridor.The results from the LTS scenarios for the hypothetical test cases closely replicated the results from the true scenarios in the refined areas of interest. The head errors of the LTS scenarios were much smaller than from the other scenarios in relation to the true solution, and the run times for the LTS models were three to six times faster than the true models for the dual well and stream-aquifer test cases, respectively. The results of the field application
Genomic DNA microextraction: a method to screen numerous samples.
Ramírez-Solis, R; Rivera-Pérez, J; Wallace, J D; Wims, M; Zheng, H; Bradley, A
1992-03-01
Many experimental designs require the analysis of genomic DNA from a large number of samples. Although the polymerase chain reaction (PCR) can be used, the Southern blot is preferred for many assays because of its inherent reliability. The rapid acceptance of PCR, despite a significant rate of false positive/negative results, is partly due to the disadvantages of the sample preparation process for Southern blot analysis. We have devised a rapid protocol to extract high-molecular-weight genomic DNA from a large number of samples. It involves the use of a single 96-well tissue culture dish to carry out all the steps of the sample preparation. This, coupled with the use of a multichannel pipette, facilitates the simultaneous analysis of multiple samples. The procedure may be automated since no centrifugation, mixing, or transferring of the samples is necessary. The method has been used to screen embryonic stem cell clones for the presence of targeted mutations at the Hox-2.6 locus and to obtain data from human blood.
Numerical methods on some structured matrix algebra problems
Jessup, E.R.
1996-06-01
This proposal concerned the design, analysis, and implementation of serial and parallel algorithms for certain structured matrix algebra problems. It emphasized large order problems and so focused on methods that can be implemented efficiently on distributed-memory MIMD multiprocessors. Such machines supply the computing power and extensive memory demanded by the large order problems. We proposed to examine three classes of matrix algebra problems: the symmetric and nonsymmetric eigenvalue problems (especially the tridiagonal cases) and the solution of linear systems with specially structured coefficient matrices. As all of these are of practical interest, a major goal of this work was to translate our research in linear algebra into useful tools for use by the computational scientists interested in these and related applications. Thus, in addition to software specific to the linear algebra problems, we proposed to produce a programming paradigm and library to aid in the design and implementation of programs for distributed-memory MIMD computers. We now report on our progress on each of the problems and on the programming tools.
NASA Astrophysics Data System (ADS)
Feng, Xueshang; Zhang, Man
2016-03-01
This paper presents a comparative study of divergence cleaning methods of magnetic field in the solar coronal three-dimensional numerical simulation. For such purpose, the diffusive method, projection method, generalized Lagrange multiplier method and constrained-transport method are used. All these methods are combined with a finite-volume scheme based on a six-component grid system in spherical coordinates. In order to see the performance between the four divergence cleaning methods, solar coronal numerical simulation for Carrington rotation 2056 has been studied. Numerical results show that the average relative divergence error is around 10^{-4.5} for the constrained-transport method, while about 10^{-3.1}- 10^{-3.6} for the other three methods. Although there exist some differences in the average relative divergence errors for the four employed methods, our tests show they can all produce basic structured solar wind.
Numerical Databases: Their Vital Role in Information Science. Part II: A Call to Action.
ERIC Educational Resources Information Center
Carter, G. C.
1985-01-01
In this second of two installments, a discussion of role of information science (IS) in numerical databases (NDBs) and vice versa highlights two elements of IS needed to develop NDBs: technical (hardware, software, artificial intelligence, degree of database reliability); social (man-machine interface, social infrastructure). Research requirements…
Equilibrium gas flow computations. II - An analysis of numerical formulations of conservation laws
NASA Technical Reports Server (NTRS)
Vinokur, Marcel; Liu, Yen
1988-01-01
Modern numerical techniques employing properties of flux Jacobian matrices are extended to general, equilibrium gas laws. Generalizations of the Beam-Warming scheme, Steger-Warming and van Leer flux-vector splittings, and Roe's approximate Riemann solver are presented for three-dimensional, time-varying grids. The approximations inherent in previous generalizations are discussed.
EFFECTS OF ELECTROOSMOSIS ON SOIL TEMPERATURE AND HYDRAULIC HEAD: II. NUMERICAL SIMULATION
A numerical model to simulate the distributions of voltage, soil temperature, and hydraulic head during the field test of electroosmosis was developed. The two-dimensional governing equations for the distributions of voltage, soil temperature, and hydraulic head within a cylindri...
NASA Astrophysics Data System (ADS)
Wang, Jiong; Steinmann, Paul
2016-05-01
This is part II of this series of papers. The aim of the current paper was to solve the governing PDE system derived in part I numerically, such that the procedure of variant reorientation in a magnetic shape memory alloy (MSMA) sample can be simulated. The sample to be considered in this paper has a 3D cuboid shape and is subject to typical magnetic and mechanical loading conditions. To investigate the demagnetization effect on the sample's response, the surrounding space of the sample is taken into account. By considering the different properties of the independent variables, an iterative numerical algorithm is proposed to solve the governing system. The related mathematical formulas and some techniques facilitating the numerical calculations are introduced. Based on the results of numerical simulations, the distributions of some important physical quantities (e.g., magnetization, demagnetization field, and mechanical stress) in the sample can be determined. Furthermore, the properties of configurational force on the twin interfaces are investigated. By virtue of the twin interface movement criteria derived in part I, the whole procedure of magnetic field- or stress-induced variant reorientations in the MSMA sample can be properly simulated.
Heck, C.L.; Andersen, J.G.M.
1985-11-01
A complete technical basis for implementation of the 3-D fast numerics in TRACB04 is presented. The 3-D fast numerics is a generalization of the predictor/corrector method previously developed for the 1-D components in TRACB. 20 figs.
NASA Astrophysics Data System (ADS)
Brooks, Jason W.; Matzner, Richard
2016-07-01
The LARES satellite is a laser-ranged space experiment to contribute to geophysics observation, and to measure the general relativistic Lense-Thirring effect. LARES consists of a solid tungsten alloy sphere, into which 92 fused-silica Cube Corner Reflectors (CCRs) are set in colatitude circles ("rows"). During its first four months in orbit it was observed to undergo an anomalous along-track orbital acceleration of approximately -0.4 pm/s2 (pm: = picometer). The first paper in this series (Eur. Phys. J. Plus 130, 206 (2015) - Paper I) computed the thermally induced along-track "thermal drag" on the LARES satellite during the first 126 days after launch. The results there suggest that the IR absorbance α and emissivity ɛ of the CCRs equal 0.60, a possible value for silica with slight surface contamination subjected to the space environment. Paper I computed an average thermal drag acceleration of -0.36 pm/s2 for a 120-day period starting with the 7th day after launch. The heating and the resultant along-track acceleration depend on the plane of the orbit, the sun position, and in particular on the occurrence of eclipses, all of which are functions of time. Thus we compute the thermal drag for specific days. The satellite is heated from two sources: sunlight and Earth's infrared (IR) radiation. Paper I worked in the fast-spin regime, where CCRs with the same colatitude can be taken to have the same temperature. Further, since all temperature variations (temporal or spatial) were small in this regime, Paper I linearized the Stefan-Boltzmann law and performed a Fourier series analysis. However, the spin rate of the satellite is expected currently ( ≈ day 1500) to be slow, of order ≈ 5 /orbit, so the "fast-spin equal-temperatures in a row" assumption is suspect. In this paper, which considers epochs up to 1580 days after launch, we do not linearize and we use direct numerical integration instead of Fourier methods. In addition to the along-track drag, this code
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.
NASA Astrophysics Data System (ADS)
Teodoro, M. F.
2012-09-01
We are particularly interested in the numerical solution of the functional differential equations with symmetric delay and advance. In this work, we consider a nonlinear forward-backward equation, the Fitz Hugh-Nagumo equation. It is presented a scheme which extends the algorithm introduced in [1]. A computational method using Newton's method, finite element method and method of steps is developped.
NASA Technical Reports Server (NTRS)
Rosenbaum, J. S.
1976-01-01
If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.
A fifth order implicit method for the numerical solution of differential-algebraic equations
NASA Astrophysics Data System (ADS)
Skvortsov, L. M.
2015-06-01
An implicit two-step Runge-Kutta method of fifth order is proposed for the numerical solution of differential and differential-algebraic equations. The location of nodes in this method makes it possible to estimate the values of higher derivatives at the initial and terminal points of an integration step. Consequently, the proposed method can be regarded as a finite-difference analog of the Obrechkoff method. Numerical results, some of which are presented in this paper, show that our method preserves its order while solving stiff equations and equations of indices two and three. This is the main advantage of the proposed method as compared with the available ones.
Chaotic structures of nonlinear magnetic fields. I - Theory. II - Numerical results
NASA Technical Reports Server (NTRS)
Lee, Nam C.; Parks, George K.
1992-01-01
A study of the evolutionary properties of nonlinear magnetic fields in flowing MHD plasmas is presented to illustrate that nonlinear magnetic fields may involve chaotic dynamics. It is shown how a suitable transformation of the coupled equations leads to Duffing's form, suggesting that the behavior of the general solution can also be chaotic. Numerical solutions of the nonlinear magnetic field equations that have been cast in the form of Duffing's equation are presented.
Advanced numerical methods for three dimensional two-phase flow calculations
Toumi, I.; Caruge, D.
1997-07-01
This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe`s method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations.
Four methods compared for measuring des-carboxy-prothrombin (PIVKA-II).
Widdershoven, J; van Munster, P; De Abreu, R; Bosman, H; van Lith, T; van der Putten-van Meyel, M; Motohara, K; Matsuda, I
1987-11-01
PIVKA-II (Protein Induced by Vitamin K Absence) is abnormal des-carboxylated prothrombin, which is present in vitamin K deficiency or in patients using warfarin. With a sensitive method for PIVKA-II, biochemical vitamin K deficiency can be established before clinical symptoms occur. We give an overview of methods used to detect PIVKA-II, and four selected methods are inter-compared: (a) measuring total factor II including PIVKA-II by using Echis carinatus snake venom as an activator of prothrombin; (b) measuring PIVKA-II by using snake venom as an activator of factor II after adsorption of functional factor II onto barium sulfate; (c) electrophoresis-immunofixation method; and (d) enzyme immunoassay. We found d to be the most sensitive and reliable method for PIVKA-II.
A numerical method for approximating antenna surfaces defined by discrete surface points
NASA Technical Reports Server (NTRS)
Lee, R. Q.; Acosta, R.
1985-01-01
A simple numerical method for the quadratic approximation of a discretely defined reflector surface is described. The numerical method was applied to interpolate the surface normal of a parabolic reflector surface from a grid of nine closest surface points to the point of incidence. After computing the surface normals, the geometrical optics and the aperture integration method using the discrete Fast Fourier Transform (FFT) were applied to compute the radiaton patterns for a symmetric and an offset antenna configurations. The computed patterns are compared to that of the analytic case and to the patterns generated from another numerical technique using the spline function approximation. In the paper, examples of computations are given. The accuracy of the numerical method is discussed.
Novel Methods for 3D Numerical Simulation of Meteor Radar Reflections
NASA Astrophysics Data System (ADS)
Räbinä, J.; Mönkölä, S.; Rossi, T.; Markkanen, J.; Gritsevich, M.; Muinonen, K.
2016-08-01
We model the radar reflections in a three-dimensional space as time-harmonic electromagnetic scattering from plasmatic obstacles. We introduce two novel methods for numerical simulation of meteor radar reflections.
The Cooperative Lifestyle Intervention Program-II (CLIP-II): Design and Methods
Marsh, Anthony P.; Janssen, James A.; Ambrosius, Walter T.; Burdette, Jonathan H.; Gaukstern, Jill E.; Morgan, Ashley R.; Nesbit, Beverly A.; Paolini, J. Brielle; Sheedy, Jessica L.; Rejeski, W. Jack
2013-01-01
A complication of cardiovascular disease (CVD) and the metabolic syndrome (MetS) among older adults is loss of mobility. The American Heart Association has identified weight management as a core component of secondary prevention programs for CVD and is an important risk factor for physical disability. The American Society for Nutrition and the Obesity Society have highlighted the need for long-term randomized clinical trials to evaluate the independent and additive effects of diet-induced weight loss (WL) and physical activity in older persons on outcomes such as mobility, muscle function, and obesity related diseases. Here we describe the rationale, design, and methods of a translational study, the Cooperative Lifestyle Intervention Program-II (CLIP-II). CLIP-II will randomize 252 obese, older adults with CVD or MetS to a weight loss only treatment (WL), aerobic exercise training (AT)+WL, or resistance exercise training (RT)+WL for 18 months. The dual primary outcomes are mobility and knee extensor strength. The interventions will be delivered by YMCA community partners with our staff as trainers and advisers. This study will provide the first large scale trial to evaluate the effects of diet-induced WL on mobility in obese, older adults with CVD or MetS as compared to WL combined with two different modes of physical activity (AT and RT). Because uncertainty exists about the best approach for promoting WL in older adults due to concerns with the loss of lean mass, the design also permits a contrast between AT+WL and RT+WL on muscle strength. PMID:23974035
NASA Technical Reports Server (NTRS)
Gottlieb, D.; Turkel, E.
1980-01-01
New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.
Impact of Energy Slope Averaging Methods on Numerical Solution of 1D Steady Gradually Varied Flow
NASA Astrophysics Data System (ADS)
Artichowicz, Wojciech; Prybytak, Dzmitry
2015-12-01
In this paper, energy slope averaging in the one-dimensional steady gradually varied flow model is considered. For this purpose, different methods of averaging the energy slope between cross-sections are used. The most popular are arithmetic, geometric, harmonic and hydraulic means. However, from the formal viewpoint, the application of different averaging formulas results in different numerical integration formulas. This study examines the basic properties of numerical methods resulting from different types of averaging.
Time-optimal control of the race car: a numerical method to emulate the ideal driver
NASA Astrophysics Data System (ADS)
Kelly, D. P.; Sharp, R. S.
2010-12-01
A numerical method for the time-optimal control of the race car is presented. The method is then used to perform the role of the driver in numerical simulations of manoeuvres at the limit of race car performance. The method does not attempt to model the driver but rather replaces the driver with methods normally associated with numerical optimal control. The method simultaneously finds the optimal driven line and the driver control inputs (steer, throttle and brake) to drive this line in minimum time. In principle, the method is capable of operation with arbitrarily complex vehicle models as it requires only limited access to the vehicle model state vector. It also requires solution of the differential equation representing the vehicle model in only the forward time direction and is hence capable of simulating the full vehicle transient response.
Numerical method for estimating the size of chaotic regions of phase space
Henyey, F.S.; Pomphrey, N.
1987-10-01
A numerical method for estimating irregular volumes of phase space is derived. The estimate weights the irregular area on a surface of section with the average return time to the section. We illustrate the method by application to the stadium and oval billiard systems and also apply the method to the continuous Henon-Heiles system. 15 refs., 10 figs. (LSP)
Antolin, P.; Okamoto, T. J.; Doorsselaere, T. Van; Yokoyama, T.
2015-08-10
Transverse magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere and may be responsible for generating the Sun’s million-degree outer atmosphere. However, direct evidence of the dissipation process and heating from these waves remains elusive. Through advanced numerical simulations combined with appropriate forward modeling of a prominence flux tube, we provide the observational signatures of transverse MHD waves in prominence plasmas. We show that these signatures are characterized by a thread-like substructure, strong transverse dynamical coherence, an out-of-phase difference between plane-of-the-sky motions and line-of-sight velocities, and enhanced line broadening and heating around most of the flux tube. A complex combination between resonant absorption and Kelvin–Helmholtz instabilities (KHIs) takes place in which the KHI extracts the energy from the resonant layer and dissipates it through vortices and current sheets, which rapidly degenerate into turbulence. An inward enlargement of the boundary is produced in which the turbulent flows conserve the characteristic dynamics from the resonance, therefore guaranteeing detectability of the resonance imprints. We show that the features described in the accompanying paper through coordinated Hinode and Interface Region Imaging Spectrograph observations match the numerical results well.
Preparation of ZrO II/nano-TiO II composite powder by sol-gel method
NASA Astrophysics Data System (ADS)
Baharvandi, H. R.; Mohammadi, E.; Abdizadeh, H.; Hadian, A. M.; Ehsani, N.
2007-07-01
The effects of concentration of TTIP, amount of distilled water, and calcination temperature on morphology and particle size distribution of ZrO II/nano-TiO II catalysts were investigated. Mixed ZrO II/nano-TiO II powders were prepared by a modified sol-gel method by varying the mole fraction of TTIP from 0.002 to 0.01, H IIO/TTIP fraction from 2 to 8, and various stirring time (2, 4, and 10 h). The prepared ZrO II/nano-TiO II powders have been characterized by scanning electron microscopy (SEM), X-ray diffraction (XRD), and TG/DTA. Each oxide was calcined at the temperature between 110 and 1000°C. The results showed that the calcinations temperature has a pronounced effect on the phase formation and particle size of the calcined zirconium titanate (ZT) powders.
Numerical evaluation of the production of radionuclides in a nuclear reactor (Part II).
Mirzadeh, S; Walsh, P
1998-04-01
A computer program called LAURA has been developed to predict the production rates of any member of a nuclei network undergoing spontaneous decay and/or induced neutron transformation in a nuclear reactor. The theoretical bases for the development of LAURA were discussed in Part I. In particular, in Part I, we described how an expression based on the Rubinson (1949) approach is used to evaluate the depletion function. In this paper (Part II), we describe the full simulation of radionuclide production including the decomposition of a reaction network into independent linear chains, provisions for periodic reactor shutdown and restart, and implementation of an approximate solution given by Raykin and Shlyakhter (1989) to account for the effect of feedback due to alpha decay. Also included are some examples which demonstrate possible uses for LAURA.
Numerical simulation of fiber and wire array Z-pinches with Trac-II
Reisman, D
1998-09-01
Trac-II is a two dimensional axisymmetric resistive MHD code. It simulates all three spatial components (r, z, φ) of the magnetic field and fluid velocity vectors, and the plasma is treated as a single fluid with two temperatures (T_{e},T_{i}). In addition, it can optionally include a self-consistent external circuit. Recent modifications to the code include the addition of the 3-T radiation model, a 4-phase (solid-liquid-vapor-plasma) equation of state model (QEOS), a 4-phase electrical/thermal conductivity model, and an implicit solution of poloidal B_{z},B_{r}) magnetic field diffusion. These changes permit a detailed study of fiber and wire array Z-pinches. Specifically, Trac-II is used to study the wire array Z-pinch at the PBFA-Z pulse power generator at Sandia National Laboratory. First, in 1-D we examine the behavior of a single wire in the Z-pinch. Then, using these results as initial radial conditions in 2-D, we investigate the dynamics of wire array configurations in the r-z and r-θ plane. In the r-z plane we examine the growth of the m=0 or "sausage" instability in single wires within the array. In the r-θ plane we examine the merging behavior between neighboring wires. Special emphasis is placed on trying to explain how instability growth affects the performance of the Z-pinch. Lastly, we introduce Trac-III, a 3-D MHD code, and illustrate the m=1 or "kink" instability. We also discuss how Trac-III can be modified to simulate the wire array Z-pinch.
A numerical simulation of barotropic instability. II Wave-wave interaction
NASA Technical Reports Server (NTRS)
Nielsen, J. E.; Schoeberl, M. R.
1984-01-01
A fully nonlinear numerical model of the point jet barotropic instability is used to test and confirm the hypothesis that the magnitude of the wave vorticity does not exceed the magnitude of the initial shear. This result arises directly from the local conservation of vorticity following a parcel and the fact that unstable waves are principally confined to the region where the zonal mean vorticity can be smoothed by the wave so as to eliminate the instability. Comparisons are made between fully nonlinear and quasi-linear models of the point jet instability and their tracer transport properties. Differences become particularly evident after wave saturation. The most important effect neglected by the wave-mean flow model appears to be the advection of wave vorticity by the most unstable mode. However, as equilibration of the instability proceeds, the globally averaged properties of both models are found to be similar.
Evolution of planetesimals. I - Dynamics: Relaxation in a thin disk. II - Numerical simulations
NASA Astrophysics Data System (ADS)
Palmer, P. L.; Lin, D. N. C.; Aarseth, S. J.
1993-01-01
The study examines the effects of density inhomogeneity and differential rotation as well as inelastic collisions on the dynamical evolution of planetesimals. Consideration is given to a three-step analysis: the dynamical evolution of the planetesimals, collisions and mass accumulation, and interaction with gas. It is shown that the velocity dispersion of a cold system of planetesimals increases rapidly due to elastic gravitational scattering. When the dispersion in the epicycle amplitude becomes comparable to the planetesimals' Roche radius, energy is transferred from the systematic Keplerian shear to the dispersive motion. With a numerical N-body scheme, gravitational scattering and physical collisions among a system of planetesimals is simulated. It is shown that dynamical equilibrium is attained with a velocity dispersion comparable to the surface escape velocity of those planetesimals which contribute most of the system mass.
A method for estimating vertical distibution of the SAGE II opaque cloud frequency
Wang, P.; Mccormick, M.P.; Minnis, P.; Kent, G.S.; Yue, G.K.; Skeens, K.M. |
1995-02-01
A method is developed to infer the vertical distribution of the occurrence frequency of clouds that are opaque to the Stratospheric Aerosol and Gas Experiment (SAGE) II instrument. An application of the method to the 1986 SAGE II observations is included in this paper. The 1986 SAGE II results are compared with the 1952-1981 cloud climatology of Warren et al. (1986, 1988)
A method for estimating vertical distibution of the SAGE II opaque cloud frequency
NASA Technical Reports Server (NTRS)
Wang, Pi-Huan; Mccormick, M. Patrick; Minnis, Patrick; Kent, Geoffrey S.; Yue, Glenn K.; Skeens, Kristi M.
1995-01-01
A method is developed to infer the vertical distribution of the occurrence frequency of clouds that are opaque to the Stratospheric Aerosol and Gas Experiment (SAGE) II instrument. An application of the method to the 1986 SAGE II observations is included in this paper. The 1986 SAGE II results are compared with the 1952-1981 cloud climatology of Warren et al. (1986, 1988)
Mathematical model and its fast numerical method for the tumor growth.
Lee, Hyun Geun; Kim, Yangjin; Kim, Junseok
2015-12-01
In this paper, we reformulate the diffuse interface model of the tumor growth (S.M. Wise et al., Three-dimensional multispecies nonlinear tumor growth-I: model and numerical method, J. Theor. Biol. 253 (2008) 524--543). In the new proposed model, we use the conservative second-order Allen--Cahn equation with a space--time dependent Lagrange multiplier instead of using the fourth-order Cahn--Hilliard equation in the original model. To numerically solve the new model, we apply a recently developed hybrid numerical method. We perform various numerical experiments. The computational results demonstrate that the new model is not only fast but also has a good feature such as distributing excess mass from the inside of tumor to its boundary regions. PMID:26775855
Review of numerical methods for simulation of the aortic root: Present and future directions
NASA Astrophysics Data System (ADS)
Mohammadi, Hossein; Cartier, Raymond; Mongrain, Rosaire
2016-05-01
Heart valvular disease is still one of the main causes of mortality and morbidity in develop countries. Numerical modeling has gained considerable attention in studying hemodynamic conditions associated with valve abnormalities. Simulating the large displacement of the valve in the course of the cardiac cycle needs a well-suited numerical method to capture the natural biomechanical phenomena which happens in the valve. The paper aims to review the principal progress of the numerical approaches for studying the hemodynamic of the aortic valve. In addition, the future directions of the current approaches as well as their potential clinical applications are discussed.
Serencam, Huseyin; Duran, Celal; Ozdes, Duygu; Bektas, Hakan
2013-01-01
A simple and highly sensitive separation and preconcentration procedure, which has minimal impact on the environment, has been developed. The procedure is based on the carrier element free coprecipitation (CEFC) of Co(II), Cu(II), and Ni(II) ions by using 2-{4-[2-(1H-indol-3-yl)ethyl]-3-(4-methylbenzyl)-5-oxo-4,5-dihydro- 1H-1,2,4-triazol-l-yl}-N'-(pyridin-2-yl methylidene)acetohydrazide (IMOTPA), as an organic coprecipitant. The levels of analyte ions were determined by flame atomic absorption spectrometry (FAAS). The detection limits for Co(II), Cu(II) and Ni(II) ions were found to be 0.40, 0.16 and 0.17 microg L(-1), respectively, and the relative standard deviations for the analyte ions were lower than 3.0%. Spike tests and certified reference material analyses were performed to validate the method. The method was successfully applied for the determination of Co(II), Cu(II) and Ni(II) ions levels in sea and stream water as liquid samples and red pepper, black pepper, and peppermint as solid samples. PMID:23878931
Quantum Dot Channel (QDC) FETs with Wraparound II-VI Gate Insulators: Numerical Simulations
NASA Astrophysics Data System (ADS)
Jain, F.; Lingalugari, M.; Kondo, J.; Mirdha, P.; Suarez, E.; Chandy, J.; Heller, E.
2016-11-01
This paper presents simulations predicting the feasibility of 9-nm wraparound quantum dot channel (QDC) field-effect transistors (FETs). In particular, II-VI lattice-matched layers which reduce the density of interface states, serving as top (tunnel gate), side, and bottom gate insulators, have been simulated. Quantum simulations show FET operation with voltage swing of ~0.2 V. Incorporation of cladded quantum dots, such as SiO x -Si and GeO x -Ge, under the gate tunnel oxide results in electrical transport in one or more quantum dot layers which form a quantum dot superlattice (QDSL). Long-channel QDC FETs have experimental multistate drain current ( I D)-gate voltage ( V G) and drain current ( I D)-drain voltage ( V D) characteristics, which can be attributed to the manifestation of extremely narrow energy minibands formed in the QDSL. An approach for modeling the multistate I D- V G characteristics is reported. The multistate characteristics of QDC FETs permit design of compact two-bit multivalued logic circuits.
Quantum Dot Channel (QDC) FETs with Wraparound II-VI Gate Insulators: Numerical Simulations
NASA Astrophysics Data System (ADS)
Jain, F.; Lingalugari, M.; Kondo, J.; Mirdha, P.; Suarez, E.; Chandy, J.; Heller, E.
2016-08-01
This paper presents simulations predicting the feasibility of 9-nm wraparound quantum dot channel (QDC) field-effect transistors (FETs). In particular, II-VI lattice-matched layers which reduce the density of interface states, serving as top (tunnel gate), side, and bottom gate insulators, have been simulated. Quantum simulations show FET operation with voltage swing of ~0.2 V. Incorporation of cladded quantum dots, such as SiO x -Si and GeO x -Ge, under the gate tunnel oxide results in electrical transport in one or more quantum dot layers which form a quantum dot superlattice (QDSL). Long-channel QDC FETs have experimental multistate drain current (I D)-gate voltage (V G) and drain current (I D)-drain voltage (V D) characteristics, which can be attributed to the manifestation of extremely narrow energy minibands formed in the QDSL. An approach for modeling the multistate I D-V G characteristics is reported. The multistate characteristics of QDC FETs permit design of compact two-bit multivalued logic circuits.
The Standardized Candle Method for Type II-Plateau Supernovae
NASA Astrophysics Data System (ADS)
Olivares, Felipe; Hamuy, Mario
reddening determination. Furthermore, we study the quality of the luminosity-expansion velocity correlation of FeII lines. Finally, we show the accuracy of the method by means of Hubble diagrams built using a set of 36 type II plateau SNe.
NASA Technical Reports Server (NTRS)
Bernstein, Ira B.; Brookshaw, Leigh; Fox, Peter A.
1992-01-01
The present numerical method for accurate and efficient solution of systems of linear equations proceeds by numerically developing a set of basis solutions characterized by slowly varying dependent variables. The solutions thus obtained are shown to have a computational overhead largely independent of the small size of the scale length which characterizes the solutions; in many cases, the technique obviates series solutions near singular points, and its known sources of error can be easily controlled without a substantial increase in computational time.
Numerical solution of differential-algebraic equations using the spline collocation-variation method
NASA Astrophysics Data System (ADS)
Bulatov, M. V.; Rakhvalov, N. P.; Solovarova, L. S.
2013-03-01
Numerical methods for solving initial value problems for differential-algebraic equations are proposed. The approximate solution is represented as a continuous vector spline whose coefficients are found using the collocation conditions stated for a subgrid with the number of collocation points less than the degree of the spline and the minimality condition for the norm of this spline in the corresponding spaces. Numerical results for some model problems are presented.
Numerical solution of hybrid fuzzy differential equations using improved predictor-corrector method
NASA Astrophysics Data System (ADS)
Kim, Hyunsoo; Sakthivel, Rathinasamy
2012-10-01
The hybrid fuzzy differential equations have a wide range of applications in science and engineering. This paper considers numerical solution for hybrid fuzzy differential equations. The improved predictor-corrector method is adapted and modified for solving the hybrid fuzzy differential equations. The proposed algorithm is illustrated by numerical examples and the results obtained using the scheme presented here agree well with the analytical solutions. The computer symbolic systems such as Maple and Mathematica allow us to perform complicated calculations of algorithm.
Numerical simulation of stratified shear flow using a higher order Taylor series expansion method
Iwashige, Kengo; Ikeda, Takashi
1995-09-01
A higher order Taylor series expansion method is applied to two-dimensional numerical simulation of stratified shear flow. In the present study, central difference scheme-like method is adopted for an even expansion order, and upwind difference scheme-like method is adopted for an odd order, and the expansion order is variable. To evaluate the effects of expansion order upon the numerical results, a stratified shear flow test in a rectangular channel (Reynolds number = 1.7x10{sup 4}) is carried out, and the numerical velocity and temperature fields are compared with experimental results measured by laser Doppler velocimetry thermocouples. The results confirm that the higher and odd order methods can simulate mean velocity distributions, root-mean-square velocity fluctuations, Reynolds stress, temperature distributions, and root-mean-square temperature fluctuations.
TYPE II-P SUPERNOVAE FROM THE SDSS-II SUPERNOVA SURVEY AND THE STANDARDIZED CANDLE METHOD
D'Andrea, Chris B.; Sako, Masao; Dilday, Benjamin; Jha, Saurabh; Frieman, Joshua A.; Kessler, Richard; Holtzman, Jon; Konishi, Kohki; Yasuda, Naoki; Schneider, D. P.; Sollerman, Jesper; Wheeler, J. Craig; Cinabro, David; Nichol, Robert C.; Lampeitl, Hubert; Smith, Mathew; Atlee, David W.; Bassett, Bruce; Castander, Francisco J.; Goobar, Ariel
2010-01-01
We apply the Standardized Candle Method (SCM) for Type II Plateau supernovae (SNe II-P), which relates the velocity of the ejecta of a SN to its luminosity during the plateau, to 15 SNe II-P discovered over the three season run of the Sloan Digital Sky Survey-II Supernova Survey. The redshifts of these SNe-0.027 < z < 0.144-cover a range hitherto sparsely sampled in the literature; in particular, our SNe II-P sample contains nearly as many SNe in the Hubble flow (z > 0.01) as all of the current literature on the SCM combined. We find that the SDSS SNe have a very small intrinsic I-band dispersion (0.22 mag), which can be attributed to selection effects. When the SCM is applied to the combined SDSS-plus-literature set of SNe II-P, the dispersion increases to 0.29 mag, larger than the scatter for either set of SNe separately. We show that the standardization cannot be further improved by eliminating SNe with positive plateau decline rates, as proposed in Poznanski et al. We thoroughly examine all potential systematic effects and conclude that for the SCM to be useful for cosmology, the methods currently used to determine the Fe II velocity at day 50 must be improved, and spectral templates able to encompass the intrinsic variations of Type II-P SNe will be needed.
Numerical implementation of the method of fictitious domains for elliptic equations
NASA Astrophysics Data System (ADS)
Temirbekov, Almas N.
2016-08-01
In the paper, we study the elliptical type equation with strongly changing coefficients. We are interested in studying such equation because the given type equations are yielded when we use the fictitious domain method. In this paper we suggest a special method for numerical solution of the elliptic equation with strongly changing coefficients. We have proved the theorem for the assessment of developed iteration process convergence rate. We have developed computational algorithm and numerical calculations have been done to illustrate the effectiveness of the suggested method.
A study of numerical methods for hyperbolic conservation laws with stiff source terms
NASA Technical Reports Server (NTRS)
Leveque, R. J.; Yee, H. C.
1990-01-01
In the present study of the behavior of typical numerical methods in the case of a model advection equation having a parameter-dependent source term, two approaches to the incorporation of the source terms are used: MacCormack-type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. The latter are found to perform slightly better. The model scalar equation is used to show that the incorrectness of the propagation speeds of discontinuities observed in the stiff case is due to the introduction of nonequilibrium values through numerical dissipation in the advection step.
Resilience of helical fields to turbulent diffusion - II. Direct numerical simulations
NASA Astrophysics Data System (ADS)
Bhat, Pallavi; Blackman, Eric G.; Subramanian, Kandaswamy
2014-03-01
Blackman and Subramanian (Paper I) found that sufficiently strong large-scale helical magnetic fields are resilient to turbulent diffusion, decaying on resistively slow rather than turbulently fast time-scales. This bolsters fossil field origins for magnetic fields in some astrophysical objects. Here, we study direct numerical simulations (DNS) of decaying large-scale helical magnetic fields in the presence of non-helical turbulence for two cases: (1) the initial helical field is large enough to decay resistively but transitions to fast decay; (2) the case of Paper I, wherein the transition energy for the initial helical field to decay fast directly is sought. Simulations and two-scale modelling (based on Paper 1) reveal the transition energy, Ec1 to be independent of the turbulent forcing scale, within a small range of RM. For case (2), the two-scale theory predicts a large-scale helical transition energy of Ec2 = (k1/kf)2Meq, where k1 and kf are the large-scale and small turbulent forcing scale, respectively, and Meq is the equipartition magnetic energy. The DNS agree qualitatively with this prediction but the RM, currently achievable, is too small to satisfy a condition 3/RM ≪ (k1/kf)2, necessary to robustly reveal the transition, Ec2. That two-scale theory and DNS agree wherever they can be compared suggests that Ec2 of Paper I should be identifiable at higher RM in DNS.
Numerical boson stars with a single Killing vector. II. The D=3 case
NASA Astrophysics Data System (ADS)
Stotyn, Sean; Chanona, Melanie; Mann, Robert B.
2014-02-01
We complete the analysis of part I in this series [S. Stotyn et. al.,Phys. Rev. D 89, 044017 (2014)] by numerically constructing boson stars in 2+1 dimensional Einstein gravity with negative cosmological constant, minimally coupled to a complex scalar field. These lower dimensional boson stars have strikingly different properties than their higher dimensional counterparts, most noticeably that there exists a finite central energy density, above which an extremal Bañados-Teitelboim-Zanelli (BTZ) black hole forms. In this limit, all of the scalar field becomes enclosed by the horizon; it does not contract to a singularity, but rather the origin remains smooth and regular and the solution represents a spinning boson star trapped inside a degenerate horizon. Additionally, whereas in higher dimensions the mass, angular momentum, and angular velocity all display damped harmonic oscillations as functions of the central energy density, in D =3 these quantities change monotonically up to the bound on the central energy density. Some implications for the holographic dual of these objects are discussed and it is argued that the boson star and extremal BTZ black hole phases are dual to a spontaneous symmetry breaking at zero temperature but finite energy scale.
Mazza, Fabio; Vulcano, Alfonso
2008-07-08
For a widespread application of dissipative braces to protect framed buildings against seismic loads, practical and reliable design procedures are needed. In this paper a design procedure based on the Direct Displacement-Based Design approach is adopted, assuming the elastic lateral storey-stiffness of the damped braces proportional to that of the unbraced frame. To check the effectiveness of the design procedure, presented in an associate paper, a six-storey reinforced concrete plane frame, representative of a medium-rise symmetric framed building, is considered as primary test structure; this structure, designed in a medium-risk region, is supposed to be retrofitted as in a high-risk region, by insertion of diagonal braces equipped with hysteretic dampers. A numerical investigation is carried out to study the nonlinear static and dynamic responses of the primary and the damped braced test structures, using step-by-step procedures described in the associate paper mentioned above; the behaviour of frame members and hysteretic dampers is idealized by bilinear models. Real and artificial accelerograms, matching EC8 response spectrum for a medium soil class, are considered for dynamic analyses.
NASA Astrophysics Data System (ADS)
Mazza, Fabio; Vulcano, Alfonso
2008-07-01
For a widespread application of dissipative braces to protect framed buildings against seismic loads, practical and reliable design procedures are needed. In this paper a design procedure based on the Direct Displacement-Based Design approach is adopted, assuming the elastic lateral storey-stiffness of the damped braces proportional to that of the unbraced frame. To check the effectiveness of the design procedure, presented in an associate paper, a six-storey reinforced concrete plane frame, representative of a medium-rise symmetric framed building, is considered as primary test structure; this structure, designed in a medium-risk region, is supposed to be retrofitted as in a high-risk region, by insertion of diagonal braces equipped with hysteretic dampers. A numerical investigation is carried out to study the nonlinear static and dynamic responses of the primary and the damped braced test structures, using step-by-step procedures described in the associate paper mentioned above; the behaviour of frame members and hysteretic dampers is idealized by bilinear models. Real and artificial accelerograms, matching EC8 response spectrum for a medium soil class, are considered for dynamic analyses.
Darby, S.E.; Thorne, Colin R.; Simon, A.
1996-01-01
In this paper the numerical model presented in the companion paper is tested and applied. Assessment of model accuracy was based on two approaches. First, predictions of evolution of a 13.5 km reach of the South Fork of the Forked Deer River, in west Tennessee, were compared to observations over a 24-yr period. Results suggest that although the model was able to qualitatively predict trends of widening and deepening, quantitative predictions were not reliable. Simulated widths and depths were within 15% of the corresponding observed values, but observed change in these parameters at the study sites were also close to these values. Simulated rates of depth adjustment were within 15% of observed rates, but observed rates of channel widening at the study sites were approximately three times those simulated by the model. In the second approach, the model was used to generate relationships between stable channel width and bank-full discharge. The model was able to successfully replicate the form of empirically derived regime-width equations. Simulations were used to demonstrate the model's ability to obtain more realistic predictions of bed evolution in widening channels.
Non-standard numerical methods applied to subsurface biobarrier formation models in porous media.
Chen, B M; Kojouharov, H V
1999-07-01
Biofilm forming microbes have complex effects on the flow properties of natural porous media. Subsurface biofilms have the potential for the formation of biobarriers to inhibit contaminant migration in groundwater. Another example of beneficial microbial effects is the biotransformation of organic contaminants to less harmful forms, thereby providing an in situ method for treatment of contaminated groundwater supplies. Mathematical models that describe contaminant transport with biodegradation involve a set of coupled convection-dispersion equations with non-linear reactions. The reactive solute transport equation is one for which numerical solution procedures continue to exhibit significant limitations for certain problems of groundwater hydrology interest. Accurate numerical simulations are crucial to the development of contaminant remediation strategies. A new numerical method is developed for simulation of reactive bacterial transport in porous media. The non-standard numerical approach is based on the ideas of the 'exact' time-stepping scheme. It leads to solutions free from the numerical instabilities that arise from incorrect modeling of derivatives and reaction terms. Applications to different biofilm models are examined and numerical results are presented to demonstrate the performance of the proposed new method.
Numerical Simulation of High Velocity Impact Phenomenon by the Distinct Element Method (dem)
NASA Astrophysics Data System (ADS)
Tsukahara, Y.; Matsuo, A.; Tanaka, K.
2007-12-01
Continuous-DEM (Distinct Element Method) for impact analysis is proposed in this paper. Continuous-DEM is based on DEM (Distinct Element Method) and the idea of the continuum theory. Numerical simulations of impacts between SUS 304 projectile and concrete target has been performed using the proposed method. The results agreed quantitatively with the impedance matching method. Experimental elastic-plastic behavior with compression and rarefaction wave under plate impact was also qualitatively reproduced, matching the result by AUTODYN®.
Efficient numerical method for analyzing optical bistability in photonic crystal microcavities.
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 method for analyzing optical bistability in photonic crystal microcavities.
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. PMID:23736417
NASA Astrophysics Data System (ADS)
Plakhov, Iu. V.; Mytsenko, A. V.; Shel'Pov, V. A.
A numerical integration method is developed that is more accurate than Everhart's (1974) implicit single-sequence approach for integrating orbits. This method can be used to solve problems of space geodesy based on the use of highly precise laser observations.
Solving the Bateman equations in CASMO5 using implicit ode numerical methods for stiff systems
Hykes, J. M.; Ferrer, R. M.
2013-07-01
The Bateman equations, which describe the transmutation of nuclides over time as a result of radioactive decay, absorption, and fission, are often numerically stiff. This is especially true if short-lived nuclides are included in the system. This paper describes the use of implicit numerical methods for o D Es applied to the stiff Bateman equations, specifically employing the Backward Differentiation Formulas (BDF) form of the linear multistep method. As is true in other domains, using an implicit method removes or lessens the (sometimes severe) step-length constraints by which explicit methods must abide. To gauge its accuracy and speed, the BDF method is compared to a variety of other solution methods, including Runge-Kutta explicit methods and matrix exponential methods such as the Chebyshev Rational Approximation Method (CRAM). A preliminary test case was chosen as representative of a PWR lattice depletion step and was solved with numerical libraries called from a Python front-end. The Figure of Merit (a combined measure of accuracy and efficiency) for the BDF method was nearly identical to that for CRAM, while explicit methods and other matrix exponential approximations trailed behind. The test case includes 319 nuclides, in which the shortest-lived nuclide is {sup 98}Nb with a half-life of 2.86 seconds. Finally, the BDF and CRAM methods were compared within CASMO5, where CRAM had a FOM about four times better than BDF, although the BDF implementation was not fully optimized. (authors)
Accretion-powered Stellar Winds. II. Numerical Solutions for Stellar Wind Torques
NASA Astrophysics Data System (ADS)
Matt, Sean; Pudritz, Ralph E.
2008-05-01
In order to explain the slow rotation observed in a large fraction of accreting pre-main-sequence stars (CTTSs), we explore the role of stellar winds in torquing down the stars. For this mechanism to be effective, the stellar winds need to have relatively high outflow rates, and thus would likely be powered by the accretion process itself. Here, we use numerical magnetohydrodynamical simulations to compute detailed two-dimensional (axisymmetric) stellar wind solutions, in order to determine the spin-down torque on the star. We discuss wind driving mechanisms and then adopt a Parker-like (thermal pressure driven) wind, modified by rotation, magnetic fields, and enhanced mass-loss rate (relative to the Sun). We explore a range of parameters relevant for CTTSs, including variations in the stellar mass, radius, spin rate, surface magnetic field strength, mass-loss rate, and wind acceleration rate. We also consider both dipole and quadrupole magnetic field geometries. Our simulations indicate that the stellar wind torque is of sufficient magnitude to be important for spinning down a "typical" CTTS, for a mass-loss rate of ~10-9 M⊙ yr-1. The winds are wide-angle, self-collimated flows, as expected of magnetic rotator winds with moderately fast rotation. The cases with quadrupolar field produce a much weaker torque than for a dipole with the same surface field strength, demonstrating that magnetic geometry plays a fundamental role in determining the torque. Cases with varying wind acceleration rate show much smaller variations in the torque, suggesting that the details of the wind driving are less important. We use our computed results to fit a semianalytic formula for the effective Alfvén radius in the wind, as well as the torque. This allows for considerable predictive power, and is an improvement over existing approximations.
Samak, M. Mosleh E. Abu; Bakar, A. Ashrif A.; Kashif, Muhammad; Zan, Mohd Saiful Dzulkifly
2016-01-01
This paper discusses numerical analysis methods for different geometrical features that have limited interval values for typically used sensor wavelengths. Compared with existing Finite Difference Time Domain (FDTD) methods, the alternating direction implicit (ADI)-FDTD method reduces the number of sub-steps by a factor of two to three, which represents a 33% time savings in each single run. The local one-dimensional (LOD)-FDTD method has similar numerical equation properties, which should be calculated as in the previous method. Generally, a small number of arithmetic processes, which result in a shorter simulation time, are desired. The alternating direction implicit technique can be considered a significant step forward for improving the efficiency of unconditionally stable FDTD schemes. This comparative study shows that the local one-dimensional method had minimum relative error ranges of less than 40% for analytical frequencies above 42.85 GHz, and the same accuracy was generated by both methods.
DETAILED NUMERICAL SIMULATIONS ON THE FORMATION OF PILLARS AROUND H II REGIONS
Gritschneder, Matthias; Burkert, Andreas; Naab, Thorsten; Walch, Stefanie
2010-11-10
We study the structural evolution of turbulent molecular clouds under the influence of ionizing radiation emitted from a nearby massive star by performing a high-resolution parameter study with the iVINE code. The temperature is taken to be 10 K or 100 K, the mean number density is either 100 cm{sup -3} or 300 cm{sup -3}. Furthermore, the turbulence is varied between Mach 1.5 and Mach 12.5, the main driving scale of the turbulence is varied between 1 pc and 8 pc. We vary the ionizing flux by an order of magnitude, corresponding to allowing between 0.5% and 5% of the mass in the domain to be ionized immediately. In our simulations, the ionizing radiation enhances the initial turbulent density distribution and thus leads to the formation of pillar-like structures observed adjacent to H II regions in a natural way. Gravitational collapse occurs regularly at the tips of the structures. We find a clear correlation between the initial state of the turbulent cold cloud and the final morphology and physical properties of the structures formed. The most favorable regime for the formation of pillars is Mach 4-10. Structures and therefore stars only form if the initial density contrast between the high-density unionized gas and the gas that is going to be ionized is lower than the temperature contrast between the hot and the cold gas. The density of the resulting pillars is determined by a pressure equilibrium between the hot and the cold gas. A thorough analysis of the simulations shows that the complex kinematical and geometrical structure of the formed elongated filaments reflects that of observed pillars to an impressive level of detail. In addition, we find that the observed line-of-sight velocities allow for a distinct determination of different formation mechanisms. Comparing the current simulations to previous results and recent observations, we conclude that, e.g., the pillars of creation in M16 formed by the mechanism proposed here and not by the radiation driven
An unconditionally stable method for numerically solving solar sail spacecraft equations of motion
NASA Astrophysics Data System (ADS)
Karwas, Alex
Solar sails use the endless supply of the Sun's radiation to propel spacecraft through space. The sails use the momentum transfer from the impinging solar radiation to provide thrust to the spacecraft while expending zero fuel. Recently, the first solar sail spacecraft, or sailcraft, named IKAROS completed a successful mission to Venus and proved the concept of solar sail propulsion. Sailcraft experimental data is difficult to gather due to the large expenses of space travel, therefore, a reliable and accurate computational method is needed to make the process more efficient. Presented in this document is a new approach to simulating solar sail spacecraft trajectories. The new method provides unconditionally stable numerical solutions for trajectory propagation and includes an improved physical description over other methods. The unconditional stability of the new method means that a unique numerical solution is always determined. The improved physical description of the trajectory provides a numerical solution and time derivatives that are continuous throughout the entire trajectory. The error of the continuous numerical solution is also known for the entire trajectory. Optimal control for maximizing thrust is also provided within the framework of the new method. Verification of the new approach is presented through a mathematical description and through numerical simulations. The mathematical description provides details of the sailcraft equations of motion, the numerical method used to solve the equations, and the formulation for implementing the equations of motion into the numerical solver. Previous work in the field is summarized to show that the new approach can act as a replacement to previous trajectory propagation methods. A code was developed to perform the simulations and it is also described in this document. Results of the simulations are compared to the flight data from the IKAROS mission. Comparison of the two sets of data show that the new approach
A numerical method to study the dynamics of capillary fluid systems
NASA Astrophysics Data System (ADS)
Herrada, M. A.; Montanero, J. M.
2016-02-01
We propose a numerical approach to study both the nonlinear dynamics and linear stability of capillary fluid systems. In the nonlinear analysis, the time-dependent fluid region is mapped onto a fixed numerical domain through a coordinate transformation. The hydrodynamic equations are spatially discretized with the Chebyshev spectral collocation technique, while an implicit time advancement is performed using second-order backward finite differences. The resulting algebraic equations are solved with the iterative Newton-Raphson technique. The most novel aspect of the method is the fact that the elements of the Jacobian of the discretized system of equations are symbolic functions calculated before running the simulation. These functions are evaluated numerically in the Newton-Raphson iterations to find the solution at each time step, which reduces considerably the computing time. Besides, this numerical procedure can be easily adapted to solve the eigenvalue problem which determines the linear global modes of the capillary system. Therefore, both the nonlinear dynamics and the linear stability analysis can be conducted with essentially the same algorithm. We validate this numerical approach by studying the dynamics of a liquid bridge close to its minimum volume stability limit. The results are virtually the same as those obtained with other methods. The proposed approach proves to be much more computationally efficient than those other methods. Finally, we show the versatility of the method by calculating the linear global modes of a gravitational jet.
Development of a numerical method for the prediction of turbulent flows in dump diffusers
NASA Astrophysics Data System (ADS)
Ando, Yasunori; Kawai, Masafumi; Sato, Yukinori; Toh, Hidemi
1987-01-01
In order to obtain an effective tool to design dump diffusers for gas turbine combustors, a finite-volume numerical calculation method has been developed for the solution of two-dimensional/axisymmetric incompressible steady Navier-Stokes equation in general curvilinear coordinate system. This method was applied to the calculations of turbulent flows in a two-dimensional dump diffuser with uniform and distorted inlet velocity profiles as well as an annular dump diffuser with uniform inlet velocity profile, and the calculated results were compared with experimental data. The numerical results showed a good agreement with experimental data in case of both inlet velocity profiles; eventually, the numerical method was confirmed to be an effective tool for the development of dump diffusers which can predict the flow pattern, velocity distribution and the pressure loss.
A method for generating numerical pilot opinion ratings using the optimal pilot model
NASA Technical Reports Server (NTRS)
Hess, R. A.
1976-01-01
A method for generating numerical pilot opinion ratings using the optimal pilot model is introduced. The method is contained in a rating hypothesis which states that the numerical rating which a human pilot assigns to a specific vehicle and task can be directly related to the numerical value of the index of performance resulting from the optimal pilot modeling procedure as applied to that vehicle and task. The hypothesis is tested using the data from four piloted simulations. The results indicate that the hypothesis is reasonable, but that the predictive capability of the method is a strong function of the accuracy of the pilot model itself. This accuracy is, in turn, dependent upon the parameters which define the optimal modeling problem. A procedure for specifying the parameters for the optimal pilot model in the absence of experimental data is suggested.
Bang, Jin-Young; Chung, Chin-Wook
2010-12-15
Electron energy distribution functions (EEDFs) were determined from probe characteristics using a numerical ac superimposed method with a distortion correction of high derivative terms by varying amplitude of a sinusoidal perturbation voltage superimposed onto the dc sweep voltage, depending on the related electron energy. Low amplitude perturbation applied around the plasma potential represented the low energy peak of the EEDF exactly, and high amplitude perturbation applied around the floating potential was effective to suppress noise or distortion of the probe characteristic, which is fatal to the tail electron distribution. When a small random noise was imposed over the stabilized prove characteristic, the numerical differentiation method was not suitable to determine the EEDF, while the numerical ac superimposed method was able to obtain a highly precise EEDF.
A numerical simulation method and analysis of a complete thermoacoustic-Stirling engine.
Ling, Hong; Luo, Ercang; Dai, Wei
2006-12-22
Thermoacoustic prime movers can generate pressure oscillation without any moving parts on self-excited thermoacoustic effect. The details of the numerical simulation methodology for thermoacoustic engines are presented in the paper. First, a four-port network method is used to build the transcendental equation of complex frequency as a criterion to judge if temperature distribution of the whole thermoacoustic system is correct for the case with given heating power. Then, the numerical simulation of a thermoacoustic-Stirling heat engine is carried out. It is proved that the numerical simulation code can run robustly and output what one is interested in. Finally, the calculated results are compared with the experiments of the thermoacoustic-Stirling heat engine (TASHE). It shows that the numerical simulation can agrees with the experimental results with acceptable accuracy. PMID:16996099
A numerical simulation method and analysis of a complete thermoacoustic-Stirling engine.
Ling, Hong; Luo, Ercang; Dai, Wei
2006-12-22
Thermoacoustic prime movers can generate pressure oscillation without any moving parts on self-excited thermoacoustic effect. The details of the numerical simulation methodology for thermoacoustic engines are presented in the paper. First, a four-port network method is used to build the transcendental equation of complex frequency as a criterion to judge if temperature distribution of the whole thermoacoustic system is correct for the case with given heating power. Then, the numerical simulation of a thermoacoustic-Stirling heat engine is carried out. It is proved that the numerical simulation code can run robustly and output what one is interested in. Finally, the calculated results are compared with the experiments of the thermoacoustic-Stirling heat engine (TASHE). It shows that the numerical simulation can agrees with the experimental results with acceptable accuracy.
A numerical method of tracing a vortical axis along local topological axis line
NASA Astrophysics Data System (ADS)
Nakayama, Katsuyuki; Hasegawa, Hideki
2016-06-01
A new numerical method is presented to trace or identify a vortical axis in flow, which is based on Galilean invariant flow topology. We focus on the local flow topology specified by the eigenvalues and eigenvectors of the velocity gradient tensor, and extract the axis component from its flow trajectory. Eigen-vortical-axis line is defined from the eigenvector of the real eigenvalue of the velocity gradient tensor where the tensor has the conjugate complex eigenvalues. This numerical method integrates the eigen-vortical-axis line and traces a vortical axis in terms of the invariant flow topology, which enables to investigate the feature of the topology-based vortical axis.
Numerical methods for large-scale, time-dependent partial differential equations
NASA Technical Reports Server (NTRS)
Turkel, E.
1979-01-01
A survey of numerical methods for time dependent partial differential equations is presented. The emphasis is on practical applications to large scale problems. A discussion of new developments in high order methods and moving grids is given. The importance of boundary conditions is stressed for both internal and external flows. A description of implicit methods is presented including generalizations to multidimensions. Shocks, aerodynamics, meteorology, plasma physics and combustion applications are also briefly described.
A numerical study of the Regge calculus and smooth lattice methods on a Kasner cosmology
NASA Astrophysics Data System (ADS)
Brewin, Leo
2015-10-01
Two lattice based methods for numerical relativity, the Regge calculus and the smooth lattice relativity, will be compared with respect to accuracy and computational speed in a full 3+1 evolution of initial data representing a standard Kasner cosmology. It will be shown that both methods provide convergent approximations to the exact Kasner cosmology. It will also be shown that the Regge calculus is of the order of 110 times slower than the smooth lattice method.
Ritter, André
2014-10-20
The shifted angular spectrum method allows a reduction of the number of samples required for numerical off-axis propagation of scalar wave fields. In this work, a modification of the shifted angular spectrum method is presented. It allows a further reduction of the spatial sampling rate for certain wave fields. We calculate the benefit of this method for spherical waves. Additionally, a working implementation is presented showing the example of a spherical wave propagating through a circular aperture. PMID:25401659
NASA Technical Reports Server (NTRS)
Heldenfels, Richard R
1951-01-01
A numerical method is presented for the stress analysis of stiffened-shell structures of arbitrary cross section under nonuniform temperature distributions. The method is based on a previously published procedure that is extended to include temperature effects and multicell construction. The application of the method to practical problems is discussed and an illustrative analysis is presented of a two-cell box beam under the combined action of vertical loads and a nonuniform temperature distribution.
NASA Astrophysics Data System (ADS)
Takahashi, Ryohei; Mamori, Hiroya; Yamamoto, Makoto
2016-02-01
A numerical method for simulating gas-liquid-solid three-phase flows based on the moving particle semi-implicit (MPS) approach was developed in this study. Computational instability often occurs in multiphase flow simulations if the deformations of the free surfaces between different phases are large, among other reasons. To avoid this instability, this paper proposes an improved coupling procedure between different phases in which the physical quantities of particles in different phases are calculated independently. We performed numerical tests on two illustrative problems: a dam-break problem and a solid-sphere impingement problem. The former problem is a gas-liquid two-phase problem, and the latter is a gas-liquid-solid three-phase problem. The computational results agree reasonably well with the experimental results. Thus, we confirmed that the proposed MPS method reproduces the interaction between different phases without inducing numerical instability.
NASA Technical Reports Server (NTRS)
Cook, C. H.
1977-01-01
The results of a comprehensive numerical investigation of the basic capabilities of the finite element method (FEM) for numerical solution of compressible flow problems governed by the two-dimensional and axis-symmetric Navier-Stokes equations in primitive variables are presented. The strong and weak points of the method as a tool for computational fluid dynamics are considered. The relation of the linear element finite element method to finite difference methods (FDM) is explored. The calculation of free shear layer and separated flows over aircraft boattail afterbodies with plume simulators indicate the strongest assets of the method are its capabilities for reliable and accurate calculation employing variable grids which readily approximate complex geometry and capably adapt to the presence of diverse regions of large solution gradients without the necessity of domain transformation.
Numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory
NASA Technical Reports Server (NTRS)
Ramos, J. I.
1987-01-01
A review of numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory is presented. The methods reviewed include explicit, implicit, quasi-linearization, time linearization, operator-splitting, random walk and finite-element techniques and methods of lines. Adaptive and nonadaptive procedures are also reviewed. These techniques are applied first to solve two model problems which have exact traveling wave solutions with which the numerical results can be compared. This comparison is performed in terms of both the wave profile and computed wave speed. It is shown that the computed wave speed is not a good indicator of the accuracy of a particular method. A fourth-order time-linearized, Hermitian compact operator technique is found to be the most accurate method for a variety of time and space sizes.
A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance
NASA Astrophysics Data System (ADS)
Witte, J. H.; Reisinger, C.
2010-09-01
We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desireable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to an order of O(1/ρ), where ρ>0 is the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.
NASA Astrophysics Data System (ADS)
Rembiasz, T.; Obergaulinger, M.; Cerdá-Durán, P.; Aloy, M. Á.; Müller, E.
2016-05-01
We study the influence of numerical methods and grid resolution on the termination of the magnetorotational instability (MRI) by means of parasitic instabilities in threedimensional shearing-disc simulations reproducing typical conditions found in core-collapse supernovae. Whether or not the MRI is able to amplify weak magnetic fields in this context strongly depends, among other factors, on the amplitude at which its growth terminates. The qualitative results of our study do not depend on the numerical scheme. In all our models, MRI termination is caused by Kelvin-Helmholtz instabilities, consistent with theoretical predictions. Quantitatively, however, there are differences, but numerical convergence can be achieved even at relatively low grid resolutions if high-order reconstruction methods are used.
Time-Space Decoupled Explicit Method for Fast Numerical Simulation of Tsunami Propagation
NASA Astrophysics Data System (ADS)
Guo, Anxin; Xiao, Shengchao; Li, Hui
2015-02-01
This study presents a novel explicit numerical scheme for simulating tsunami propagation using the exact solution of the wave equations. The objective of this study is to develop a fast and stable numerical scheme by decoupling the wave equation in both the time and space domains. First, the finite difference scheme of the shallow-water equations for tsunami simulation are briefly introduced. The time-space decoupled explicit method based on the exact solution of the wave equation is given for the simulation of tsunami propagation without including frequency dispersive effects. Then, to consider wave dispersion, the second-order accurate numerical scheme to solve the shallow-water equations, which mimics the physical frequency dispersion with numerical dispersion, is derived. Lastly, the computation efficiency and the accuracy of the two types of numerical schemes are investigated by the 2004 Indonesia tsunami and the solution of the Boussinesq equation for a tsunami with Gaussian hump over both uniform and varying water depths. The simulation results indicate that the proposed numerical scheme can achieve a fast and stable tsunami propagation simulation while maintaining computation accuracy.
NASA Technical Reports Server (NTRS)
Green, M. J.; Nachtsheim, P. R.
1972-01-01
A numerical method for the solution of large systems of nonlinear differential equations of the boundary-layer type is described. The method is a modification of the technique for satisfying asymptotic boundary conditions. The present method employs inverse interpolation instead of the Newton method to adjust the initial conditions of the related initial-value problem. This eliminates the so-called perturbation equations. The elimination of the perturbation equations not only reduces the user's preliminary work in the application of the method, but also reduces the number of time-consuming initial-value problems to be numerically solved at each iteration. For further ease of application, the solution of the overdetermined system for the unknown initial conditions is obtained automatically by applying Golub's linear least-squares algorithm. The relative ease of application of the proposed numerical method increases directly as the order of the differential-equation system increases. Hence, the method is especially attractive for the solution of large-order systems. After the method is described, it is applied to a fifth-order problem from boundary-layer theory.
Simplified method for measuring minor gas constituents from ILAS-II transmittance spectra
NASA Astrophysics Data System (ADS)
Hanaizumi, Hiroshi; Yokota, Tatsuya
2002-02-01
In order to measure vertical profiles of minor gas concentrations in the stratosphere, Improved Limb Atmosphere Spectrometers (ILAS and ILAS-II) have been developed. ILAS was the first generation sensor and made observations in 1996 and 1997. ILAS-II will measure atmospheric limb transmittance in 66 spectral bands (whereas 44 for ILAS) in the thermal infrared region by observing solar ray passed through the atmosphere. Vertical profiles of minor gases are simultaneously retrieved by a spectral fitting algorithm with an onion-peeling method for vertical profiling. This algorithm adopts a precise radiative transfer calculation and is very accurate, but usually the standard radiative transfer calculation needs huge volume of line-by-line calculations of molecular absorption to simulate theoretical limb transmittance spectra by using the HITRAN database. Methods for accelerating the algorithm have been required. In the ILAS operational program, a table look-up method, which needs an excellent computer system, was used for rapid calculations. We proposed a simplified method, which predicts the gas profiles from the measured limb transmittance spectra and vertical profiles of atmospheric pressure and temperature without iterative calculations by using a multiple regression technique. The Principal Component Expansion (PCE) is used for reducing the scale of the multiple regression model. In the training process, coefficients of the model are estimated from the previously retrieved data sets including measured limb transmittance spectra, vertical profiles of atmospheric pressure and temperature, and retrieved gas profiles. Then, the method predicts gas profiles from the newly measured limb transmittance spectra and pressure and temperature profiles. The validity of the method was confirmed by numerical simulation using the MODTRAN v.3.5 radiative transfer code. The proposed method was also applied to the actual 3474 ILAS observation data sets. The model trained by 3373
Numerical simulations of optically thick accretion onto a black hole. II. Rotating flow
Fragile, P. Chris; Olejar, Ally; Anninos, Peter
2014-11-20
In this paper, we report on recent upgrades to our general relativistic radiation magnetohydrodynamics code, Cosmos++, including the development of a new primitive inversion scheme and a hybrid implicit-explicit solver with a more general M {sub 1} closure relation for the radiation equations. The new hybrid solver helps stabilize the treatment of the radiation source terms, while the new closure allows for a much broader range of optical depths to be considered. These changes allow us to expand by orders of magnitude the range of temperatures, opacities, and mass accretion rates, and move a step closer toward our goal of performing global simulations of radiation-pressure-dominated black hole accretion disks. In this work, we test and validate the new method against an array of problems. We also demonstrate its ability to handle super-Eddington, quasi-spherical accretion. Even with just a single proof-of-principle simulation, we already see tantalizing hints of the interesting phenomenology associated with the coupling of radiation and gas in super-Eddington accretion flows.
ERIC Educational Resources Information Center
Biekert, Russell
Accompanying the rapid changes in technology has been a greater dependence on automation and numerical control, which has resulted in the need to find ways of preparing programers for industrial machines using numerical control. To compare the hands-on equipment method and a visual media method of teaching numerical control, an experimental and a…
Guo, Hanming; Zhuang, Songlin; Guo, Shuwen; Chen, Jiabi; Liang, Zhongcheng
2008-07-01
In terms of the electromagnetic theory described in Part I of our current investigations [J. Opt. Soc. Am. A24, 1776 (2007)], the numerical method for and results of numerical computations corresponding to the electromagnetic theory of a waveguide multilayered optical memory are presented. Here the characteristics of the cross talk and the modulation contrast, the power of readout signals, the variation of the power of the readout signals with the scanning position along the track, and the distribution of the light intensity at the detector are investigated in detail. Results show that the polarization of the reading light, the feature sizes of bits, and the distances between the two adjacent tracks and the two adjacent bits on the same track have significant effects on the distribution of the light intensity at the detector, the power of the readout signals, the cross talk, and the modulation contrast. In addition, the optimal polarization of the reading light is also suggested.
Numerical simulation of rip-raps with the distinct element method
NASA Astrophysics Data System (ADS)
Mittelbach, Livia
2013-06-01
and costal shores. They have to resist hydraulic loads such as ship and wind induced waves, tidal and ship induced currents, tidal varying water levels and storm surges. The numerical modelling of rip-rap revetments is undertaken by using the Distinct Element Method in three dimensions. With the DEM rip-rap stones can be modelled as autonomous objects with any degrees of freedom. Typical shapes of stones are formed by using clumped spherical particles. A method for the generation of the rip-rap stones based on geometrical and probabilistic parameters has been developed in order to generate stones with a realistic size and mass distribution. The DEM program is coupled with a computational fluid dynamics program to account for the influence of the hydraulic loads on the rip-rap stones. The acting forces can be simulated realistically for waves, currents and tidal varying water levels. Field measurements and model tests serve as validation for the numerical model. Physical model tests are carried out in a hydraulic flume with an instrumented rip-rap section for the calibration of the numerical stones material parameters. The behaviour of the particles depends on properties such as density, friction coefficient, normal and shear stiffness as well as the accuracy of the numerical representation of the rip-rap stones. Influences on the accuracy of the modelling of rip-raps with regard to the variation of these parameters are examined by comparing the results of the physical flume tests and numerical model.
Methods for numerical study of tube bundle vibrations in cross-flows
NASA Astrophysics Data System (ADS)
Longatte, E.; Bendjeddou, Z.; Souli, M.
2003-11-01
In many industrial applications, mechanical structures like heat exchanger tube bundles are subjected to complex flows causing possible vibrations and damage. Part of fluid forces are coupled with tube motion and the so-called fluid-elastic forces can affect the structure dynamic behaviour generating possible instabilities and leading to possible short term failures through high amplitude vibrations. Most classical fluid force identification methods rely on structure response experimental measurements associated with convenient data processes. Owing to recent improvements in Computational Fluid Dynamics, numerical simulation of flow-induced vibrations is now practicable for industrial purposes. The present paper is devoted to the numerical identification of fluid-elastic effects affecting tube bundle motion in presence of fluid at rest and one-phase cross-flows. What is the numerical process? When fluid-elastic effects are not significant and are restricted to added mass effects, there is no strong coupling between structure and fluid motions. The structure displacement is not supposed to affect flow patterns. Thus it is possible to solve flow and structure problems separately by using a fixed nonmoving mesh for the fluid dynamic computation. Power spectral density and time record of lift and drag forces acting on tube bundles can be computed numerically by using an unsteady fluid computation involving for example a large Eddy simulation. Fluid force spectra or time record can then be introduced as inlet conditions into the structure code providing the tube dynamic response generated by flow. Such a computation is not possible in presence of strong flow structure coupling. When fluid-elastic effects cannot be neglected, in presence of tube bundles subjected to cross-flows for example, a coupling between flow and structure computations is required. Appropriate numerical methods are investigated in the present work. The purpose is to be able to provide a numerical
Interactive Computing With a Programmable Calculator; Student Experimentations in Numerical Methods.
ERIC Educational Resources Information Center
Gerald, Curtis F.
Programable desk calculators can provide students with personal experience in the use of numerical methods. Courses at California Polytechnic State University at San Luis Obispo use the Compucorp Model 025 Educator Experiences with it as a teaching device for solving non-linear equations and differential equations show that students can by-pass…
Peskin, Michael E
2003-02-13
In upper-division undergraduate physics courses, it is desirable to give numerical problem-solving exercises integrated naturally into weekly problem sets. I explain a method for doing this that makes use of the built-in class structure of the Java programming language. I also supply a Java class library that can assist instructors in writing programs of this type.
A fast numerical method for the valuation of American lookback put options
NASA Astrophysics Data System (ADS)
Song, Haiming; Zhang, Qi; Zhang, Ran
2015-10-01
A fast and efficient numerical method is proposed and analyzed for the valuation of American lookback options. American lookback option pricing problem is essentially a two-dimensional unbounded nonlinear parabolic problem. We reformulate it into a two-dimensional parabolic linear complementary problem (LCP) on an unbounded domain. The numeraire transformation and domain truncation technique are employed to convert the two-dimensional unbounded LCP into a one-dimensional bounded one. Furthermore, the variational inequality (VI) form corresponding to the one-dimensional bounded LCP is obtained skillfully by some discussions. The resulting bounded VI is discretized by a finite element method. Meanwhile, the stability of the semi-discrete solution and the symmetric positive definiteness of the full-discrete matrix are established for the bounded VI. The discretized VI related to options is solved by a projection and contraction method. Numerical experiments are conducted to test the performance of the proposed method.
Willis, Catherine; Rubin, Jacob
1987-01-01
In this paper we consider examples of chemistry-affected transport processes in porous media. A moving boundary problem which arises during transport with precipitation-dissolution reactions is solved by three different numerical methods. Two of these methods (one explicit and one implicit) are based on an integral formulation of mass balance and lead to an approximation of a weak solution. These methods are compared to a front-tracking scheme. Although the two approaches are conceptually different, the numerical solutions showed good agreement. As the ratio of dispersion to convection decreases, the methods based on the integral formulation become computationally more efficient. Specific reactions were modeled to examine the dependence of the system on the physical and chemical parameters.
Numerical Simulation of Parachute Inflation Process Using AN Overset Deforming Grids Method
NASA Astrophysics Data System (ADS)
Xia, Jian; Tian, Shuling; Wu, Yizhao
A numerical method for the simulation of parachute inflation process is presented in this paper. The unsteady compressible N-S equations are fully coupled with MSD (Mass Spring Damper) structure model and integrated forward in time. The CFD solver is based on an unstructured finite volume algorithm and the preconditioning technique is applied to alleviate the stiffness caused by low Mach number. The Spalart-Allmaras one-equation turbulence model is implemented to evaluate the turbulent viscosity. The whole system (fluid equations and structural model equations) is marched implicitly in time using a dual time stepping method. An overset deforming grids method is adopted in this paper to deal with the very large domain deformation during the parachute inflation process. Finally numerical test is performed to validate the robustness of this method.
NASA Astrophysics Data System (ADS)
Bochkovskii, D. A.; Matvienko, G. G.; Romanovskii, O. A.; Kharchenko, O. V.; Yakovlev, S. V.
2014-11-01
This paper reports the development of LIDAS (LIdar Differential Absorption Sensing) program-algorithmic system for laser remote sensing of minor gas constituents (MGCs) of the atmosphere by the differential absorption method (DIAL). The system includes modules for the search of wavelengths informative for laser gas analysis by the differential absorption method, for numerical simulation of lidar sensing of atmospheric MGCs, and for calculation of errors of methodical, atmospheric, spectral, and instrumental origin. Lidar sensing of gas constituents by the differential absorption method as applied to problems of sensing of atmospheric MGCs is simulated numerically. Results of experiments on remote sensing of gas constituents of the atmosphere with the use of RO laser are presented.
NASA Astrophysics Data System (ADS)
Chen, Xueli; Yang, Defu; Zhang, Qitan; Liang, Jimin
2014-05-01
Even though bioluminescence tomography (BLT) exhibits significant potential and wide applications in macroscopic imaging of small animals in vivo, the inverse reconstruction is still a tough problem that has plagued researchers in a related area. The ill-posedness of inverse reconstruction arises from insufficient measurements and modeling errors, so that the inverse reconstruction cannot be solved directly. In this study, an l1/2 regularization based numerical method was developed for effective reconstruction of BLT. In the method, the inverse reconstruction of BLT was constrained into an l1/2 regularization problem, and then the weighted interior-point algorithm (WIPA) was applied to solve the problem through transforming it into obtaining the solution of a series of l1 regularizers. The feasibility and effectiveness of the proposed method were demonstrated with numerical simulations on a digital mouse. Stability verification experiments further illustrated the robustness of the proposed method for different levels of Gaussian noise.
Numerical Manifold Method for the Forced Vibration of Thin Plates during Bending
Jun, Ding; Song, Chen; Wei-Bin, Wen; Shao-Ming, Luo; Xia, Huang
2014-01-01
A novel numerical manifold method was derived from the cubic B-spline basis function. The new interpolation function is characterized by high-order coordination at the boundary of a manifold element. The linear elastic-dynamic equation used to solve the bending vibration of thin plates was derived according to the principle of minimum instantaneous potential energy. The method for the initialization of the dynamic equation and its solution process were provided. Moreover, the analysis showed that the calculated stiffness matrix exhibited favorable performance. Numerical results showed that the generalized degrees of freedom were significantly fewer and that the calculation accuracy was higher for the manifold method than for the conventional finite element method. PMID:24883403
An iterative analytic—numerical method for scattering from a target buried beneath a rough surface
NASA Astrophysics Data System (ADS)
Xu, Run-Wen; Guo, Li-Xin; Wang, Rui
2014-11-01
An efficiently iterative analytical—numerical method is proposed for two-dimensional (2D) electromagnetic scattering from a perfectly electric conducting (PEC) target buried under a dielectric rough surface. The basic idea is to employ the Kirchhoff approximation (KA) to accelerate the boundary integral method (BIM). Below the rough surface, an iterative system is designed between the rough surface and the target. The KA is used to simulate the initial field on the rough surface based on the Fresnel theory, while the target is analyzed by the boundary integral method to obtain a precise result. The fields between the rough surface and the target can be linked by the boundary integral equations below the rough surface. The technique presented here is highly efficient in terms of computational memory, time, and versatility. Numerical simulations of two typical models are carried out to validate the method.
Numerical study of three-parameter matrix eigenvalue problem by Rayleigh quotient method
NASA Astrophysics Data System (ADS)
Bora, Niranjan; Baruah, Arun Kumar
2016-06-01
In this paper, an attempt is done to find approximate eigenvalues and the corresponding eigenvectors of three-parameter matrix eigenvalue problem by extending Rayleigh Quotient Iteration Method (RQIM), which is generally used to solve generalized eigenvalue problems of the form Ax = λBx. Convergence criteria of RQIM will be derived in terms of matrix 2-norm. We will test the computational efficiency of the Method analytically with the help of numerical examples. All calculations are done in MATLAB software.
Applications of numerical optimization methods to helicopter design problems: A survey
NASA Technical Reports Server (NTRS)
Miura, H.
1984-01-01
A survey of applications of mathematical programming methods is used to improve the design of helicopters and their components. Applications of multivariable search techniques in the finite dimensional space are considered. Five categories of helicopter design problems are considered: (1) conceptual and preliminary design, (2) rotor-system design, (3) airframe structures design, (4) control system design, and (5) flight trajectory planning. Key technical progress in numerical optimization methods relevant to rotorcraft applications are summarized.
NASA Astrophysics Data System (ADS)
Muzik, Tomas; Safarik, Pavel; Tucek, Antonín
2014-08-01
This paper deals with the description of water film behaviour on the airfoil NACA0012 using experimental and numerical methods. Properties of the water film on the profile and its breakup into droplets behind the profile are investigated in the aerodynamic tunnel and using CFD methods. The characteristic parameters of the water film, like its thickness and shape for different flow modes are described. Hereafter are described droplets drifted by the air, which water film is broken behind the profile.
Numerical simulation of dynamic processes in biomechanics using the grid-characteristic method
NASA Astrophysics Data System (ADS)
Beklemysheva, K. A.; Vasyukov, A. V.; Petrov, I. B.
2015-08-01
Results of the numerical simulation of mechanical processes occurring in biological tissues under dynamic actions are presented. The grid-characteristic method on unstructured grids is used to solve the system of equations of mechanics of deformable solids; this method takes into account the characteristic properties of the constitutive system of partial differential equations and produces adequate algorithms on interfaces between media and on the boundaries of integration domains.
A numerical method for DNS/LES of turbulent reacting flows
Doom, Jeff; Hou, Yucheng; Mahesh, Krishnan
2007-09-10
A spatially non-dissipative, implicit numerical method to simulate turbulent reacting flows over a range of Mach numbers, is described. The compressible Navier-Stokes equations are rescaled so that the zero Mach number equations are discretely recovered in the limit of zero Mach number. The dependent variables are co-located in space, and thermodynamic variables are staggered from velocity in time. The algorithm discretely conserves kinetic energy in the incompressible, inviscid, non-reacting limit. The chemical source terms are implicit in time to allow for stiff chemical mechanisms. The algorithm is readily extended to complex chemical mechanisms. Numerical examples using both simple and complex chemical mechanisms are presented.
A gyrokinetic continuum code based on the numerical Lie transform (NLT) method
NASA Astrophysics Data System (ADS)
Ye, Lei; Xu, Yingfeng; Xiao, Xiaotao; Dai, Zongliang; Wang, Shaojie
2016-07-01
In this work, we report a novel gyrokinetic simulation method named numerical Lie transform (NLT), which depends on a new physical model derived from the I-transform theory. In this model, the perturbed motion of a particle is decoupled from the unperturbed motion. Due to this property, the unperturbed orbit can be computed in advance and saved as numerical tables for real-time computation. A 4D tensor B-spline interpolation module is developed and applied with the semi-Lagrangian scheme to avoid operator splitting. The NLT code is verified by the Rosenbluth-Hinton test and the linear ITG Cyclone test.
NASA Technical Reports Server (NTRS)
Mcmurtry, Patrick A.; Givi, Peyman
1992-01-01
An account is given of the implementation of the spectral-element technique for simulating a chemically reacting, spatially developing turbulent mixing layer. Attention is given to experimental and numerical studies that have investigated the development, evolution, and mixing characteristics of shear flows. A mathematical formulation is presented of the physical configuration of the spatially developing reacting mixing layer, in conjunction with a detailed representation of the spectral-element method's application to the numerical simulation of mixing layers. Results from 2D and 3D calculations of chemically reacting mixing layers are given.
Numerical radiative transfer with state-of-the-art iterative methods made easy
NASA Astrophysics Data System (ADS)
Lambert, Julien; Paletou, Frédéric; Josselin, Eric; Glorian, Jean-Michel
2016-01-01
This article presents an on-line tool and its accompanying software resources for the numerical solution of basic radiation transfer out of local thermodynamic equilibrium (LTE). State-of-the-art stationary iterative methods such as Accelerated Λ-iteration and Gauss-Seidel schemes, using a short characteristics-based formal solver are used. We also comment on typical numerical experiments associated to the basic non-LTE radiation problem. These resources are intended for the largest use and benefit, in support to more classical radiation transfer lectures usually given at the Master level.
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
NASA Astrophysics Data System (ADS)
Tang, Xiaojun
2016-04-01
The main purpose of this work is to provide multiple-interval integral Gegenbauer pseudospectral methods for solving optimal control problems. The latest developed single-interval integral Gauss/(flipped Radau) pseudospectral methods can be viewed as special cases of the proposed methods. We present an exact and efficient approach to compute the mesh pseudospectral integration matrices for the Gegenbauer-Gauss and flipped Gegenbauer-Gauss-Radau points. Numerical results on benchmark optimal control problems confirm the ability of the proposed methods to obtain highly accurate solutions.
Numerical Simulation of Supercavitating Flows using a Viscous-Potential Method
NASA Astrophysics Data System (ADS)
Kim, Ji-Hye; Ahn, Byoung-Kwon
2015-12-01
A numerical method was developed to predict the supercavity around axi-symmetric bodies. Employing potential flow, the proposed method computes the cavity shape and drag force, which are the important features of practical concern for supercavitating objects. A method to calculate the frictional drag acting on the wetted body surface was implemented, which is called the viscous-potential method. The results revealed details of the drag curve appearing in the course of an increase in speed and cavity growth. In addition, the supercavity and drag features of the actual shape of the supercavitating torpedo were investigated according to the different depth conditions.
A constrained-gradient method to control divergence errors in numerical MHD
NASA Astrophysics Data System (ADS)
Hopkins, Philip F.
2016-10-01
In numerical magnetohydrodynamics (MHD), a major challenge is maintaining nabla \\cdot {B}=0. Constrained transport (CT) schemes achieve this but have been restricted to specific methods. For more general (meshless, moving-mesh, ALE) methods, `divergence-cleaning' schemes reduce the nabla \\cdot {B} errors; however they can still be significant and can lead to systematic errors which converge away slowly. We propose a new constrained gradient (CG) scheme which augments these with a projection step, and can be applied to any numerical scheme with a reconstruction. This iteratively approximates the least-squares minimizing, globally divergence-free reconstruction of the fluid. Unlike `locally divergence free' methods, this actually minimizes the numerically unstable nabla \\cdot {B} terms, without affecting the convergence order of the method. We implement this in the mesh-free code GIZMO and compare various test problems. Compared to cleaning schemes, our CG method reduces the maximum nabla \\cdot {B} errors by ˜1-3 orders of magnitude (˜2-5 dex below typical errors if no nabla \\cdot {B} cleaning is used). By preventing large nabla \\cdot {B} at discontinuities, this eliminates systematic errors at jumps. Our CG results are comparable to CT methods; for practical purposes, the nabla \\cdot {B} errors are eliminated. The cost is modest, ˜30 per cent of the hydro algorithm, and the CG correction can be implemented in a range of numerical MHD methods. While for many problems, we find Dedner-type cleaning schemes are sufficient for good results, we identify a range of problems where using only Powell or `8-wave' cleaning can produce order-of-magnitude errors.
Nonlinear evolution of cylindrical gravitational waves: Numerical method and physical aspects
NASA Astrophysics Data System (ADS)
Celestino, Juliana; de Oliveira, H. P.; Rodrigues, E. L.
2016-05-01
General cylindrical waves are the simplest axisymmetrical gravitational waves that contain both + and × modes of polarization. In this paper, we have studied the evolution of general cylindrical gravitational waves in the realm of the characteristic scheme with a numerical code based on the Galerkin-Collocation method. The investigation consists of the numerical realization of concepts such as Bondi mass and the news functions adapted to cylindrical symmetry. The Bondi mass decays due to the presence of the news functions associated with both polarization modes. We have interpreted each polarization mode as channels from which mass is extracted. Under this perspective, we have presented the enhancement effect of the polarization mode + due to the nonlinear interaction with the mode ×. After discussing the role of matter in cylindrical symmetry, we have extended the numerical code to include electromagnetic fields.
A wavelet-optimized, very high order adaptive grid and order numerical method
NASA Technical Reports Server (NTRS)
Jameson, Leland
1996-01-01
Differencing operators of arbitrarily high order can be constructed by interpolating a polynomial through a set of data followed by differentiation of this polynomial and finally evaluation of the polynomial at the point where a derivative approximation is desired. Furthermore, the interpolating polynomial can be constructed from algebraic, trigonometric, or, perhaps exponential polynomials. This paper begins with a comparison of such differencing operator construction. Next, the issue of proper grids for high order polynomials is addressed. Finally, an adaptive numerical method is introduced which adapts the numerical grid and the order of the differencing operator depending on the data. The numerical grid adaptation is performed on a Chebyshev grid. That is, at each level of refinement the grid is a Chebvshev grid and this grid is refined locally based on wavelet analysis.
Talamo, Alberto
2013-05-01
This study presents three numerical algorithms to solve the time dependent neutron transport equation by the method of the characteristics. The algorithms have been developed taking into account delayed neutrons and they have been implemented into the novel MCART code, which solves the neutron transport equation for two-dimensional geometry and an arbitrary number of energy groups. The MCART code uses regular mesh for the representation of the spatial domain, it models up-scattering, and takes advantage of OPENMP and OPENGL algorithms for parallel computing and plotting, respectively. The code has been benchmarked with the multiplication factor results of a Boiling Water Reactor, with the analytical results for a prompt jump transient in an infinite medium, and with PARTISN and TDTORT results for cross section and source transients. The numerical simulations have shown that only two numerical algorithms are stable for small time steps.
Liu, Peigui; Elshall, Ahmed S.; Ye, Ming; Beerli, Peter; Zeng, Xiankui; Lu, Dan; Tao, Yuezan
2016-02-05
Evaluating marginal likelihood is the most critical and computationally expensive task, when conducting Bayesian model averaging to quantify parametric and model uncertainties. The evaluation is commonly done by using Laplace approximations to evaluate semianalytical expressions of the marginal likelihood or by using Monte Carlo (MC) methods to evaluate arithmetic or harmonic mean of a joint likelihood function. This study introduces a new MC method, i.e., thermodynamic integration, which has not been attempted in environmental modeling. Instead of using samples only from prior parameter space (as in arithmetic mean evaluation) or posterior parameter space (as in harmonic mean evaluation), the thermodynamicmore » integration method uses samples generated gradually from the prior to posterior parameter space. This is done through a path sampling that conducts Markov chain Monte Carlo simulation with different power coefficient values applied to the joint likelihood function. The thermodynamic integration method is evaluated using three analytical functions by comparing the method with two variants of the Laplace approximation method and three MC methods, including the nested sampling method that is recently introduced into environmental modeling. The thermodynamic integration method outperforms the other methods in terms of their accuracy, convergence, and consistency. The thermodynamic integration method is also applied to a synthetic case of groundwater modeling with four alternative models. The application shows that model probabilities obtained using the thermodynamic integration method improves predictive performance of Bayesian model averaging. As a result, the thermodynamic integration method is mathematically rigorous, and its MC implementation is computationally general for a wide range of environmental problems.« less
Estimation of region of attraction for polynomial nonlinear systems: a numerical method.
Khodadadi, Larissa; Samadi, Behzad; Khaloozadeh, Hamid
2014-01-01
This paper introduces a numerical method to estimate the region of attraction for polynomial nonlinear systems using sum of squares programming. This method computes a local Lyapunov function and an invariant set around a locally asymptotically stable equilibrium point. The invariant set is an estimation of the region of attraction for the equilibrium point. In order to enlarge the estimation, a subset of the invariant set defined by a shape factor is enlarged by solving a sum of squares optimization problem. In this paper, a new algorithm is proposed to select the shape factor based on the linearized dynamic model of the system. The shape factor is updated in each iteration using the computed local Lyapunov function from the previous iteration. The efficiency of the proposed method is shown by a few numerical examples.
NASA Astrophysics Data System (ADS)
Fukuchi, Tsugio
2014-06-01
The finite difference method (FDM) based on Cartesian coordinate systems can be applied to numerical analyses over any complex domain. A complex domain is usually taken to mean that the geometry of an immersed body in a fluid is complex; here, it means simply an analytical domain of arbitrary configuration. In such an approach, we do not need to treat the outer and inner boundaries differently in numerical calculations; both are treated in the same way. Using a method that adopts algebraic polynomial interpolations in the calculation around near-wall elements, all the calculations over irregular domains reduce to those over regular domains. Discretization of the space differential in the FDM is usually derived using the Taylor series expansion; however, if we use the polynomial interpolation systematically, exceptional advantages are gained in deriving high-order differences. In using the polynomial interpolations, we can numerically solve the Poisson equation freely over any complex domain. Only a particular type of partial differential equation, Poisson's equations, is treated; however, the arguments put forward have wider generality in numerical calculations using the FDM.
A Fourier collocation time domain method for numerically solving Maxwell's equations
NASA Technical Reports Server (NTRS)
Shebalin, John V.
1991-01-01
A new method for solving Maxwell's equations in the time domain for arbitrary values of permittivity, conductivity, and permeability is presented. Spatial derivatives are found by a Fourier transform method and time integration is performed using a second order, semi-implicit procedure. Electric and magnetic fields are collocated on the same grid points, rather than on interleaved points, as in the Finite Difference Time Domain (FDTD) method. Numerical results are presented for the propagation of a 2-D Transverse Electromagnetic (TEM) mode out of a parallel plate waveguide and into a dielectric and conducting medium.
NASA Astrophysics Data System (ADS)
Biryukov, V. A.; Miryakha, V. A.; Petrov, I. B.; Khokhlov, N. I.
2016-06-01
For wave propagation in heterogeneous media, we compare numerical results produced by grid-characteristic methods on structured rectangular and unstructured triangular meshes and by a discontinuous Galerkin method on unstructured triangular meshes as applied to the linear system of elasticity equations in the context of direct seismic exploration with an anticlinal trap model. It is shown that the resulting synthetic seismograms are in reasonable quantitative agreement. The grid-characteristic method on structured meshes requires more nodes for approximating curved boundaries, but it has a higher computation speed, which makes it preferable for the given class of problems.
NASA Technical Reports Server (NTRS)
Schneider, Harold
1959-01-01
This method is investigated for semi-infinite multiple-slab configurations of arbitrary width, composition, and source distribution. Isotropic scattering in the laboratory system is assumed. Isotropic scattering implies that the fraction of neutrons scattered in the i(sup th) volume element or subregion that will make their next collision in the j(sup th) volume element or subregion is the same for all collisions. These so-called "transfer probabilities" between subregions are calculated and used to obtain successive-collision densities from which the flux and transmission probabilities directly follow. For a thick slab with little or no absorption, a successive-collisions technique proves impractical because an unreasonably large number of collisions must be followed in order to obtain the flux. Here the appropriate integral equation is converted into a set of linear simultaneous algebraic equations that are solved for the average total flux in each subregion. When ordinary diffusion theory applies with satisfactory precision in a portion of the multiple-slab configuration, the problem is solved by ordinary diffusion theory, but the flux is plotted only in the region of validity. The angular distribution of neutrons entering the remaining portion is determined from the known diffusion flux and the remaining region is solved by higher order theory. Several procedures for applying the numerical method are presented and discussed. To illustrate the calculational procedure, a symmetrical slab ia vacuum is worked by the numerical, Monte Carlo, and P(sub 3) spherical harmonics methods. In addition, an unsymmetrical double-slab problem is solved by the numerical and Monte Carlo methods. The numerical approach proved faster and more accurate in these examples. Adaptation of the method to anisotropic scattering in slabs is indicated, although no example is included in this paper.
Gao, Kai; Chung, Eric T.; Gibson, Richard L.; Fu, Shubin; Efendiev, Yalchin
2015-06-05
The development of reliable methods for upscaling fine scale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures. In such cases, the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation. However, such theories cannot be applied directly to homogenize elastic media with more complex, arbitrary spatial heterogeneity. We therefore propose a numerical homogenization algorithm based on multiscale finite element methods for simulating elastic wave propagation in heterogeneous, anisotropic elastic media. Specifically, our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions. Homogenized, effective medium parameters were then computed using these basis functions, and the approach applied a numerical discretization that is similar to the rotated staggered-grid finite difference scheme. Comparisons of the results from our method and from conventional, analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry. Additional tests examined anisotropic models with arbitrary spatial heterogeneity where the average size of the heterogeneities ranged from several centimeters to several meters, and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100. Comparisons to finite-difference simulations proved that the numerical homogenization was equally accurate for these complex cases.
Gao, Kai; Chung, Eric T.; Gibson, Richard L.; Fu, Shubin; Efendiev, Yalchin
2015-06-05
The development of reliable methods for upscaling fine scale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures. In such cases, the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation. However, such theories cannot be applied directly to homogenize elastic media with more complex, arbitrary spatial heterogeneity. We therefore propose a numerical homogenization algorithm based on multiscale finite element methods for simulating elasticmore » wave propagation in heterogeneous, anisotropic elastic media. Specifically, our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions. Homogenized, effective medium parameters were then computed using these basis functions, and the approach applied a numerical discretization that is similar to the rotated staggered-grid finite difference scheme. Comparisons of the results from our method and from conventional, analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry. Additional tests examined anisotropic models with arbitrary spatial heterogeneity where the average size of the heterogeneities ranged from several centimeters to several meters, and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100. Comparisons to finite-difference simulations proved that the numerical homogenization was equally accurate for these complex cases.« less
24 CFR Appendix II to Subpart C of... - Development of Standards; Calculation Methods
Code of Federal Regulations, 2010 CFR
2010-04-01
...; Calculation Methods II Appendix II to Subpart C of Part 51 Housing and Urban Development Office of the...; Calculation Methods I. Background Information Concerning the Standards (a) Thermal Radiation: (1) Introduction... some distance away from the site of the fire. (2) Criteria for Acceptable Separation Distance...
NASA Astrophysics Data System (ADS)
Gustafsson, Johan; Nilsson, Per; Sjögreen Gleisner, Katarina
2013-03-01
We have previously shown analytically that the biologically effective dose (BED), including effects of repair during irradiation and of incomplete repair between fractions, can be formulated using a convolution between the absorbed dose rate function and the function describing repair. In this work, a discrete formalism is derived along with its implementation via the fast Fourier transform. The implementation takes the intrinsic periodicity of the discrete Fourier transform into consideration, as well as possible inconsistencies that may arise due to discretization and truncation of the functions describing the absorbed dose rate and repair. Numerically and analytically calculated BED values are compared for various situations in external beam radiotherapy, brachytherapy and radionuclide therapy, including the use of different repair models. The numerical method is shown to be accurate and versatile since it can be applied to any kind of absorbed dose rate function and allows for the incorporation of different repair models. Typical accuracies for clinically realistic examples are in the order of 10-3% to 10-5%. The method has thus the potential of being a useful tool for the calculation of BED, also in situations with complicated irradiation patterns or repair functions.
Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method
NASA Technical Reports Server (NTRS)
Loulou, Patrick; Moser, Robert D.; Mansour, Nagi N.; Cantwell, Brian J.
1997-01-01
A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.
Twizell, E H
1989-01-01
A family of numerical methods is developed and analyzed for the numerical solution of the parabolic partial differential equation together with the associated initial and boundary conditions, which arise in a mathematical model of the transient stage of percutaneous drug absorption. Two global extrapolation procedures are described, the first in time only, the second in both space and time, for improving the accuracy of the computed concentration profiles. The behaviours of two members of the family of methods, before and after extrapolation, are examined by repeating a number of experiments reported in the literature. Modifications to the algorithms, which are necessary in computing concentration profiles after the ointment is removed at the steady state, are outlined.
A spectral-based numerical method for Kolmogorov equations in Hilbert spaces
NASA Astrophysics Data System (ADS)
Delgado-Vences, Francisco; Flandoli, Franco
2016-08-01
We propose a numerical solution for the solution of the Fokker-Planck-Kolmogorov (FPK) equations associated with stochastic partial differential equations in Hilbert spaces. The method is based on the spectral decomposition of the Ornstein-Uhlenbeck semigroup associated to the Kolmogorov equation. This allows us to write the solution of the Kolmogorov equation as a deterministic version of the Wiener-Chaos Expansion. By using this expansion we reformulate the Kolmogorov equation as an infinite system of ordinary differential equations, and by truncating it we set a linear finite system of differential equations. The solution of such system allow us to build an approximation to the solution of the Kolmogorov equations. We test the numerical method with the Kolmogorov equations associated with a stochastic diffusion equation, a Fisher-KPP stochastic equation and a stochastic Burgers equation in dimension 1.
Borazjani, Iman; Westerdale, John; McMahon, Eileen M.; Rajaraman, Prathish K.; Heys, Jeffrey J.
2013-01-01
The left ventricle (LV) pumps oxygenated blood from the lungs to the rest of the body through systemic circulation. The efficiency of such a pumping function is dependent on blood flow within the LV chamber. It is therefore crucial to accurately characterize LV hemodynamics. Improved understanding of LV hemodynamics is expected to provide important clinical diagnostic and prognostic information. We review the recent advances in numerical and experimental methods for characterizing LV flows and focus on analysis of intraventricular flow fields by echocardiographic particle image velocimetry (echo-PIV), due to its potential for broad and practical utility. Future research directions to advance patient-specific LV simulations include development of methods capable of resolving heart valves, higher temporal resolution, automated generation of three-dimensional (3D) geometry, and incorporating actual flow measurements into the numerical solution of the 3D cardiovascular fluid dynamics. PMID:23690874
Rider, William; Kamm, J. R.; Tomkins, C. D.; Zoldi, C. A.; Prestridge, K. P.; Marr-Lyon, M.; Rightley, P. M.; Benjamin, R. F.
2002-01-01
We consider the detailed structures of mixing flows for Richtmyer-Meshkov experiments of Prestridge et al. [PRE 00] and Tomkins et al. [TOM 01] and examine the most recent measurements from the experimental apparatus. Numerical simulations of these experiments are performed with three different versions of high resolution finite volume Godunov methods. We compare experimental data with simulations for configurations of one and two diffuse cylinders of SF{sub 6} in air using integral measures as well as fractal analysis and continuous wavelet transforms. The details of the initial conditions have a significant effect on the computed results, especially in the case of the double cylinder. Additionally, these comparisons reveal sensitive dependence of the computed solution on the numerical method.
One-level prediction-A numerical method for estimating undiscovered metal endowment
McCammon, R.B.; Kork, J.O.
1992-01-01
One-level prediction has been developed as a numerical method for estimating undiscovered metal endowment within large areas. The method is based on a presumed relationship between a numerical measure of geologic favorability and the spatial distribution of metal endowment. Metal endowment within an unexplored area for which the favorability measure is greater than a favorability threshold level is estimated to be proportional to the area of that unexplored portion. The constant of proportionality is the ratio of the discovered endowment found within a suitably chosen control region, which has been explored, to the area of that explored region. In addition to the estimate of undiscovered endowment, a measure of the error of the estimate is also calculated. One-level prediction has been used to estimate the undiscovered uranium endowment in the San Juan basin, New Mexico, U.S.A. A subroutine to perform the necessary calculations is included. ?? 1992 Oxford University Press.
Li, Xianting; Shao, Xiaoliang; Ma, Xiaojun; Zhang, Yuanhui; Cai, Hao
2011-08-15
Ventilation system with air recirculation is designed to conserve energy, yet at the same time may result in transporting hazardous substance among different rooms in the same building, which is a concern in indoor air quality control. There is a lack of effective methods to predict indoor contaminant distribution primarily because of uncertainty of the contaminant concentration in supply air which in turn due to the mixing ratio of fresh and recirculation air. In this paper, a versatile numerical method to determine the pollutant distribution of ventilation system with recirculation at steady state is proposed based on typical ventilation systems with accessibility of supply air (ASA) and accessibility of contaminant source (ACS). The relationship is established between contaminant concentrations of supply air and return air in a ventilated room or zone. The concentrations of supply air and contaminant distribution in each room can be determined using such parameters as ASA and ACS. The proposed method is validated by both experimental data and numerical simulation result. The computing speed of the proposed method is compared with the iteration method. The comparisons between the proposed method and the lumped parameter model are also conducted. The advantages of the proposed method in terms of accuracy, speed and versatility make it advantageous to be applied in air quality control of complex ventilation systems with recirculation.
A new numerical method for calculating extrema of received power for polarimetric SAR
Zhang, Y.; Zhang, Jiahua; Lu, Zhiming; 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.
NASA Astrophysics Data System (ADS)
Jalali Farahani, R.; Li, S.; Mohammed, F.; Astill, S.; Williams, C. R.; Lee, R.; Wilson, P. S.; Srinvias, B.
2014-12-01
Six transoceanic historical tsunami events including Japan Tohoku tsunami (2011), Chile Maule tsunami (2010), Indian Ocean tsunami (2004), Japan Nankai tsunami (1946), Chile Valdivia tsunami (1960), and Alaska tsunami (1964) have been modeled using a 2D well-balanced shallow water numerical model. The model solves the nonlinear 2D shallow water equations using an upwind finite volume method and is shown in this study to be capable of modeling the tsunami waves and resulting inundations over complex topography and bathymetry. The finite volume method is capable of modeling the wetting and drying of the bed surface at the coastline with no numerical instabilities and the inundation is modeled by allowing the computational cells to dynamically change from dry to wet. The numerical model implements parallel computations on Graphics Processing Units (GPUs), which enables the model to implement detailed modeling of inundation of small-scale coastal regions in a short simulation time. The slip distribution and seismic moment of the six earthquake driven tsunami events are introduced to the model as the initial condition including coastal uplift and subsidence. Both local regions and far-field regions affected by these tsunami waves are numerically studied and the resulting run-up and tsunami inundations are compared with the recorded observation data provided by National Oceanic and Atmospheric Administration (NOAA) including coastal tide gauges and eyewitness observation data. The GPU-based finite volume model indicates accuracy and robustness as well as short simulation time that can be used for transoceanic tsunami waves modeling including real-time numerical modeling of tsunami events and their inland inundations.
A numerical method for the dynamics of non-spherical cavitation bubbles
NASA Technical Reports Server (NTRS)
Lucca, G.; Prosperetti, A.
1982-01-01
A boundary integral numerical method for the dynamics of nonspherical cavitation bubbles in inviscid incompressible liquids is described. Only surface values of the velocity potential and its first derivatives are involved. The problem of solving the Laplace equation in the entire domain occupied by the liquid is thus avoided. The collapse of a bubble in the vicinity of a solid wall and the collapse of three bubbles with collinear centers are considered.
Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies
NASA Astrophysics Data System (ADS)
Khoromskaia, Venera; Khoromskij, Boris N.
We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, led to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in $O(n\\log n)$ complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D $n\\times n\\times n $ Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D ``density fitting`` scheme. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excited states, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is related to the recent attempts to develop a tensor-based Hartree-Fock numerical scheme for finite lattice-structured systems, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a $L\\times L\\times L$ lattice manifests the linear in $L$ computational work, $O(L)$, instead of the usual $O(L^3 \\log L)$ scaling by the Ewald-type approaches.
Numerical study of a matrix-free trust-region SQP method for equality constrained optimization.
Heinkenschloss, Matthias; Ridzal, Denis; Aguilo, Miguel Antonio
2011-12-01
This is a companion publication to the paper 'A Matrix-Free Trust-Region SQP Algorithm for Equality Constrained Optimization' [11]. In [11], we develop and analyze a trust-region sequential quadratic programming (SQP) method that supports the matrix-free (iterative, in-exact) solution of linear systems. In this report, we document the numerical behavior of the algorithm applied to a variety of equality constrained optimization problems, with constraints given by partial differential equations (PDEs).
NASA Astrophysics Data System (ADS)
Grigorov, Igor V.
2009-12-01
In article the algorithm of numerical modelling of the nonlinear equation of Korteweg-de Vrieze which generates nonlinear algorithm of digital processing of signals is considered. For realisation of the specified algorithm it is offered to use a inverse scattering method (ISM). Algorithms of direct and return spectral problems, and also problems of evolution of the spectral data are in detail considered. Results of modelling are resulted.
AN EFFICIENT NUMERICAL METHOD FOR THE SOLUTION OF THE L(2) OPTIMAL MASS TRANSFER PROBLEM.
Haber, Eldad; Rehman, Tauseef; Tannenbaum, Allen
2010-01-01
In this paper we present a new computationally efficient numerical scheme for the minimizing flow approach for the computation of the optimal L(2) mass transport mapping. In contrast to the integration of a time dependent partial differential equation proposed in [S. Angenent, S. Haker, and A. Tannenbaum, SIAM J. Math. Anal., 35 (2003), pp. 61-97], we employ in the present work a direct variational method. The efficacy of the approach is demonstrated on both real and synthetic data. PMID:21278828
AN EFFICIENT NUMERICAL METHOD FOR THE SOLUTION OF THE L2 OPTIMAL MASS TRANSFER PROBLEM*
Haber, Eldad; Rehman, Tauseef; Tannenbaum, Allen
2010-01-01
In this paper we present a new computationally efficient numerical scheme for the minimizing flow approach for the computation of the optimal L2 mass transport mapping. In contrast to the integration of a time dependent partial differential equation proposed in [S. Angenent, S. Haker, and A. Tannenbaum, SIAM J. Math. Anal., 35 (2003), pp. 61–97], we employ in the present work a direct variational method. The efficacy of the approach is demonstrated on both real and synthetic data. PMID:21278828
Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.
Khoromskaia, Venera; Khoromskij, Boris N
2015-12-21
We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches. PMID:26016539
NASA Astrophysics Data System (ADS)
Wetzstein, M.; Nelson, Andrew F.; Naab, T.; Burkert, A.
2009-10-01
We present a numerical code for simulating the evolution of astrophysical systems using particles to represent the underlying fluid flow. The code is written in Fortran 95 and is designed to be versatile, flexible, and extensible, with modular options that can be selected either at the time the code is compiled or at run time through a text input file. We include a number of general purpose modules describing a variety of physical processes commonly required in the astrophysical community and we expect that the effort required to integrate additional or alternate modules into the code will be small. In its simplest form the code can evolve the dynamical trajectories of a set of particles in two or three dimensions using a module which implements either a Leapfrog or Runge-Kutta-Fehlberg integrator, selected by the user at compile time. The user may choose to allow the integrator to evolve the system using individual time steps for each particle or with a single, global time step for all. Particles may interact gravitationally as N-body particles, and all or any subset may also interact hydrodynamically, using the smoothed particle hydrodynamic (SPH) method by selecting the SPH module. A third particle species can be included with a module to model massive point particles which may accrete nearby SPH or N-body particles. Such particles may be used to model, e.g., stars in a molecular cloud. Free boundary conditions are implemented by default, and a module may be selected to include periodic boundary conditions. We use a binary "Press" tree to organize particles for rapid access in gravity and SPH calculations. Modules implementing an interface with special purpose "GRAPE" hardware may also be selected to accelerate the gravity calculations. If available, forces obtained from the GRAPE coprocessors may be transparently substituted for those obtained from the tree, or both tree and GRAPE may be used as a combination GRAPE/tree code. The code may be run without
Wetzstein, M.; Nelson, Andrew F.; Naab, T.; Burkert, A.
2009-10-01
We present a numerical code for simulating the evolution of astrophysical systems using particles to represent the underlying fluid flow. The code is written in Fortran 95 and is designed to be versatile, flexible, and extensible, with modular options that can be selected either at the time the code is compiled or at run time through a text input file. We include a number of general purpose modules describing a variety of physical processes commonly required in the astrophysical community and we expect that the effort required to integrate additional or alternate modules into the code will be small. In its simplest form the code can evolve the dynamical trajectories of a set of particles in two or three dimensions using a module which implements either a Leapfrog or Runge-Kutta-Fehlberg integrator, selected by the user at compile time. The user may choose to allow the integrator to evolve the system using individual time steps for each particle or with a single, global time step for all. Particles may interact gravitationally as N-body particles, and all or any subset may also interact hydrodynamically, using the smoothed particle hydrodynamic (SPH) method by selecting the SPH module. A third particle species can be included with a module to model massive point particles which may accrete nearby SPH or N-body particles. Such particles may be used to model, e.g., stars in a molecular cloud. Free boundary conditions are implemented by default, and a module may be selected to include periodic boundary conditions. We use a binary 'Press' tree to organize particles for rapid access in gravity and SPH calculations. Modules implementing an interface with special purpose 'GRAPE' hardware may also be selected to accelerate the gravity calculations. If available, forces obtained from the GRAPE coprocessors may be transparently substituted for those obtained from the tree, or both tree and GRAPE may be used as a combination GRAPE/tree code. The code may be run without
Method of manufacturing semiconductor having group II-group VI compounds doped with nitrogen
Compaan, Alvin D.; Price, Kent J.; Ma, Xianda; Makhratchev, Konstantin
2005-02-08
A method of making a semiconductor comprises depositing a group II-group VI compound onto a substrate in the presence of nitrogen using sputtering to produce a nitrogen-doped semiconductor. This method can be used for making a photovoltaic cell using sputtering to apply a back contact layer of group II-group VI compound to a substrate in the presence of nitrogen, the back coating layer being doped with nitrogen. A semiconductor comprising a group II-group VI compound doped with nitrogen, and a photovoltaic cell comprising a substrate on which is deposited a layer of a group II-group VI compound doped with nitrogen, are also included.
A numerical method for determining the strain rate intensity factor under plane strain conditions
NASA Astrophysics Data System (ADS)
Alexandrov, S.; Kuo, C.-Y.; Jeng, Y.-R.
2016-07-01
Using the classical model of rigid perfectly plastic solids, the strain rate intensity factor has been previously introduced as the coefficient of the leading singular term in a series expansion of the equivalent strain rate in the vicinity of maximum friction surfaces. Since then, many strain rate intensity factors have been determined by means of analytical and semi-analytical solutions. However, no attempt has been made to develop a numerical method for calculating the strain rate intensity factor. This paper presents such a method for planar flow. The method is based on the theory of characteristics. First, the strain rate intensity factor is derived in characteristic coordinates. Then, a standard numerical slip-line technique is supplemented with a procedure to calculate the strain rate intensity factor. The distribution of the strain rate intensity factor along the friction surface in compression of a layer between two parallel plates is determined. A high accuracy of this numerical solution for the strain rate intensity factor is confirmed by comparison with an analytic solution. It is shown that the distribution of the strain rate intensity factor is in general discontinuous.
Numerical Simulation of the Friction Stir Welding Process Using Coupled Eulerian Lagrangian Method
NASA Astrophysics Data System (ADS)
Iordache, M.; Badulescu, C.; Iacomi, D.; Nitu, E.; Ciuca, C.
2016-08-01
Friction Stir Welding (FSW) is a solid state joining process that relies on frictional heating and plastic deformation realized at the interaction between a non-consumable welding tool that rotates on the contact surfaces of the combined parts. The experiments are often time consuming and costly. To overcome these problems, numerical analysis has frequently been used in last years. Several simplified numerical models were designed to elucidate various aspects of the complex thermo-mechanical phenomena associated with FSW. This research investigates a thermo-mechanical finite element model based on Coupled Eulerian Lagrangian method to simulate the friction stir welding of the AA 6082-T6 alloy. Abaqus/cae software is used in order to simulate the welding stage of the Friction Stir Welding process. This paper presents the steps of the numerical simulation using the finite elements method, in order to evaluate the boundary conditions of the model and the geometry of the tools by using the Coupled Eulerian Lagrangian method.
NASA Technical Reports Server (NTRS)
Hu, Fang Q.
1994-01-01
It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converges slowly for high frequency waves. In this paper, we present a fast number solution for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of the integral kernels are removed and dealt with accurately. The proposed method preserves the spectral accuracy and is shown to have an exponential rate of convergence. Aspects of efficient implementation using FFT are discussed. Moreover, the boundary integral equations of combined single and double-layer representation are used in the present paper. This ensures the uniqueness of the numerical solution for the scattering problem at all frequencies. Although a strongly singular kernel is encountered for the Neumann boundary conditions, we show that the hypersingularity can be handled easily in the spectral method. Numerical examples that demonstrate the validity of the method are also presented.
Xie, Lie-Jun; Zhou, Cai-Lian; Xu, Song
2016-01-01
In this work, an effective numerical method is developed to solve a class of singular boundary value problems arising in various physical models by using the improved differential transform method (IDTM). The IDTM applies the Adomian polynomials to handle the differential transforms of the nonlinearities arising in the given differential equation. The relation between the Adomian polynomials of those nonlinear functions and the coefficients of unknown truncated series solution is given by a simple formula, through which one can easily deduce the approximate solution which takes the form of a convergent series. An upper bound for the estimation of approximate error is presented. Several physical problems are discussed as illustrative examples to testify the validity and applicability of the proposed method. Comparisons are made between the present method and the other existing methods. PMID:27462514
Sphericity measurements by the radial method: II. Experimental verification
NASA Astrophysics Data System (ADS)
Janecki, D.; Stępień, K.; Adamczak, S.
2016-01-01
The new concept of sphericity measurements enables accurate measurement of spherical elements. This concept assumes that measurements can be performed using a typical radial roundness measuring instrument equipped with a special mechanism for controlled positioning of a measured element. The concept requires solving numerous theoretical problems, and this was described in the previous companion paper. This second paper discusses the measuring equipment and the results of the experimental verification of the concept.
NASA Technical Reports Server (NTRS)
Zeng, S.; Wesseling, P.
1993-01-01
The performance of a linear multigrid method using four smoothing methods, called SCGS (Symmetrical Coupled GauBeta-Seidel), CLGS (Collective Line GauBeta-Seidel), SILU (Scalar ILU), and CILU (Collective ILU), is investigated for the incompressible Navier-Stokes equations in general coordinates, in association with Galerkin coarse grid approximation. Robustness and efficiency are measured and compared by application to test problems. The numerical results show that CILU is the most robust, SILU the least, with CLGS and SCGS in between. CLGS is the best in efficiency, SCGS and CILU follow, and SILU is the worst.
Numerical methods for the weakly compressible Generalized Langevin Model in Eulerian reference frame
NASA Astrophysics Data System (ADS)
Azarnykh, Dmitrii; 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 solved 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.
Numerical Methods in Atmospheric and Oceanic Modelling: The Andre J. Robert Memorial Volume
NASA Astrophysics Data System (ADS)
Rosmond, Tom
Most people, even including some in the scientific community, do not realize how much the weather forecasts they use to guide the activities of their daily lives depend on very complex mathematics and numerical methods that are the basis of modern numerical weather prediction (NWP). André Robert (1929-1993), to whom Numerical Methods in Atmospheric and Oceanic Modelling is dedicated, had a career that contributed greatly to the growth of NWP and the role that the atmospheric computer models of NWP play in our society. There are probably no NWP models running anywhere in the world today that do not use numerical methods introduced by Robert, and those of us who work with and use these models everyday are indebted to him.The first two chapters of the volume are chronicles of Robert's life and career. The first is a 1987 interview by Harold Ritchie, one of Robert's many proteges and colleagues at the Canadian Atmospheric Environment Service. The interview traces Robert's life from his birth in New York to French Canadian parents, to his emigration to Quebec at an early age, his education and early employment, and his rise in stature as one of the preeminent research meteorologists of our time. An amusing anecdote he relates is his impression of weather forecasts while he was considering his first job as a meteorologist in the early 1950s. A newspaper of the time placed the weather forecast and daily horoscope side by side, and Robert regarded each to have a similar scientific basis. Thankfully he soon realized there was a difference between the two, and his subsequent career certainly confirmed the distinction.
An efficient numerical method for computing dynamics of spin F = 2 Bose-Einstein condensates
Wang Hanquan
2011-07-01
In this paper, we extend the efficient time-splitting Fourier pseudospectral method to solve the generalized Gross-Pitaevskii (GP) equations, which model the dynamics of spin F = 2 Bose-Einstein condensates at extremely low temperature. Using the time-splitting technique, we split the generalized GP equations into one linear part and two nonlinear parts: the linear part is solved with the Fourier pseudospectral method; one of nonlinear parts is solved analytically while the other one is reformulated into a matrix formulation and solved by diagonalization. We show that the method keeps well the conservation laws related to generalized GP equations in 1D and 2D. We also show that the method is of second-order in time and spectrally accurate in space through a one-dimensional numerical test. We apply the method to investigate the dynamics of spin F = 2 Bose-Einstein condensates confined in a uniform/nonuniform magnetic field.
Performance of Higher Order Campbell methods, Part I: review and numerical convergence study
NASA Astrophysics Data System (ADS)
Elter, Zs.; Bakkali, M.; Jammes, C.; Pázsit, I.
2016-06-01
This paper investigates, through numerical simulations, the performance of a signal analysis method by which a high temperature fission chamber can be used over a wide range of count rates. Results reported in a previous paper (Elter et al., 2015 [1]) indicated that the traditional Campbell method and the pulse mode cannot provide a sufficient overlap at medium count rates. Hence the use of the so-called Higher Order Campbell (HOC) methods is proposed and their performance is investigated. It is shown that the HOC methods can guarantee the linearity (i.e. correctness) of the neutron flux estimation over a wide count rate, even during transient conditions. The capabilities of these methods for suppressing parasitic noise (originating from various sources) are verified.
NASA Astrophysics Data System (ADS)
Luque, Alejandro; Villanueva, Jordi
2016-06-01
We present a numerical method for computing initial conditions of Lagrangian quasi-periodic invariant tori of Hamiltonian systems and symplectic maps. Such initial conditions are found by solving, using the Newton method, a nonlinear system obtained by imposing suitable conditions on the frequency map. The basic tool is a newly developed methodology to perform the frequency analysis of a discrete quasi-periodic signal, allowing to compute frequencies and their derivatives with respect to parameters. Roughly speaking, this method consists in computing suitable weighted averages of the iterates of the signal and using the Richardson extrapolation method. The proposed approach performs with high accuracy at a moderate computational cost. We illustrate the method by considering a discrete FPU model and the vicinity of the point L4 in a RTBP.
Numerical Analysis of Cold Spray Particles Impacting Behavior by the Eulerian Method: A Review
NASA Astrophysics Data System (ADS)
Li, W. Y.; Yang, K.; Yin, S.; Guo, X. P.
2016-08-01
Numerical simulations have been widely used to study particles impacting behavior in cold spraying. Among the used simulation methods, the Eulerian frame becomes increasingly attractive for its absence of mesh distortion which happens in the Lagrangian frame. It has been proved that particle deformation behaviors upon impacting calculated by the Eulerian method are well comparable to the experimental observations. In this review article, the literature on modeling particle impacting by the Eulerian method was summarized. In the second part, the Eulerian method was detailedly introduced. In the third part, the particle/substrate impacting behavior, and its influencing factors, i.e., mesh resolution, particle impacting velocity, preheating (particle or/and substrate) and oxide film, were summarized. Additionally, the prediction of critical velocity and residual stresses by using the Eulerian method was also discussed in detail. Finally, the current issues, problems and prospects existing in the Eulerian simulations of particle impacting were explored.
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.
Multiscale numerical methods for passive advection-diffusion in incompressible turbulent flow fields
NASA Astrophysics Data System (ADS)
Lee, Yoonsang; Engquist, Bjorn
2016-07-01
We propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection-diffusion equations with steady incompressible velocity fields with multi-spatial scales. The method uses decompositions of the velocity fields in the Fourier space, which are similar to the decomposition in large eddy simulations. It also uses a hierarchy of local domains with different resolutions as in multigrid methods. The effective diffusivity from finer scale is used for the next coarser level computation and this process is repeated up to the coarsest scale of interest. The grids are only in local domains whose sizes decrease depending on the resolution level so that the overall computational complexity increases linearly as the number of different resolution grids increases. The method captures interactions between finer and coarser scales but has to sacrifice some of interactions between different scales. The proposed method is numerically tested with 2D examples including a successful approximation to a continuous spectrum flow.
NASA Astrophysics Data System (ADS)
Hatanaka, K.; Hayashi, M.; Kawahara, M.
A novel FEM scheme that is based on the fractional-step method for solving time-dependent, incompressible viscous flow is presented and employed in the solution of a free-surface flow. The equations are given in indicial notation, as well as in the summation convention for repeated indices. The numerical results obtained exhibit good stability without the specification of Neumann conditions, and are compared in tabular form with the solutions given by Laitone's (1960) approximation. The method is also applicable to problems with artificial, open boundaries.
Ren, K
1990-07-01
A new numerical method of determining potentiometric titration end-points is presented. It consists in calculating the coefficients of approximative spline functions describing the experimental data (e.m.f., volume of titrant added). The end-point (the inflection point of the curve) is determined by calculating zero points of the second derivative of the approximative spline function. This spline function, unlike rational spline functions, is free from oscillations and its course is largely independent of random errors in e.m.f. measurements. The proposed method is useful for direct analysis of titration data and especially as a basis for construction of microcomputer-controlled automatic titrators. PMID:18964999
Development of Numerical Simulation Method for Compressible Gas-Liquid Two-Phase Flows
NASA Astrophysics Data System (ADS)
Tamura, Y.
2015-12-01
A numerical simulation method of compressible gas-liquid two-phase flow is developed for analyses of a cavitation bubble. Thermodynamic state of both phases is described with stiffened gas equation of state. Interface of two phases is captured by Level-Set method. As internal energy jump between two phases is critical for the stability of computation, total energy equation is modified so that inviscid flux of energy is smoothly connected across the interface. Detail of governing equations as well as their discretization is described followed by the result of one-dimensional simple example computation.
A method for data handling numerical results in parallel OpenFOAM simulations
Anton, Alin; Muntean, Sebastian
2015-12-31
Parallel computational fluid dynamics simulations produce vast amount of numerical result data. This paper introduces a method for reducing the size of the data by replaying the interprocessor traffic. The results are recovered only in certain regions of interest configured by the user. A known test case is used for several mesh partitioning scenarios using the OpenFOAM toolkit{sup ®}[1]. The space savings obtained with classic algorithms remain constant for more than 60 Gb of floating point data. Our method is most efficient on large simulation meshes and is much better suited for compressing large scale simulation results than the regular algorithms.
NASA Astrophysics Data System (ADS)
Burago, N. G.; Nikitin, I. S.; Yakushev, V. L.
2016-06-01
Techniques that improve the accuracy of numerical solutions and reduce their computational costs are discussed as applied to continuum mechanics problems with complex time-varying geometry. The approach combines shock-capturing computations with the following methods: (1) overlapping meshes for specifying complex geometry; (2) elastic arbitrarily moving adaptive meshes for minimizing the approximation errors near shock waves, boundary layers, contact discontinuities, and moving boundaries; (3) matrix-free implementation of efficient iterative and explicit-implicit finite element schemes; (4) balancing viscosity (version of the stabilized Petrov-Galerkin method); (5) exponential adjustment of physical viscosity coefficients; and (6) stepwise correction of solutions for providing their monotonicity and conservativeness.
MOLECULAR LINE EMISSION FROM MULTIFLUID SHOCK WAVES. I. NUMERICAL METHODS AND BENCHMARK TESTS
Ciolek, Glenn E.; Roberge, Wayne G. E-mail: roberw@rpi.edu
2013-05-01
We describe a numerical scheme for studying time-dependent, multifluid, magnetohydrodynamic shock waves in weakly ionized interstellar clouds and cores. Shocks are modeled as propagating perpendicular to the magnetic field and consist of a neutral molecular fluid plus a fluid of ions and electrons. The scheme is based on operator splitting, wherein time integration of the governing equations is split into separate parts. In one part, independent homogeneous Riemann problems for the two fluids are solved using Godunov's method. In the other, equations containing the source terms for transfer of mass, momentum, and energy between the fluids are integrated using standard numerical techniques. We show that, for the frequent case where the thermal pressures of the ions and electrons are << magnetic pressure, the Riemann problems for the neutral and ion-electron fluids have a similar mathematical structure which facilitates numerical coding. Implementation of the scheme is discussed and several benchmark tests confirming its accuracy are presented, including (1) MHD wave packets ranging over orders of magnitude in length- and timescales, (2) early evolution of multifluid shocks caused by two colliding clouds, and (3) a multifluid shock with mass transfer between the fluids by cosmic-ray ionization and ion-electron recombination, demonstrating the effect of ion mass loading on magnetic precursors of MHD shocks. An exact solution to an MHD Riemann problem forming the basis for an approximate numerical solver used in the homogeneous part of our scheme is presented, along with derivations of the analytic benchmark solutions and tests showing the convergence of the numerical algorithm.
Molecular Line Emission from Multifluid Shock Waves. I. Numerical Methods and Benchmark Tests
NASA Astrophysics Data System (ADS)
Ciolek, Glenn E.; Roberge, Wayne G.
2013-05-01
We describe a numerical scheme for studying time-dependent, multifluid, magnetohydrodynamic shock waves in weakly ionized interstellar clouds and cores. Shocks are modeled as propagating perpendicular to the magnetic field and consist of a neutral molecular fluid plus a fluid of ions and electrons. The scheme is based on operator splitting, wherein time integration of the governing equations is split into separate parts. In one part, independent homogeneous Riemann problems for the two fluids are solved using Godunov's method. In the other, equations containing the source terms for transfer of mass, momentum, and energy between the fluids are integrated using standard numerical techniques. We show that, for the frequent case where the thermal pressures of the ions and electrons are Lt magnetic pressure, the Riemann problems for the neutral and ion-electron fluids have a similar mathematical structure which facilitates numerical coding. Implementation of the scheme is discussed and several benchmark tests confirming its accuracy are presented, including (1) MHD wave packets ranging over orders of magnitude in length- and timescales, (2) early evolution of multifluid shocks caused by two colliding clouds, and (3) a multifluid shock with mass transfer between the fluids by cosmic-ray ionization and ion-electron recombination, demonstrating the effect of ion mass loading on magnetic precursors of MHD shocks. An exact solution to an MHD Riemann problem forming the basis for an approximate numerical solver used in the homogeneous part of our scheme is presented, along with derivations of the analytic benchmark solutions and tests showing the convergence of the numerical algorithm.
Numerical time dependent sheet cavitation simulations using a higher order panel method
NASA Astrophysics Data System (ADS)
Dekoninggans, H. J.
1994-03-01
This thesis deals with sheet cavitation. The investigation is aimed at profile design with respect to cavitation control. At present it is possible to predict the shape of cavities on an arbitrary two-dimensional profile in stationary flows. To compute the flow around an arbitrary profile, a higher order three-dimensional panel method program has been developed. The main algorithm used in this program is based on a special case of Green's theorem, called 'de Morino formulation'. This computer program (flow program) can calculate the potential on the body and the velocities at the surface of the body or in the flow field. A theoretical method is developed for time simulation of unsteady sheet cavitation. Numerical simulations of the flow around profiles and of cavitation have been carried out. The numerical results of the panel methods have been compared with other calculations of the two-dimensional flow around profiles and of three-dimensional flow around a sphere and a wing. Simulations of the growth of sheet cavitation on a foil have also been carried out. The conclusion is that higher order panel methods are more accurate than the zero order methods. Further refinement of the Kutta condition is required, however.
NASA Technical Reports Server (NTRS)
Thomas, P. D.
1979-01-01
The theoretical foundation and formulation of a numerical method for predicting the viscous flowfield in and about isolated three dimensional nozzles of geometrically complex configuration are presented. High Reynolds number turbulent flows are of primary interest for any combination of subsonic, transonic, and supersonic flow conditions inside or outside the nozzle. An alternating-direction implicit (ADI) numerical technique is employed to integrate the unsteady Navier-Stokes equations until an asymptotic steady-state solution is reached. Boundary conditions are computed with an implicit technique compatible with the ADI technique employed at interior points of the flow region. The equations are formulated and solved in a boundary-conforming curvilinear coordinate system. The curvilinear coordinate system and computational grid is generated numerically as the solution to an elliptic boundary value problem. A method is developed that automatically adjusts the elliptic system so that the interior grid spacing is controlled directly by the a priori selection of the grid spacing on the boundaries of the flow region.
Stress analysis and damage evaluation of flawed composite laminates by hybrid-numerical methods
NASA Technical Reports Server (NTRS)
Yang, Yii-Ching
1992-01-01
Structural components in flight vehicles is often inherited flaws, such as microcracks, voids, holes, and delamination. These defects will degrade structures the same as that due to damages in service, such as impact, corrosion, and erosion. It is very important to know how a structural component can be useful and survive after these flaws and damages. To understand the behavior and limitation of these structural components researchers usually do experimental tests or theoretical analyses on structures with simulated flaws. However, neither approach has been completely successful. As Durelli states that 'Seldom does one method give a complete solution, with the most efficiency'. Examples of this principle is seen in photomechanics which additional strain-gage testing can only average stresses at locations of high concentration. On the other hand, theoretical analyses including numerical analyses are implemented with simplified assumptions which may not reflect actual boundary conditions. Hybrid-Numerical methods which combine photomechanics and numerical analysis have been used to correct this inefficiency since 1950's. But its application is limited until 1970's when modern computer codes became available. In recent years, researchers have enhanced the data obtained from photoelasticity, laser speckle, holography and moire' interferometry for input of finite element analysis on metals. Nevertheless, there is only few of literature being done on composite laminates. Therefore, this research is dedicated to this highly anisotropic material.
NASA Astrophysics Data System (ADS)
Enukashvily, Isaac M.
1980-11-01
An extension of Bleck' method and of the method of moments is developed for the numerical integration of the kinetic equation of coalescence and breakup of cloud droplets. The number density function nk(x,t) in each separate cloud droplet packet between droplet mass grid points (xk,xk+1) is represented by an expansion in orthogonal polynomials with a given weighting function wk(x,k). The expansion coefficients describe the deviations of nk(x,t) from wk(x,k). In this way droplet number concentrations, liquid water contents and other moments in each droplet packet are conserved, and the problem of solving the kinetic equation is replaced by one of solving a set of coupled differential equations for the moments of the number density function nk(x,t). Equations for these moments in each droplet packet are derived. The method is tested against existing solutions of the coalescence equation. Numerical results are obtained when Bleck's uniform distribution hypothesis for nk(x,t) and Golovin's asymptotic solution of the coalescence equation is chosen for the, weighting function wk(x, k). A comparison between numerical results computed by Bleck's method and by the method of this study is made. It is shown that for the correct computation of the coalescence and breakup interactions between cloud droplet packets it is very important that the, approximation of the nk(x,t) between grid points (xk,xk+1) satisfies the conservation conditions for the number concentration, liquid water content and other moments of the cloud droplet packets. If these conservation conditions are provided, even the quasi-linear approximation of the nk(x,t) in comparison with Berry's six-point interpolation will give reasonable results which are very close to the existing analytic solutions.
Numerical divergence effects of equivalence theory in the nodal expansion method
Zika, M.R.; Downar, T.J. )
1993-11-01
Accurate solutions of the advanced nodal equations require the use of discontinuity factors (DFs) to account for the homogenization errors that are inherent in all coarse-mesh nodal methods. During the last several years, nodal equivalence theory (NET) has successfully been implemented for the Cartesian geometry and has received widespread acceptance in the light water reactor industry. The extension of NET to other reactor types has had limited success. Recent efforts to implement NET within the framework of the nodal expansion method have successfully been applied to the fast breeder reactor. However, attempts to apply the same methods to thermal reactors such as the Modular High-Temperature Gas Reactor (MHTGR) have led to numerical divergence problems that can be attributed directly to the magnitude of the DFs. In the work performed here, it was found that the numerical problems occur in the inner and upscatter iterations of the solution algorithm. These iterations use a Gauss-Seidel iterative technique that is always convergent for problems with unity DFs. However, for an MHTGR model that requires large DFs, both the inner and upscatter iterations were divergent. Initial investigations into methods for bounding the DFs have proven unsatisfactory as a means of remedying the convergence problems. Although the DFs could be bounded to yield a convergent solution, several cases were encountered where the resulting flux solution was less accurate than the solution without DFs. For the specific case of problems without upscattering, an alternate numerical method for the inner iteration, an LU decomposition, was identified and shown to be feasible.
Bao, Weizhu; Chern, I-Liang; Zhang, Yanzhi
2013-11-15
In this paper, we propose efficient numerical methods for computing ground states of spin-1 Bose–Einstein condensates (BECs) with/without the Ioffe–Pritchard magnetic field B(x). When B(x)≠0, a numerical method is introduced to compute the ground states and it is also applied to study properties of ground states. Numerical results suggest that the densities of m{sub F}=±1 components in ground states are identical for any nonzero B(x). In particular, if B(x)≡B≠0 is a constant, the ground states satisfy the single-mode approximation. When B(x)≡0, efficient and simpler numerical methods are presented to solve the ground states of spin-1 BECs based on their ferromagnetic/antiferromagnetic characterizations. Numerical simulations show that our methods are more efficient than those in the literature. In addition, some conjectures are made from our numerical observations.
A numerical method for generating rapidly rotating bipolytropic structures in equilibrium
NASA Astrophysics Data System (ADS)
Kadam, Kundan; Motl, Patrick M.; Frank, Juhan; Clayton, Geoffrey C.; Marcello, Dominic C.
2016-10-01
We demonstrate that rapidly rotating bipolytropic (composite polytropic) stars and toroidal discs can be obtained using Hachisu's self-consistent field technique. The core and the envelope in such a structure can have different polytropic indices and also different average molecular weights. The models converge for high T/|W| cases, where T is the kinetic energy and W is the gravitational energy of the system. The agreement between our numerical solutions with known analytical as well as previously calculated numerical results is excellent. We show that the uniform rotation lowers the maximum core mass fraction or the Schönberg-Chandrasekhar limit for a bipolytropic sequence. We also discuss the applications of this method to magnetic braking in low-mass stars with convective envelopes.
Fourth-Order Method for Numerical Integration of Age- and Size-Structured Population Models
Iannelli, M; Kostova, T; Milner, F A
2008-01-08
In many applications of age- and size-structured population models, there is an interest in obtaining good approximations of total population numbers rather than of their densities. Therefore, it is reasonable in such cases to solve numerically not the PDE model equations themselves, but rather their integral equivalents. For this purpose quadrature formulae are used in place of the integrals. Because quadratures can be designed with any order of accuracy, one can obtain numerical approximations of the solutions with very fast convergence. In this article, we present a general framework and a specific example of a fourth-order method based on composite Newton-Cotes quadratures for a size-structured population model.
Numerical solution of flame sheet problems with and without multigrid methods
NASA Technical Reports Server (NTRS)
Douglas, Craig C.; Ern, Alexandre
1993-01-01
Flame sheet problems are on the natural route to the numerical solution of multidimensional flames, which, in turn, are important in many engineering applications. In order to model the structure of flames more accurately, we use the vorticity-velocity formulation of the fluid flow equations, as opposed to the streamfunction-vorticity approach. The numerical solution of the resulting nonlinear coupled elliptic partial differential equations involves a pseudo transient process and a steady state Newton iteration. Rather than working with dimensionless variables, we introduce scale factors that can yield significant savings in the execution time. In this context, we also investigate the applicability and performance of several multigrid methods, focusing on nonlinear damped Newton multigrid, using either one way or correction schemes.
Numerical simulation of dam-break problem using staggered finite volume method
NASA Astrophysics Data System (ADS)
Budiasih, L. K.; Wiryanto, L. H.
2016-02-01
A problem in a dam-break is when a wall separating two sides of water is removed. A shock wave occurs and propagates. The behavior of the wave is interesting to be investigated with respect to the water depth and its wave speed. The aim of this research is to model dam-break problem using the non-linear shallow water equations and solve them numerically using staggered finite volume method. The solution is used to simulate the dam-break on a wet bed. Our numerical solution will be compared to the analytical solution of shallow water equations for dam-break problem. The momentum non-conservative finite volume scheme on a staggered grid will give a good agreement for dam-break problem on a wet bed, for depth ratios greater than 0.25.
NASA Technical Reports Server (NTRS)
Walitt, L.; Trulio, J. G.
1971-01-01
A numerical method is presented for the calculation of steady, three-dimensional, viscous, compressible flow fields about slender bodies at angle of attack and at supersonic speeds. Approximations are introduced in modeling the flow in the longitudinal direction. Accordingly, the flow fields calculated with the program were computed with a model that permits viscous crossflow together with inviscid axial flow. An analysis of the errors introduced by such a treatment is presented. Numerical calculations were made and compared with experimental results for an ogive-cylinder and an airplane fuselage configuration. Generally, good agreement with experiment was obtained. However, boundary layer separation and body vortex positions differed from experimental locations on the ogive-cylinder, and the shock induced by the fuselage canopy was predicted at a slightly different location.
NASA Astrophysics Data System (ADS)
Zhao, Xuzhe
High efficiency hydrogen storage method is significant in development of fuel cell vehicle. Seeking for a high energy density material as the fuel becomes the key of wide spreading fuel cell vehicle. LiBH4 + MgH 2 system is a strong candidate due to their high hydrogen storage density and the reaction between them is reversible. However, LiBH4 + MgH 2 system usually requires the high temperature and hydrogen pressure for hydrogen release and uptake reaction. In order to reduce the requirements of this system, nanoengineering is the simple and efficient method to improve the thermodynamic properties and reduce kinetic barrier of reaction between LiBH4 and MgH2. Based on ab initio density functional theory (DFT) calculations, the previous study has indicated that the reaction between LiBH4 and MgH2 can take place at temperature near 200°C or below. However, the predictions have been shown to be inconsistent with many experiments. Therefore, it is the first time that our experiment using ball milling with aerosol spraying (BMAS) to prove the reaction between LiBH4 and MgH2 can happen during high energy ball milling at room temperature. Through this BMAS process we have found undoubtedly the formation of MgB 2 and LiH during ball milling of MgH2 while aerosol spraying of the LiBH4/THF solution. Aerosol nanoparticles from LiBH 4/THF solution leads to form Li2B12H12 during BMAS process. The Li2B12H12 formed then reacts with MgH2 in situ during ball milling to form MgB 2 and LiH. Discrete element modeling (DEM) is a useful tool to describe operation of various ball milling processes. EDEM is software based on DEM to predict power consumption, liner and media wear and mill output. In order to further improve the milling efficiency of BMAS process, EDEM is conducted to make analysis for complicated ball milling process. Milling speed and ball's filling ratio inside the canister as the variables are considered to determine the milling efficiency. The average and maximum
Parachute technique: a complimentary method in zone II tendon repair.
Mozafari, Naser; Hosseini, Seyed Nejat; Abdolzadeh, Madjid; Mozafari, Mohammed Ali
2011-06-01
Flexor tendon lacerations still represent a challenging problem for the hand and the plastic surgeon, particularly in zone II. Many techniques have been devised accordingly to make the surgery of this zone easier. Hence, we too have devised an added complementary technique (ie, the parachute technique) to the common surgical techniques of the tendon repair to ease the repairing process and improve the outcomes. In this study, 79 patients, from whom 21 patients had 2 injured fingers, with flexor tendon injury in zone II (ie, 100 fingers) underwent this new technique. Finally, the results were hopeful. Thus, this complementary parachute technique combined with an early active mobilization with almost full range of flexion and extension, starting on the first postoperative day, resulted in improved outcomes compared with both passive mobilization and gentle active mobilization with a limited range of motion (ie, "controlled"). The Strickland formula (total active motion) system was used to evaluate the functional results of the flexor tendon repair. Finally, this technique is applicable for tendon repairs, and is shown to produce good results in their hands.
Don, W-S; Gotllieb, D; Shu, C-W; Jameson, L
2001-11-26
For flows that contain significant structure, high order schemes offer large advantages over low order schemes. Fundamentally, the reason comes from the truncation error of the differencing operators. If one examines carefully the expression for the truncation error, one will see that for a fixed computational cost that the error can be made much smaller by increasing the numerical order than by increasing the number of grid points. One can readily derive the following expression which holds for systems dominated by hyperbolic effects and advanced explicitly in time: flops = const * p{sup 2} * k{sup (d+1)(p+1)/p}/E{sup (d+1)/p} where flops denotes floating point operations, p denotes numerical order, d denotes spatial dimension, where E denotes the truncation error of the difference operator, and where k denotes the Fourier wavenumber. For flows that contain structure, such as turbulent flows or any calculation where, say, vortices are present, there will be significant energy in the high values of k. Thus, one can see that the rate of growth of the flops is very different for different values of p. Further, the constant in front of the expression is also very different. With a low order scheme, one quickly reaches the limit of the computer. With the high order scheme, one can obtain far more modes before the limit of the computer is reached. Here we examine the application of spectral methods and the Weighted Essentially Non-Oscillatory (WENO) scheme to the Richtmyer-Meshkov Instability. We show the intricate structure that these high order schemes can calculate and we show that the two methods, though very different, converge to the same numerical solution indicating that the numerical solution is very likely physically correct.
A high-order photon Monte Carlo method for radiative transfer in direct numerical simulation
Wu, Y.; Modest, M.F.; Haworth, D.C. . E-mail: dch12@psu.edu
2007-05-01
A high-order photon Monte Carlo method is developed to solve the radiative transfer equation. The statistical and discretization errors of the computed radiative heat flux and radiation source term are isolated and quantified. Up to sixth-order spatial accuracy is demonstrated for the radiative heat flux, and up to fourth-order accuracy for the radiation source term. This demonstrates the compatibility of the method with high-fidelity direct numerical simulation (DNS) for chemically reacting flows. The method is applied to address radiative heat transfer in a one-dimensional laminar premixed flame and a statistically one-dimensional turbulent premixed flame. Modifications of the flame structure with radiation are noted in both cases, and the effects of turbulence/radiation interactions on the local reaction zone structure are revealed for the turbulent flame. Computational issues in using a photon Monte Carlo method for DNS of turbulent reacting flows are discussed.
Numerical solution of differential algebraic equations (DAEs) by mix-multistep method
NASA Astrophysics Data System (ADS)
Rahim, Yong Faezah; Suleiman, Mohamed; Ibrahim, Zarina Bibi
2014-06-01
Differential Algebraic Equations (DAEs) are regarded as stiff Ordinary Differential Equations (ODEs). Therefore they are solved using implicit method such as Backward Differentiation Formula (BDF) type of methods which require the use of Newton iteration which need much computational effort. However, not all of the ODEs in DAE system are stiff. In this paper, we describe a new technique for solving DAE, where the ODEs are treated as non-stiff at the start of the integration and putting the non-stiff ODEs into stiff subsystem should instability occurs. Adams type of method is used to solve the non-stiff part and BDF method for solving the stiff part. This strategy is shown to be competitive in terms of computational effort and accuracy. Numerical experiments are presented to validate its efficiency.
Curvature-Based Method for Measuring Numerical Black-Hole Spins
NASA Astrophysics Data System (ADS)
Kelly, Bernard; Finch, Tehani; van Meter, James; Baker, John
2015-04-01
Accurate determination of spin magnitude and direction over time is crucial for the development of gravitational-wave templates that faithfully reflect the dynamics of generic comparable-mass black-hole binary mergers. We report on the development of a new method for measuring black-hole spins during numerical-relativity simulations of black-hole binary mergers. This method is based on the ``spin scalar,'' a complex scalar field derived from the Coulomb scalar of Beetle & Burko (2002). Our new method can be used to derive both spin magnitude and direction, and can be combined with other techniques, such as isolated-horizon methods. We present convergence studies, and demonstrations of behavior during precessing mergers of spinning black holes.
Numerical method to compute acoustic scattering effect of a moving source.
Song, Hao; Yi, Mingxu; Huang, Jun; Pan, Yalin; Liu, Dawei
2016-01-01
In this paper, the aerodynamic characteristic of a ducted tail rotor in hover has been numerically studied using CFD method. An analytical time domain formulation based on Ffowcs Williams-Hawkings (FW-H) equation is derived for the prediction of the acoustic velocity field and used as Neumann boundary condition on a rigid scattering surface. In order to predict the aerodynamic noise, a hybrid method combing computational aeroacoustics with an acoustic thin-body boundary element method has been proposed. The aerodynamic results and the calculated sound pressure levels (SPLs) are compared with the known method for validation. Simulation results show that the duct can change the value of SPLs and the sound directivity. Compared with the isolate tail rotor, the SPLs of the ducted tail rotor are smaller at certain azimuth. PMID:27610323
Numerical method to compute acoustic scattering effect of a moving source.
Song, Hao; Yi, Mingxu; Huang, Jun; Pan, Yalin; Liu, Dawei
2016-01-01
In this paper, the aerodynamic characteristic of a ducted tail rotor in hover has been numerically studied using CFD method. An analytical time domain formulation based on Ffowcs Williams-Hawkings (FW-H) equation is derived for the prediction of the acoustic velocity field and used as Neumann boundary condition on a rigid scattering surface. In order to predict the aerodynamic noise, a hybrid method combing computational aeroacoustics with an acoustic thin-body boundary element method has been proposed. The aerodynamic results and the calculated sound pressure levels (SPLs) are compared with the known method for validation. Simulation results show that the duct can change the value of SPLs and the sound directivity. Compared with the isolate tail rotor, the SPLs of the ducted tail rotor are smaller at certain azimuth.
NASA Astrophysics Data System (ADS)
Lolla, Madhuri Udayanjani
In this dissertation first, we compute the equilibrium shapes of 2D crystals under anisotropic surface free energies. An equilibrium shape minimizes the total surface free energy. The governing equation in polar coordinates is a nonlinear ordinary differential equation. Two numerical methods, finite difference and the finite element are used and compared. We investigate the accuracy, order of convergence and efficiency of the two methods in computing the equilibrium shapes. Secondly, we consider the surface of the crystal evolving under surface diffusion and compute the final shape in the evolution which is the equilibrium shape. The surface diffusion equation in polar coordinates is a time-dependent nonlinear 4th order partial differential equation. Again we apply the two methods finite difference and finite element. The results are observed at different stages of evolution of the crystal for the isotropy case. Then we compare the accuracy, order of convergence and efficiency of the two methods.
A numerical method to optimize the design of a space inflatable membrane reflector
NASA Astrophysics Data System (ADS)
Bouzidi, Rabah; Lecieux, Yann
2012-05-01
A numerical method is proposed to optimize the design of a space inflatable membrane reflector. The initial geometry is expressed by polynomial series weighted by a set of shape parameters. The problem is formulated as a minimization of a cost function representing the difference between the effective shape of the reflector and a perfect parabolic surface. The minimization is performed using the Nelder-Mead method or downhill simplex method. The cost function is computed at each vertex of a simplex defined in the space of optimization parameters by solving direct problem thanks to a finite element method. The finite element model handles geometrical non-linearities and takes into account phenomena like membrane wrinkling and torus buckling which may affect the reflector shape when inflated.
Discontinuous Galerkin Method with Numerical Roe Flux for Spherical Shallow Water Equations
NASA Astrophysics Data System (ADS)
Yi, T.; Choi, S.; Kang, S.
2013-12-01
In developing the dynamic core of a numerical weather prediction model with discontinuous Galerkin method, a numerical flux at the boundaries of grid elements plays a vital role since it preserves the local conservation properties and has a significant impact on the accuracy and stability of numerical solutions. Due to these reasons, we developed the numerical Roe flux based on an approximate Riemann problem for spherical shallow water equations in Cartesian coordinates [1] to find out its stability and accuracy. In order to compare the performance with its counterpart flux, we used the Lax-Friedrichs flux, which has been used in many dynamic cores such as NUMA [1], CAM-DG [2] and MCore [3] because of its simplicity. The Lax-Friedrichs flux is implemented by a flux difference between left and right states plus the maximum characteristic wave speed across the boundaries of elements. It has been shown that the Lax-Friedrichs flux with the finite volume method is more dissipative and unstable than other numerical fluxes such as HLLC, AUSM+ and Roe. The Roe flux implemented in this study is based on the decomposition of flux difference over the element boundaries where the nonlinear equations are linearized. It is rarely used in dynamic cores due to its complexity and thus computational expensiveness. To compare the stability and accuracy of the Roe flux with the Lax-Friedrichs, two- and three-dimensional test cases are performed on a plane and cubed-sphere, respectively, with various numbers of element and polynomial order. For the two-dimensional case, the Gaussian bell is simulated on the plane with two different numbers of elements at the fixed polynomial orders. In three-dimensional cases on the cubed-sphere, we performed the test cases of a zonal flow over an isolated mountain and a Rossby-Haurwitz wave, of which initial conditions are the same as those of Williamson [4]. This study presented that the Roe flux with the discontinuous Galerkin method is less
Numerical study of the vortex tube reconnection using vortex particle method on many graphics cards
NASA Astrophysics Data System (ADS)
Kudela, Henryk; Kosior, Andrzej
2014-08-01
Vortex Particle Methods are one of the most convenient ways of tracking the vorticity evolution. In the article we presented numerical recreation of the real life experiment concerning head-on collision of two vortex rings. In the experiment the evolution and reconnection of the vortex structures is tracked with passive markers (paint particles) which in viscous fluid does not follow the evolution of vorticity field. In numerical computations we showed the difference between vorticity evolution and movement of passive markers. The agreement with the experiment was very good. Due to problems with very long time of computations on a single processor the Vortex-in-Cell method was implemented on the multicore architecture of the graphics cards (GPUs). Vortex Particle Methods are very well suited for parallel computations. As there are myriads of particles in the flow and for each of them the same equations of motion have to be solved the SIMD architecture used in GPUs seems to be perfect. The main disadvantage in this case is the small amount of the RAM memory. To overcome this problem we created a multiGPU implementation of the VIC method. Some remarks on parallel computing are given in the article.
NASA Astrophysics Data System (ADS)
Anda, E.; Chiappe, G.; Busser, C.; Davidovich, M.; Martins, G.; H-Meisner, F.; Dagotto, E.
2008-03-01
A numerical algorithm to study transport properties of highly correlated local structures is proposed. The method, dubbed the Logarithmic Discretization Embedded Cluster Approximation (LDECA), consists of diagonalizing a finite cluster containing the many-body terms of the Hamiltonian and embedding it into the rest of the system, combined with Wilson's ideas of a logarithmic discretization of the representation of the Hamiltonian. LDECA's rapid convergence eliminates finite-size effects commonly present in the embedding cluster approximation (ECA) method. The physics associated with both one embedded dot and a string of two dots side-coupled to leads is discussed. In the former case, our results accurately agree with Bethe ansatz (BA) data, while in the latter, the results are framed in the conceptual background of a two-stage Kondo problem. A diagrammatic expansion provides the theoretical foundation for the method. It is argued that LDECA allows for the study of complex problems that are beyond the reach of currently available numerical methods.
Chen, Xueli E-mail: jimleung@mail.xidian.edu.cn; Yang, Defu; Zhang, Qitan; Liang, Jimin E-mail: jimleung@mail.xidian.edu.cn
2014-05-14
Even though bioluminescence tomography (BLT) exhibits significant potential and wide applications in macroscopic imaging of small animals in vivo, the inverse reconstruction is still a tough problem that has plagued researchers in a related area. The ill-posedness of inverse reconstruction arises from insufficient measurements and modeling errors, so that the inverse reconstruction cannot be solved directly. In this study, an l{sub 1/2} regularization based numerical method was developed for effective reconstruction of BLT. In the method, the inverse reconstruction of BLT was constrained into an l{sub 1/2} regularization problem, and then the weighted interior-point algorithm (WIPA) was applied to solve the problem through transforming it into obtaining the solution of a series of l{sub 1} regularizers. The feasibility and effectiveness of the proposed method were demonstrated with numerical simulations on a digital mouse. Stability verification experiments further illustrated the robustness of the proposed method for different levels of Gaussian noise.
Simulation of Intra-Aneurysmal Blood Flow by Different Numerical Methods
Weichert, Frank; Walczak, Lars; Fisseler, Denis; Opfermann, Tobias; Münster, Raphael; Grunwald, Iris; Roth, Christian; Veith, Christian; Wagner, Mathias
2013-01-01
The occlusional performance of sole endoluminal stenting of intracranial aneurysms is controversially discussed in the literature. Simulation of blood flow has been studied to shed light on possible causal attributions. The outcome, however, largely depends on the numerical method and various free parameters. The present study is therefore conducted to find ways to define parameters and efficiently explore the huge parameter space with finite element methods (FEMs) and lattice Boltzmann methods (LBMs). The goal is to identify both the impact of different parameters on the results of computational fluid dynamics (CFD) and their advantages and disadvantages. CFD is applied to assess flow and aneurysmal vorticity in 2D and 3D models. To assess and compare initial simulation results, simplified 2D and 3D models based on key features of real geometries and medical expert knowledge were used. A result obtained from this analysis indicates that a combined use of the different numerical methods, LBM for fast exploration and FEM for a more in-depth look, may result in a better understanding of blood flow and may also lead to more accurate information about factors that influence conditions for stenting of intracranial aneurysms. PMID:23662158
A simple numerical method for snowmelt simulation based on the equation of heat energy.
Stojković, Milan; Jaćimović, Nenad
2016-01-01
This paper presents one-dimensional numerical model for snowmelt/accumulation simulations, based on the equation of heat energy. It is assumed that the snow column is homogeneous at the current time step; however, its characteristics such as snow density and thermal conductivity are treated as functions of time. The equation of heat energy for snow column is solved using the implicit finite difference method. The incoming energy at the snow surface includes the following parts: conduction, convection, radiation and the raindrop energy. Along with the snow melting process, the model includes a model for snow accumulation. The Euler method for the numerical integration of the balance equation is utilized in the proposed model. The model applicability is demonstrated at the meteorological station Zlatibor, located in the western region of Serbia at 1,028 meters above sea level (m.a.s.l.) Simulation results of snowmelt/accumulation suggest that the proposed model achieved better agreement with observed data in comparison with the temperature index method. The proposed method may be utilized as part of a deterministic hydrological model in order to improve short and long term predictions of possible flood events. PMID:27054726
A simple numerical method for snowmelt simulation based on the equation of heat energy.
Stojković, Milan; Jaćimović, Nenad
2016-01-01
This paper presents one-dimensional numerical model for snowmelt/accumulation simulations, based on the equation of heat energy. It is assumed that the snow column is homogeneous at the current time step; however, its characteristics such as snow density and thermal conductivity are treated as functions of time. The equation of heat energy for snow column is solved using the implicit finite difference method. The incoming energy at the snow surface includes the following parts: conduction, convection, radiation and the raindrop energy. Along with the snow melting process, the model includes a model for snow accumulation. The Euler method for the numerical integration of the balance equation is utilized in the proposed model. The model applicability is demonstrated at the meteorological station Zlatibor, located in the western region of Serbia at 1,028 meters above sea level (m.a.s.l.) Simulation results of snowmelt/accumulation suggest that the proposed model achieved better agreement with observed data in comparison with the temperature index method. The proposed method may be utilized as part of a deterministic hydrological model in order to improve short and long term predictions of possible flood events.
Two step hybrid methods of 7th and 8th order for the numerical integration of second order IVPs
NASA Astrophysics Data System (ADS)
Kalogiratou, Z.; Monovasilis, Th.; Simos, T. E.
2016-06-01
In this work we consider the numerical integration of second order ODEs where the first derivative is missing. We construct two step hybrid methods with six and seven stages and seventh and eighth algebraic order. We apply the new methods on the numerical integration of several test problems.
NASA Astrophysics Data System (ADS)
Lee, K.; Gibson, R. L.
2002-12-01
The wavefront construction method is an efficient way to model wave propagation in anisotropic media. This method is based on asymptotic ray theory, and it explicitly tracks the propagation of wavefronts through the earth model. The first step is to trace a fan of rays through the earth model, initializing the wavefront by constructing a mesh from the set of all ray points at a specified travel time. The wavefront is thus a mesh composed of quadrilateral cells defined by four neighboring rays. Rays are computed by kinematic ray tracing using Runge-Kutta methods. The basic geometry, or coordinate system, used to select the rays comprising the initial mesh has significant affects on the precision and performance of the numerical calculation. A common approach is to trace rays with regular increments in the azimuthal and declination takeoff angles. These two angles, along with travel time, define a ray coordinate system that is commonly used for implementations of conventional ray tracing for wavefront construction schemes. While the ray coordinate system is straightforward to implement and has been used extensively, it has some drawbacks (Gibson et al., 2002). The most important is that the derivatives of Cartesian coordinates on the ray with respect to the azimuthal takeoff angle vanish near the poles of the coordinate system, leading to potential numerical errors. Our implementation applies paraxial methods, and the poor estimates of derivatives can seriously degrade the performance of the algorithm. Also, specifying an initial ray field with even increments in takeoff angles leads to large concentrations of rays near the poles, which is numerically inefficient. To overcome these important limitations of the ray coordinate system, we apply a new mesh generation algorithm that utilizes a cubic gnomonic mesh. A cubic gnomonic mesh maps points chosen at regular intervals on the surface of a cube surrounding the source point to the focal sphere. In essence, the initial
Papacharalampopoulos, Alexios; Vavva, Maria G; Protopappas, Vasilios C; Fotiadis, Dimitrios I; Polyzos, Demosthenes
2011-08-01
Cortical bone is a multiscale heterogeneous natural material characterized by microstructural effects. Thus guided waves propagating in cortical bone undergo dispersion due to both material microstructure and bone geometry. However, above 0.8 MHz, ultrasound propagates rather as a dispersive surface Rayleigh wave than a dispersive guided wave because at those frequencies, the corresponding wavelengths are smaller than the thickness of cortical bone. Classical elasticity, although it has been largely used for wave propagation modeling in bones, is not able to support dispersion in bulk and Rayleigh waves. This is possible with the use of Mindlin's Form-II gradient elastic theory, which introduces in its equation of motion intrinsic parameters that correlate microstructure with the macrostructure. In this work, the boundary element method in conjunction with the reassigned smoothed pseudo Wigner-Ville transform are employed for the numerical determination of time-frequency diagrams corresponding to the dispersion curves of Rayleigh and guided waves propagating in a cortical bone. A composite material model for the determination of the internal length scale parameters imposed by Mindlin's elastic theory is exploited. The obtained results demonstrate the dispersive nature of Rayleigh wave propagating along the complex structure of bone as well as how microstructure affects guided waves.
Jordan, Richard C K; Daniels, Troy E; Greenspan, John S; Regezi, Joseph A
2002-01-01
The practice of pathology is currently undergoing significant change, in large part due to advances in the analysis of DNA, RNA, and proteins in tissues. These advances have permitted improved biologic insights into many developmental, inflammatory, metabolic, infectious, and neoplastic diseases. Moreover, molecular analysis has also led to improvements in the accuracy of disease diagnosis and classification. It is likely that, in the future, these methods will increasingly enter into the day-to-day diagnosis and management of patients. The pathologist will continue to play a fundamental role in diagnosis and will likely be in a pivotal position to guide the implementation and interpretation of these tests as they move from the research laboratory into diagnostic pathology. The purpose of this 2-part series is to provide an overview of the principles and applications of current molecular biologic and immunologic tests. In Part I, the biologic fundamentals of DNA, RNA, and proteins and methods that are currently available or likely to become available to the pathologist in the next several years for their isolation and analysis in tissue biopsies were discussed. In Part II, advances in immunohistochemistry and immunofluorescence methods and their application to modern diagnostic pathology are reviewed. PMID:11805778
NASA Technical Reports Server (NTRS)
Zhai, Chengxing; Milman, Mark H.; Regehr, Martin W.; Best, Paul K.
2007-01-01
In the companion paper, [Appl. Opt. 46, 5853 (2007)] a highly accurate white light interference model was developed from just a few key parameters characterized in terms of various moments of the source and instrument transmission function. We develop and implement the end-to-end process of calibrating these moment parameters together with the differential dispersion of the instrument and applying them to the algorithms developed in the companion paper. The calibration procedure developed herein is based on first obtaining the standard monochromatic parameters at the pixel level: wavenumber, phase, intensity, and visibility parameters via a nonlinear least-squares procedure that exploits the structure of the model. The pixel level parameters are then combined to obtain the required 'global' moment and dispersion parameters. The process is applied to both simulated scenarios of astrometric observations and to data from the microarcsecond metrology testbed (MAM), an interferometer testbed that has played a prominent role in the development of this technology.
NASA Astrophysics Data System (ADS)
Ellmer, Matthias; Mayer-Gürr, Torsten
2016-04-01
Future gravity missions like GRACE-FO and beyond will deliver low-low satellite-to-satellite (ll-sst) ranging measurements of much increased precision. This necessitates a re-evaluation of the processes used in gravity field determination with an eye to numerical stability. When computing gravity fields from ll-sst data, precise positions of both satellites are needed in the setup of the observation equations. These positions thus have an immediate effect on the sought-after gravity field parameters. We use reduced-dynamic orbits which are computed through integration of all accelerations experienced by the satellite, as determined through a priori models and observed through the accelerometer. Our simulations showed that computing the orbit of the satellite through complete integration of all acting forces leads to numeric instabilities magnitudes larger than the expected ranging accuracy. We introduce a numerically stable approach employing a best-fit keplerian reference orbit based on Encke's method. Our investigations revealed that using canonical formulations for the evaluation of the reference keplerian orbit and accelerations lead to insufficient precision, necessitating an alternative formulation like the equinoctial elements.
NASA Technical Reports Server (NTRS)
Lang, Steve; Tao, W.-K.; Simpson, J.; Ferrier, B.; Einaudi, Franco (Technical Monitor)
2001-01-01
Six different convective-stratiform separation techniques, including a new technique that utilizes the ratio of vertical and terminal velocities, are compared and evaluated using two-dimensional numerical simulations of a tropical [Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE)] and midlatitude continental [Preliminary Regional Experiment for STORM-Central (PRESTORM)] squall line. The simulations are made using two different numerical advection schemes: 4th order and positive definite advection. Comparisons are made in terms of rainfall, cloud coverage, mass fluxes, apparent heating and moistening, mean hydrometeor profiles, CFADs (Contoured Frequency with Altitude Diagrams), microphysics, and latent heating retrieval. Overall, it was found that the different separation techniques produced results that qualitatively agreed. However, the quantitative differences were significant. Observational comparisons were unable to conclusively evaluate the performance of the techniques. Latent heating retrieval was shown to be sensitive to the use of separation technique mainly due to the stratiform region for methods that found very little stratiform rain. The midlatitude PRESTORM simulation was found to be nearly invariant with respect to advection type for most quantities while for TOGA COARE fourth order advection produced numerous shallow convective cores and positive definite advection fewer cells that were both broader and deeper penetrating above the freezing level.
A modular numerical method for implicit 0D/3D coupling in cardiovascular finite element simulations
NASA Astrophysics Data System (ADS)
Moghadam, Mahdi Esmaily; Vignon-Clementel, Irene E.; Figliola, Richard; Marsden, Alison L.; Modeling Of Congenital Hearts Alliance (Mocha) Investigators
2013-07-01
Implementation of boundary conditions in cardiovascular simulations poses numerical challenges due to the complex dynamic behavior of the circulatory system. The use of elaborate closed-loop lumped parameter network (LPN) models of the heart and the circulatory system as boundary conditions for computational fluid dynamics (CFD) simulations can provide valuable global dynamic information, particularly for patient specific simulations. In this paper, the necessary formulation for coupling an arbitrary LPN to a finite element Navier-Stokes solver is presented. A circuit analogy closed-loop LPN is solved numerically, and pressure and flow information is iteratively passed between the 0D and 3D domains at interface boundaries, resulting in a time-implicit scheme. For Neumann boundaries, an implicit method, regardless of the LPN, is presented to achieve the desired stability and convergence properties. Numerical procedures for passing flow and pressure information between the 0D and 3D domains are described, and implicit, semi-implicit, and explicit quasi-Newton formulations are compared. The issue of divergence in the presence of backflow is addressed via a stabilized boundary formulation. The requirements for coupling Dirichlet boundary conditions are also discussed and this approach is compared in detail to that of the Neumann coupled boundaries. Having the option to select between Dirichlet and Neumann coupled boundary conditions increases the flexibility of current framework by allowing a wide range of components to be used at the 3D-0D interface.
NASA Astrophysics Data System (ADS)
Liu, Yuk Tung; Etienne, Zachariah; Shapiro, Stuart
2011-04-01
The Illinois relativity group has written and tested a new GRMHD code, which is compatible with adaptive-mesh refinement (AMR) provided by the widely-used Cactus/Carpet infrastructure. Our code solves the Einstein-Maxwell-MHD system of coupled equations in full 3+1 dimensions, evolving the metric via the BSSN formalism and the MHD and magnetic induction equations via a conservative, high-resolution shock-capturing scheme. The induction equations are recast as an evolution equation for the magnetic vector potential. The divergenceless constraint div(B) = 0 is enforced by the curl of the vector potential. In simulations with uniform grid spacing, our MHD scheme is numerically equivalent to a commonly used, staggered-mesh constrained-transport scheme. We will present numerical method and code validation tests for both Minkowski and curved spacetimes. The tests include magnetized shocks, nonlinear Alfven waves, cylindrical explosions, cylindrical rotating disks, magnetized Bondi tests, and the collapse of a magnetized rotating star. Some of the more stringent tests involve black holes. We find good agreement between analytic and numerical solutions in these tests, and achieve convergence at the expected order.
Numerical Simulation of Dry Granular Flow Impacting a Rigid Wall Using the Discrete Element Method.
Wu, Fengyuan; Fan, Yunyun; Liang, Li; Wang, Chao
2016-01-01
This paper presents a clump model based on Discrete Element Method. The clump model was more close to the real particle than a spherical particle. Numerical simulations of several tests of dry granular flow impacting a rigid wall flowing in an inclined chute have been achieved. Five clump models with different sphericity have been used in the simulations. By comparing the simulation results with the experimental results of normal force on the rigid wall, a clump model with better sphericity was selected to complete the following numerical simulation analysis and discussion. The calculation results of normal force showed good agreement with the experimental results, which verify the effectiveness of the clump model. Then, total normal force and bending moment of the rigid wall and motion process of the granular flow were further analyzed. Finally, comparison analysis of the numerical simulations using the clump model with different grain composition was obtained. By observing normal force on the rigid wall and distribution of particle size at the front of the rigid wall at the final state, the effect of grain composition on the force of the rigid wall has been revealed. It mainly showed that, with the increase of the particle size, the peak force at the retaining wall also increase. The result can provide a basis for the research of relevant disaster and the design of protective structures. PMID:27513661
Numerical Simulation of Dry Granular Flow Impacting a Rigid Wall Using the Discrete Element Method
Wu, Fengyuan; Fan, Yunyun; Liang, Li; Wang, Chao
2016-01-01
This paper presents a clump model based on Discrete Element Method. The clump model was more close to the real particle than a spherical particle. Numerical simulations of several tests of dry granular flow impacting a rigid wall flowing in an inclined chute have been achieved. Five clump models with different sphericity have been used in the simulations. By comparing the simulation results with the experimental results of normal force on the rigid wall, a clump model with better sphericity was selected to complete the following numerical simulation analysis and discussion. The calculation results of normal force showed good agreement with the experimental results, which verify the effectiveness of the clump model. Then, total normal force and bending moment of the rigid wall and motion process of the granular flow were further analyzed. Finally, comparison analysis of the numerical simulations using the clump model with different grain composition was obtained. By observing normal force on the rigid wall and distribution of particle size at the front of the rigid wall at the final state, the effect of grain composition on the force of the rigid wall has been revealed. It mainly showed that, with the increase of the particle size, the peak force at the retaining wall also increase. The result can provide a basis for the research of relevant disaster and the design of protective structures. PMID:27513661
The Formation of a Milky Way-sized Disk Galaxy. I. A Comparison of Numerical Methods
NASA Astrophysics Data System (ADS)
Zhu, Qirong; Li, Yuexing
2016-11-01
The long-standing challenge of creating a Milky Way- (MW-) like disk galaxy from cosmological simulations has motivated significant developments in both numerical methods and physical models. We investigate these two fundamental aspects in a new comparison project using a set of cosmological hydrodynamic simulations of an MW-sized galaxy. In this study, we focus on the comparison of two particle-based hydrodynamics methods: an improved smoothed particle hydrodynamics (SPH) code Gadget, and a Lagrangian Meshless Finite-Mass (MFM) code Gizmo. All the simulations in this paper use the same initial conditions and physical models, which include star formation, “energy-driven” outflows, metal-dependent cooling, stellar evolution, and metal enrichment. We find that both numerical schemes produce a late-type galaxy with extended gaseous and stellar disks. However, notable differences are present in a wide range of galaxy properties and their evolution, including star-formation history, gas content, disk structure, and kinematics. Compared to Gizmo, the Gadget simulation produced a larger fraction of cold, dense gas at high redshift which fuels rapid star formation and results in a higher stellar mass by 20% and a lower gas fraction by 10% at z = 0, and the resulting gas disk is smoother and more coherent in rotation due to damping of turbulent motion by the numerical viscosity in SPH, in contrast to the Gizmo simulation, which shows a more prominent spiral structure. Given its better convergence properties and lower computational cost, we argue that the MFM method is a promising alternative to SPH in cosmological hydrodynamic simulations.
Two Approaches in the Lunar Libration Theory: Analytical vs. Numerical Methods
NASA Astrophysics Data System (ADS)
Petrova, Natalia; Zagidullin, Arthur; Nefediev, Yurii; Kosulin, Valerii
2016-10-01
Observation of the physical libration of the Moon and the celestial bodies is one of the astronomical methods to remotely evaluate the internal structure of a celestial body without using expensive space experiments. Review of the results obtained due to the physical libration study, is presented in the report.The main emphasis is placed on the description of successful lunar laser ranging for libration determination and on the methods of simulating the physical libration. As a result, estimation of the viscoelastic and dissipative properties of the lunar body, of the lunar core parameters were done. The core's existence was confirmed by the recent reprocessing of seismic data Apollo missions. Attention is paid to the physical interpretation of the phenomenon of free libration and methods of its determination.A significant part of the report is devoted to describing the practical application of the most accurate to date the analytical tables of lunar libration built by comprehensive analytical processing of residual differences obtained when comparing the long-term series of laser observations with numerical ephemeris DE421 [1].In general, the basic outline of the report reflects the effectiveness of two approaches in the libration theory - numerical and analytical solution. It is shown that the two approaches complement each other for the study of the Moon in different aspects: numerical approach provides high accuracy of the theory necessary for adequate treatment of modern high-accurate observations and the analytic approach allows you to see the essence of the various kind manifestations in the lunar rotation, predict and interpret the new effects in observations of physical libration [2].[1] Rambaux, N., J. G. Williams, 2011, The Moon's physical librations and determination of their free modes, Celest. Mech. Dyn. Astron., 109, 85–100.[2] Petrova N., A. Zagidullin, Yu. Nefediev. Analysis of long-periodic variations of lunar libration parameters on the basis
A pressure-based high resolution numerical method for resistive MHD
NASA Astrophysics Data System (ADS)
Xisto, Carlos M.; Páscoa, José C.; Oliveira, Paulo J.
2014-10-01
In the paper we describe in detail a numerical method for the resistive magnetohydrodynamic (MHD) equations involving viscous flow and report the results of application to a number of typical MHD test cases. The method is of the finite volume type but mixes aspects of pressure-correction and density based solvers; the algorithm arrangement is patterned on the well-known PISO algorithm, which is a pressure method, while the flux computation makes use of the AUSM-MHD scheme, which originates from density based methods. Five groups of test cases are addressed to verify and validate the method. We start with two resistive MHD cases, namely the Shercliff and Hunt flow problems, which are intended to validate the method for low-speed resistive MHD flows. The remaining three test cases, namely the cloud-shock interaction, the MHD rotor and the MHD blast wave, are standard 2D ideal MHD problems that serve to validate the method under high-speed flow and complex interaction of MHD shocks. Finally, we demonstrate the method with a more complex application problem, and discuss results of simulation for a quasi-bi-dimensional self-field magnetoplasmadynamic (MPD) thruster, for which we study the effect of cathode length upon the electromagnetic nozzle performance.
NASA Astrophysics Data System (ADS)
Chew, Huck Beng; Hong, Soonsung; Kim, Kyung-Suk
2009-08-01
Modeling ductile fracture processes using Gurson-type cell elements has achieved considerable success in recent years. However, incorporating the full mechanisms of void growth and coalescence in cohesive zone laws for ductile fracture still remains an open challenge. In this work, a planar field projection method, combined with equilibrium field regularization, is used to extract crack-tip cohesive zone laws of void growth in an elastic-plastic solid. To this end, a single row of void-containing cell elements is deployed directly ahead of a crack in an elastic-plastic medium subjected to a remote K-field loading; the macroscopic behavior of each cell element is governed by the Gurson porous material relation, extended to incorporate vapor pressure effects. A thin elastic strip surrounding this fracture process zone is introduced, from which the cohesive zone variables can be extracted via the planar field projection method. We show that the material's initial porosity induces a highly convex traction-separation relationship — the cohesive traction reaches the peak almost instantaneously and decreases gradually with void growth, before succumbing to rapid softening during coalescence. The profile of this numerically extracted cohesive zone law is consistent with experimentally determined cohesive zone law in Part I for multiple micro-crazing in HIPS. In the presence of vapor pressure, both the cohesive traction and energy are dramatically lowered; the shape of the cohesive zone law, however, remains highly convex, which suggests that diffusive damage is still the governing failure mechanism.
Yang, Chao; Mao, Zai-Sha
2005-03-01
The mirror fluid method is proposed for simulating solid-fluid two-phase flow. The whole computational domain is modeled as an Eulerian one for the fluid with a Lagrangian subdomain embedded in it. The boundary condition is enforced implicitly on solid-fluid surface segments by mirror relations. Thus, the total flow is solved in the one domain, in which the solid particle region is replaced with the virtual flow as the mirror image of outside flow. The mirror fluid method is implemented to compute the motion of a rigid spherical or elliptic particle in a Newtonian fluid for the purpose of method validation. The control volume formulation with the SIMPLE algorithm incorporated is used to solve the governing equations on a staggered grid in a two-dimensional coordinate system. A number of numerical experiments on falling particles are performed and the computational results are in good agreement with the reported experimental data.
Numerical method to determine mechanical parameters of engineering design in rock masses.
Xue, Ting-He; Xiang, Yi-Qiang; Guo, Fa-Zhong
2004-07-01
This paper proposes a new continuity model for engineering in rock masses and a new schematic method for reporting the engineering of rock continuity. This method can be used to evaluate the mechanics of every kind of medium; and is a new way to determine the mechanical parameters used in engineering design in rock masses. In the numerical simulation, the experimental parameters of intact rock were combined with the structural properties of field rock. The experimental results for orthogonally-jointed rock are given. The results included the curves of the stress-strain relationship of some rock masses, the curve of the relationship between the dimension Delta and the uniaxial pressure-resistant strength sc of these rock masses, and pictures of the destructive procedure of some rock masses in uniaxial or triaxial tests, etc. Application of the method to engineering design in rock masses showed the potential of its application to engineering practice.
Quan, Y.; Harris, J.M.; Chen, X.
1994-12-31
The centroid frequency shift method is proposed to estimate seismic attenuation from full waveform acoustic logs. This approach along with the amplitude ratio method is applied to investigate the attenuation properties of the P head wave in fluid-filled boreholes. The generalized reflection and transmission coefficients method is used to perform forward modeling. The authors suggest an empirical formula to describe the frequency-dependent geometrical spreading of the P-wave in a borehole. They simulate a more realistic borehole by including a mudcake and an invaded zone which are modeled by a large number of radially symmetric thin layers. The numerical tests show that this invaded zone exhibits very strong influence on the attenuation measurement.
Broken wires diagnosis method numerical simulation based on smart cable structure
NASA Astrophysics Data System (ADS)
Li, Sheng; Zhou, Min; Yang, Yan
2014-12-01
The smart cable with embedded distributed fiber optical Bragg grating (FBG) sensors was chosen as the object to study a new diagnosis method about broken wires of the bridge cable. The diagnosis strategy based on cable force and stress distribution state of steel wires was put forward. By establishing the bridge-cable and cable-steel wires model, the broken wires sample database was simulated numerically. A method of the characterization cable state pattern which can both represent the degree and location of broken wires inside a cable was put forward. The training and predicting results of the sample database by the back propagation (BP) neural network showed that the proposed broken wires diagnosis method was feasible and expanded the broken wires diagnosis research area by using the smart cable which was used to be only representing cable force.
A rapid numerical method for horizontal fluid flow in unsaturated soils
NASA Astrophysics Data System (ADS)
Kirby, J. M.
1984-06-01
A rapid numerical method for the horizontal flow of water is presented, based on the approximation for conductivity k = k0 exp (αψ). A simple expression for the velocity of flow is obtained, which produces accurate solutions to horizontal infiltration problems even with very large time and length steps. The method is compared with previous solutions, including the much studied Yolo light clay infiltration problems. These examples are used to demonstrate the accuracy and economy (in terms of the time and necessary computer power) of the solution. The method is accurate for any choice of length step, provided that the time step is below a certain limit which is related to the length step. An expression for estimating the maximum permissible time step is presented and its use demonstrated via one of the examples.
McCammon, R.B.; Finch, W.I.; Kork, J.O.; Bridges, N.J.
1994-01-01
An integrated data-directed numerical method has been developed to estimate the undiscovered mineral endowment within a given area. The method has been used to estimate the undiscovered uranium endowment in the San Juan Basin, New Mexico, U.S.A. The favorability of uranium concentration was evaluated in each of 2,068 cells defined within the Basin. Favorability was based on the correlated similarity of the geologic characteristics of each cell to the geologic characteristics of five area-related deposit models. Estimates of the undiscovered endowment for each cell were categorized according to deposit type, depth, and cutoff grade. The method can be applied to any mineral or energy commodity provided that the data collected reflect discovered endowment. ?? 1994 Oxford University Press.
Chia, Nicholas; Bundschuh, Ralf
2005-11-01
In the universality class of the one-dimensional Kardar-Parisi-Zhang (KPZ) surface growth, Derrida and Lebowitz conjectured the universality of not only the scaling exponents, but of an entire scaling function. Since and Derrida and Lebowitz's original publication [Phys. Rev. Lett. 80, 209 (1998)] this universality has been verified for a variety of continuous-time, periodic-boundary systems in the KPZ universality class. Here, we present a numerical method for directly examining the entire particle flux of the asymmetric exclusion process (ASEP), thus providing an alternative to more difficult cumulant ratios studies. Using this method, we find that the Derrida-Lebowitz scaling function (DLSF) properly characterizes the large-system-size limit (N--> infinity) of a single-particle discrete time system, even in the case of very small system sizes (N< or =22). This fact allows us to not only verify that the DLSF properly characterizes multiple-particle discrete-time asymmetric exclusion processes, but also provides a way to numerically solve for quantities of interest, such as the particle hopping flux. This method can thus serve to further increase the ease and accessibility of studies involving even more challenging dynamics, such as the open-boundary ASEP. PMID:16383588
Wang, Jinfeng; Zhao, Meng; Zhang, Min; Liu, Yang; Li, Hong
2014-01-01
We discuss and analyze an H(1)-Galerkin mixed finite element (H(1)-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H(1)-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H(1)-GMFE method. Based on the discussion on the theoretical error analysis in L(2)-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H(1)-norm. Moreover, we derive and analyze the stability of H(1)-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure.
Numerical sedimentation particle-size analysis using the Discrete Element Method
NASA Astrophysics Data System (ADS)
Bravo, R.; Pérez-Aparicio, J. L.; Gómez-Hernández, J. J.
2015-12-01
Sedimentation tests are widely used to determine the particle size distribution of a granular sample. In this work, the Discrete Element Method interacts with the simulation of flow using the well known one-way-coupling method, a computationally affordable approach for the time-consuming numerical simulation of the hydrometer, buoyancy and pipette sedimentation tests. These tests are used in the laboratory to determine the particle-size distribution of fine-grained aggregates. Five samples with different particle-size distributions are modeled by about six million rigid spheres projected on two-dimensions, with diameters ranging from 2.5 ×10-6 m to 70 ×10-6 m, forming a water suspension in a sedimentation cylinder. DEM simulates the particle's movement considering laminar flow interactions of buoyant, drag and lubrication forces. The simulation provides the temporal/spatial distributions of densities and concentrations of the suspension. The numerical simulations cannot replace the laboratory tests since they need the final granulometry as initial data, but, as the results show, these simulations can identify the strong and weak points of each method and eventually recommend useful variations and draw conclusions on their validity, aspects very difficult to achieve in the laboratory.
An Efficient numerical method to calculate the conductivity tensor for disordered topological matter
NASA Astrophysics Data System (ADS)
Garcia, Jose H.; Covaci, Lucian; Rappoport, Tatiana G.
2015-03-01
We propose a new efficient numerical approach to calculate the conductivity tensor in solids. We use a real-space implementation of the Kubo formalism where both diagonal and off-diagonal conductivities are treated in the same footing. We adopt a formulation of the Kubo theory that is known as Bastin formula and expand the Green's functions involved in terms of Chebyshev polynomials using the kernel polynomial method. Within this method, all the computational effort is on the calculation of the expansion coefficients. It also has the advantage of obtaining both conductivities in a single calculation step and for various values of temperature and chemical potential, capturing the topology of the band-structure. Our numerical technique is very general and is suitable for the calculation of transport properties of disordered systems. We analyze how the method's accuracy varies with the number of moments used in the expansion and illustrate our approach by calculating the transverse conductivity of different topological systems. T.G.R, J.H.G and L.C. acknowledge Brazilian agencies CNPq, FAPERJ and INCT de Nanoestruturas de Carbono, Flemish Science Foundation for financial support.
Keeping the edge: an accurate numerical method to solve the stream power law
NASA Astrophysics Data System (ADS)
Campforts, B.; Govers, G.
2015-12-01
Bedrock rivers set the base level of surrounding hill slopes and mediate the dynamic interplay between mountain building and denudation. The propensity of rivers to preserve pulses of increased tectonic uplift also allows to reconstruct long term uplift histories from longitudinal river profiles. An accurate reconstruction of river profile development at different timescales is therefore essential. Long term river development is typically modeled by means of the stream power law. Under specific conditions this equation can be solved analytically but numerical Finite Difference Methods (FDMs) are most frequently used. Nonetheless, FDMs suffer from numerical smearing, especially at knickpoint zones which are key to understand transient landscapes. Here, we solve the stream power law by means of a Finite Volume Method (FVM) which is Total Variation Diminishing (TVD). Total volume methods are designed to simulate sharp discontinuities making them very suitable to model river incision. In contrast to FDMs, the TVD_FVM is well capable of preserving knickpoints as illustrated for the fast propagating Niagara falls. Moreover, we show that the TVD_FVM performs much better when reconstructing uplift at timescales exceeding 100 Myr, using Eastern Australia as an example. Finally, uncertainty associated with parameter calibration is dramatically reduced when the TVD_FVM is applied. Therefore, the use of a TVD_FVM to understand long term landscape evolution is an important addition to the toolbox at the disposition of geomorphologists.
NASA Astrophysics Data System (ADS)
Takiguchi, Yu; Takamoto, Hisayoshi; Kanada, Masamitsu; Inoue, Takashi; Matsumoto, Naoya; Terakawa, Susumu
2014-03-01
We have developed a confocal fluorescence laser scanning microscopy (CFLSM) incorporating a liquid crystal on silicon spatial light modulator (LCOS-SLM). To achieve high-resolution and high-contrast imaging for deeper part of the tissue with CFLSM, high numerical aperture objective lenses are required to tightly focus excitation light to meet Rayleigh limit(criterion) for the specimens. However, mismatch of refractive index at the boundary of interfacing materials, such as atmosphere, glass cover, and biological tissues, causes spherical aberration. Recently, we proposed a numerical method for correcting spherical aberration. In this method a pre-distorted wavefront pattern for aberration correction is calculated by ray tracing from a hypothetical focal point inside a specimen to the pupil plane. The resulting microscope can correct such spherical aberration. We observed 6.0μm fluorescent micro-beads dispersed three-dimensionally in agarose gel to confirm effectiveness of aberration correction. We reconstructed a three-dimensional image by taking 20 images by changing the depth with 1 μm interval and stacking them. It was apparent that the longitudinal/depth resolution was improved and that the intensity of fluorescence image was increased with aberration correction. While this method is applicable to other laser scanning microscopes, it has potential to enhance the signals for various super-resolution microscopic techniques, such as stimulated- emission-depletion (STED) fluorescence microscopy.
Wang, Jinfeng; Zhao, Meng; Zhang, Min; Liu, Yang; Li, Hong
2014-01-01
We discuss and analyze an H(1)-Galerkin mixed finite element (H(1)-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H(1)-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H(1)-GMFE method. Based on the discussion on the theoretical error analysis in L(2)-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H(1)-norm. Moreover, we derive and analyze the stability of H(1)-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure. PMID:25184148
Numerical improvement of the three-dimensional indirect boundary element method
NASA Astrophysics Data System (ADS)
Ortiz-Aleman, C.; Gil-Zepeda, S. A.; Luzon, F.; Sanchez-Sesma, F. J.
2003-04-01
In recent years, several numerical techniques for the estimation of the seismic response in complex geologic configurations have been developed. The flexibility and versatility of these techniques have increased along with the improvement of computational systems, and they altogether have allowed the study of 3D geometries to model several sedimentary basins around the world. In this article we study the structure of the linear systems derived from the Indirect Boundary Element Method (IBEM). We apply a LU-sparse decomposition solver to the inversion of the IBEM coefficient matrix in order to optimise the numerical burden of such method. As pointed out before, special emphasis is given to understanding the main features of ground motion in sedimentary basins. We compute the seismic response of a 3D alluvial valley of irregular shape, as originally proposed by Sánchez-Sesma and Luzón (1995), and we establish comparisons on time consumption and memory allocation. Inversion of linear systems by using this new algorithm lead us to a significant saving on CPU time and memory allocation relative to the original IBEM formulation. Results represent an extension in the range of application of the IBEM method.
Computation of Nonlinear Backscattering Using a High-Order Numerical Method
NASA Technical Reports Server (NTRS)
Fibich, G.; Ilan, B.; Tsynkov, S.
2001-01-01
The nonlinear Schrodinger equation (NLS) is the standard model for propagation of intense laser beams in Kerr media. The NLS is derived from the nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. In this study we use a fourth-order finite-difference method supplemented by special two-way artificial boundary conditions (ABCs) to solve the NLH as a boundary value problem. Our numerical methodology allows for a direct comparison of the NLH and NLS models and for an accurate quantitative assessment of the backscattered signal.
A numerical study of unsteady cavitation on a hydrofoil by LES and URANS method
NASA Astrophysics Data System (ADS)
Li, Zi-ru; Zhang, Guang-ming; He, Wei; van Terwisga, Tom
2015-12-01
In this paper, the unsteady cavitation phenomena on a NACA0015 hydrofoil is numerically simulated by unsteady Reynolds-Averaged Navier-Stokes (URANS) method and Large Eddy Simulation (LES) in single-fluid approaches to multiphase modelling, respectively. It is observed that the large-scale structures and characteristic periodic shedding predicted by the URANS with the modified SST k-ω turbulence model show a good qualitative match with the experimental observations but with quantitative discrepancies, such as a different cavity length and volume, and a different location of shedding. Compared to the URANS results, the LES results reproduce more details of unsteady dynamics with an improved quantitative agreement.
A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations
NASA Technical Reports Server (NTRS)
Radhakrishnan, K.
1984-01-01
The efficiency of several algorithms used for numerical integration of stiff ordinary differential equations was compared. The methods examined included two general purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes were applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code available for the integration of combustion kinetic rate equations. It is shown that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient then evaluating the temperature by integrating its time-derivative.
A new numerical method for the simulation of three dimensional flow in a pipe
NASA Technical Reports Server (NTRS)
Leonard, A.; Wray, A.
1982-01-01
A new numerical technique for simulating three dimensional, unsteady, incompressible pipe flows is presented and its utility and accuracy is shown. Each vector function in the expansion of the velocity field is divergence free and satisfies the boundary conditions for viscous flow. Some of the benefits of the expansion technique are that pressure is eliminated from the dynamics, only two unknowns per mesh point are required, implicit treatment of the viscous terms is provided at no extra computational cost, and no fractional time steps are required. The method uses spectral expansions: Fourier series in the azimuthal and streamwise directions, and Jacobi polynominals in the radial direction.
Numerical study of human vocal folds vibration using Immersed Finite Element Method
NASA Astrophysics Data System (ADS)
Wang, Xingshi; Zhang, Lucy; Krane, Michael
2011-11-01
The voice production procedure is a self-oscillating, fluid-structure interaction problem. In this study, the vocal folds vibration during phonation will be simulated by self-oscillated layered-structure vocal folds model, using Immersed Finite Element Method. With the numerical results, we will find out the vocal folds vibration pattern, and also show how the lung pressure, stiffness and geometry of vocal folds will affect the vocal folds vibration. With further analysis, we shall get better understanding of the dynamics of voice production. National Institute on Deafness and Other Communication Disorders.
NASA Astrophysics Data System (ADS)
Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E.
2007-11-01
The numerical integration of Hamiltonian systems by symplectic and trigonometrically fitted (TF) symplectic method is considered in this work. We construct new trigonometrically fitted symplectic methods of third and fourth order. We apply our new methods as well as other existing methods to the numerical integration of the harmonic oscillator, the 2D harmonic oscillator with an integer frequency ratio and an orbit problem studied by Stiefel and Bettis.
Numerical Modeling of Deep Mantle Convection: Advection and Diffusion Schemes for Marker Methods
NASA Astrophysics Data System (ADS)
Mulyukova, Elvira; Dabrowski, Marcin; Steinberger, Bernhard
2013-04-01
Thermal and chemical evolution of Earth's deep mantle can be studied by modeling vigorous convection in a chemically heterogeneous fluid. Numerical modeling of such a system poses several computational challenges. Dominance of heat advection over the diffusive heat transport, and a negligible amount of chemical diffusion results in sharp gradients of thermal and chemical fields. The exponential dependence of the viscosity of mantle materials on temperature also leads to high gradients of the velocity field. The accuracy of many numerical advection schemes degrades quickly with increasing gradient of the solution, while the computational effort, in terms of the scheme complexity and required resolution, grows. Additional numerical challenges arise due to a large range of length-scales characteristic of a thermochemical convection system with highly variable viscosity. To examplify, the thickness of the stem of a rising thermal plume may be a few percent of the mantle thickness. An even thinner filament of an anomalous material that is entrained by that plume may consitute less than a tenth of a percent of the mantle thickness. We have developed a two-dimensional FEM code to model thermochemical convection in a hollow cylinder domain, with a depth- and temperature-dependent viscosity representative of the mantle (Steinberger and Calderwood, 2006). We use marker-in-cell method for advection of chemical and thermal fields. The main advantage of perfoming advection using markers is absence of numerical diffusion during the advection step, as opposed to the more diffusive field-methods. However, in the common implementation of the marker-methods, the solution of the momentum and energy equations takes place on a computational grid, and nodes do not generally coincide with the positions of the markers. Transferring velocity-, temperature-, and chemistry- information between nodes and markers introduces errors inherent to inter- and extrapolation. In the numerical scheme
NASA Astrophysics Data System (ADS)
Zanotti, O.; Dumbser, M.; Fambri, F.
2016-05-01
We describe a new method for the solution of the ideal MHD equations in special relativity which adopts the following strategy: (i) the main scheme is based on Discontinuous Galerkin (DG) methods, allowing for an arbitrary accuracy of order N+1, where N is the degree of the basis polynomials; (ii) in order to cope with oscillations at discontinuities, an ”a-posteriori” sub-cell limiter is activated, which scatters the DG polynomials of the previous time-step onto a set of 2N+1 sub-cells, over which the solution is recomputed by means of a robust finite volume scheme; (iii) a local spacetime Discontinuous-Galerkin predictor is applied both on the main grid of the DG scheme and on the sub-grid of the finite volume scheme; (iv) adaptive mesh refinement (AMR) with local time-stepping is used. We validate the new scheme and comment on its potential applications in high energy astrophysics.
A numerical method for the calibration of in situ gamma ray spectroscopy systems.
Dewey, S C; Whetstone, Z D; Kearfott, K J
2010-05-01
High purity germanium in situ gamma ray spectroscopy systems are typically calibrated using pre-calculated tables and empirical formulas to estimate the response of a detector to an exponentially distributed source in a soil matrix. Although this method is effective, it has estimated uncertainties of 10-15%, is limited to only a restricted set of measurement scenarios, and the approach only applies to an exponentially distributed source. In addition, the only soil parameters that can be varied are density and moisture content, while soil attenuation properties are fixed. This paper presents a more flexible method for performing such calibrations. For this new method, a three- or four-dimensional analytical expression is derived that is a combination of a theoretical equation and experimentally measured data. Numerical methods are used to integrate this expression, which approximates the response of a detector to a large variety of source distributions within any soil, concrete, or other matrix. The calculation method is flexible enough to allow for the variation of multiple parameters, including media attenuation properties and the measurement geometry. The method could easily be adapted to horizontally non-uniform sources as well. Detector responses are calculated analytically and Monte Carlo radiation transport simulations are used to verify the results. Results indicate that the method adds an uncertainty of only approximately 5% to the other uncertainties typically associated with the calibration of a detector system. PMID:20386196
Cobb, J.W.
1995-02-01
There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.
Piotron. II. Methods and initial results of dynamic pion therapy in phase II studies
von Essen, C.F.; Blattmann, H.; Bodendoerfer, G.; Mizoe, J.; Pedroni, E.; Walder, E.; Zimmermann, A.
1985-02-01
Negative pi-meson (pion) therapy employing dynamic scanning with a focused spot of convergent beams has been in use since 1981 at SIN. Three-dimensional conformation of the treatment volume to the target volume can thus be achieved. Following previously reported Phase I and Ib clinical trials, a Phase II trial was initiated with the goal of treating primary deep-seated tumors in a dose optimization schedule which included stepwise increase of total pion dose and of target volume. Patients with multicentric superficial bladder tumors who were cystectomy candidates were initially selected. Since then, more invasive cases have been treated. Treatment reactions ranged from a faint erythema and increase of bladder frequency to dry desquamation, mild nausea, moderate dysuria, and moderate proctitis or diarrhea with mucus. These reactions were closely related to treatment volume and site. One severe late cystitis has occurred in a patient treated with 2 courses of pions (4475 rad). Mild to moderate late proctitis has been seen in 4 patients. Ten of 13 bladder cancer patients had local control of disease while all 3 pancreas or biliary tract cancer patients had microscopic residual disease locally at time of death from metastasis. A total of 11 of 17 patients are thus clinically or pathologically free of local tumor to time of last observation.
Study on the determination of trace Ni (II) by the catalytic kinetic spectrophotometric method
NASA Astrophysics Data System (ADS)
Ji, Hongwei; Cao, Hengxia; Xin, Huizhen; Li, Shuang
2010-03-01
A new kinetic spectrophotometric method has been developed for the determination of trace Ni (II) in natural water. The method is based on the catalytic effect of Ni (II) on the oxidation of weak acid brilliant blue dye (RAWL) by KIO4 in acid medium. The concentration of nickel (II) can be determined spectrophotometrically by measuring the decrease of absorbance of RAWL at λ = 626 nm using the fix-time method. The influencing factors are investigated by the orthogonal experimental design. The obtained optimum analytical conditions are: pH = 2.00, c RAWL = 5.00×10-5 mol L-1, c KIO 4 = 2.00×10-5 mol L -1, the reaction time t = 10 min and the temperature T = 25°C. Under the optimum conditions, the developed method allows the measurement of Ni (II) in a range of 0-40.0 ng mL-1. The standard deviation of eleven independent measurements of blank reaction is S = 3.08×10-3 and the limit of detection is 2.20 ng mL-1. The relative standard deviations (RSDs) in six replicate determinations of 5 ng mL-1 and 8 ng mL-1 Ni (II) are 2.87% and 1.11%, respectively. Moreover, the experiments show few cations and anions can interfere with the measurement of Ni (II). The recovery efficiencies of this method are in a range of 97.0%-102.5% in freshwater samples. But there is a decreasing effect, which is about 0.2 times the added Ni (II) in seawater medium. After reasonable calibration this processing method is used for the determination of Ni (II) in seawater samples successfully. The results show this developed method has high accuracy and precision, high sensitivity, large range of linearity and high speed. The method can, therefore, be employed at room temperature.
NASA Astrophysics Data System (ADS)
Gross, L.; Shaw, S.
2016-04-01
Mapping the horizontal distribution of permeability is a key problem for the coal seam gas industry. Poststack seismic data with anisotropy attributes provide estimates for fracture density and orientation which are then interpreted in terms of permeability. This approach delivers an indirect measure of permeability and can fail if other sources of anisotropy (for instance stress) come into play. Seismo-electric methods, based on recording the electric signal from pore fluid movements stimulated through a seismic wave, measure permeability directly. In this paper we use numerical simulations to demonstrate that the seismo-electric method is potentially suitable to map the horizontal distribution of permeability changes across coal seams. We propose the use of an amplitude to offset (AVO) analysis of the electrical signal in combination with poststack seismic data collected during the exploration phase. Recording of electrical signals from a simple seismic source can be closer to production planning and operations. The numerical model is based on a sonic wave propagation model under the low frequency, saturated media assumption and uses a coupled high order spectral element and low order finite element solver. We investigate the impact of seam thickness, coal seam layering, layering in the overburden and horizontal heterogeneity of permeability.
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.
NASA Astrophysics Data System (ADS)
Campforts, Benjamin; Govers, Gerard
2015-07-01
The stream power equation is commonly used to model river incision into bedrock. Although specific conditions allow an analytical approach, finite difference methods (FDMs) are most frequently used to solve this equation. FDMs inevitably suffer from numerical smearing which may affect their suitability for transient river incision modeling. We propose the use of a finite volume method (FVM) which is total variation diminishing (TVD) to simulate river incision in a more accurate way. The TVD_FVM is designed to simulate sharp discontinuities, making it very suitable to simulate river incision pulses. We show that the TVD_FVM is much better capable of preserving propagating knickpoints than FDMs, using Niagara Falls as an example. Comparison of numerical results obtained using the TVD_FVM with analytical solutions shows a very good agreement. Furthermore, the uncertainty associated with parameter calibration is dramatically reduced when the TVD_FVM is applied. The high accuracy of the TVD_FDM allows correct simulation of transient incision waves as a consequence of older uplift pulses. This implies that the TVD_FVM is much more suitable than FDMs to reconstruct regional uplift histories from current river profile morphology and to simulate river incision processes in general.
Study of plasma equilibrium in toroidal fusion devices using mesh-free numerical calculation method
NASA Astrophysics Data System (ADS)
Rasouli, C.; Abbasi Davani, F.; Rokrok, B.
2016-08-01
Plasma confinement using external magnetic field is one of the successful ways leading to the controlled nuclear fusion. Development and validation of the solution process for plasma equilibrium in the experimental toroidal fusion devices is the main subject of this work. Solution of the nonlinear 2D stationary problem as posed by the Grad-Shafranov equation gives quantitative information about plasma equilibrium inside the vacuum chamber of hot fusion devices. This study suggests solving plasma equilibrium equation which is essential in toroidal nuclear fusion devices, using a mesh-free method in a condition that the plasma boundary is unknown. The Grad-Shafranov equation has been solved numerically by the point interpolation collocation mesh-free method. Important features of this approach include truly mesh free, simple mathematical relationships between points and acceptable precision in comparison with the parametric results. The calculation process has been done by using the regular and irregular nodal distribution and support domains with different points. The relative error between numerical and analytical solution is discussed for several test examples such as small size Damavand tokamak, ITER-like equilibrium, NSTX-like equilibrium, and typical Spheromak.
A numerical method for solving the three-dimensional parabolized Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Dambrosio, Domenic; Marsilio, Robert
1995-01-01
A numerical technique that solves the parabolized form of the Navier-Stokes equations is presented. Such a method makes it possible to obtain very detailed descriptions of the flowfield in a relatively modest CPU time. The present approach is based on a space-marching technique, uses a finite volume discretization and an upwind flux-difference splitting scheme for the evaluation of the inviscid fluxes. Second order accuracy is achieved following the guidelines of the the ENO schemes. The methodology is used to investigate three-dimensional supersonic viscous flows over symmetric corners. Primary and secondary streamwise vortical structures embedded in the boundary layer and originated by the interaction with shock waves are detected and studied. For purpose of validation, results are compared with experimental data extracted from literature. The agreement is found to be satisfactory. In conclusion, the numerical method proposed seems to be promising as it permits, at a reasonable computational expense, investigation of complex three-dimensional flowfields in great detail.
Numerical modelling of a granular step collapse using the Material Point Method
NASA Astrophysics Data System (ADS)
Fernandez Merodo, Jose Antonio; Mira, Pablo; Pastor, Manuel
2014-05-01
In the last decade, the Material Point Method (MPM) has been successfully applied to model geotechnical problems. The dual description of the media (lagrangian material points and eulerian numerical mesh) provides the MPM capabilities of handling problems involving large deformation. This paper presents the capability of the method to accurately capture the physics of the dynamic evolution of landslides in a unified mathematical framework. A simplified example is proposed reproducing the initiation-propagation transition of a granular step collapse. Influence of geometry (aspect ratio a), material properties (internal friction angle) and contact properties between the material and the sliding surface (basal friction angle) have been analyzed. Profile runouts have also been compared to previous published simulations [1] and experiments [2], [3] among others. References [1] G. B. Crosta, S. Imposimato and D. Roddeman (2009). Numerical modeling of 2-D granular step collapse on erodible and nonerodible surface. Journal Of Geophysical Research, Vol. 114, F03020, DOI:10.1029/2008jf001186. [2] Lajeunesse, E., J. B. Monnier, and G. M. Homsy (2005), Granular slumping on a horizontal surface, Phys. Fluids, 17, 103302.1 - 103302.15, DOI:10.1063/1.2087687. [3] Lube, G., H. Huppert, S. Sparks, and A. Freundt (2005), Collapses of two dimensional granular columns, Phys. Rev. E, 72, 041301.1- 041301.10, DOI:10.1103/PhysRevE.72.041301.
Fast and accurate numerical method for predicting gas chromatography retention time.
Claumann, Carlos Alberto; Wüst Zibetti, André; Bolzan, Ariovaldo; Machado, Ricardo A F; Pinto, Leonel Teixeira
2015-08-01
Predictive modeling for gas chromatography compound retention depends on the retention factor (ki) and on the flow of the mobile phase. Thus, different approaches for determining an analyte ki in column chromatography have been developed. The main one is based on the thermodynamic properties of the component and on the characteristics of the stationary phase. These models can be used to estimate the parameters and to optimize the programming of temperatures, in gas chromatography, for the separation of compounds. Different authors have proposed the use of numerical methods for solving these models, but these methods demand greater computational time. Hence, a new method for solving the predictive modeling of analyte retention time is presented. This algorithm is an alternative to traditional methods because it transforms its attainments into root determination problems within defined intervals. The proposed approach allows for tr calculation, with accuracy determined by the user of the methods, and significant reductions in computational time; it can also be used to evaluate the performance of other prediction methods.
Mikesell, T. Dylan; Malcolm, Alison E.; Yang, Di; Haney, Matthew M.
2015-01-01
Time-shift estimation between arrivals in two seismic traces before and after a velocity perturbation is a crucial step in many seismic methods. The accuracy of the estimated velocity perturbation location and amplitude depend on this time shift. Windowed cross correlation and trace stretching are two techniques commonly used to estimate local time shifts in seismic signals. In the work presented here, we implement Dynamic Time Warping (DTW) to estimate the warping function – a vector of local time shifts that globally minimizes the misfit between two seismic traces. We illustrate the differences of all three methods compared to one another using acoustic numerical experiments. We show that DTW is comparable to or better than the other two methods when the velocity perturbation is homogeneous and the signal-to-noise ratio is high. When the signal-to-noise ratio is low, we find that DTW and windowed cross correlation are more accurate than the stretching method. Finally, we show that the DTW algorithm has better time resolution when identifying small differences in the seismic traces for a model with an isolated velocity perturbation. These results impact current methods that utilize not only time shifts between (multiply) scattered waves, but also amplitude and decoherence measurements. DTW is a new tool that may find new applications in seismology and other geophysical methods (e.g., as a waveform inversion misfit function).
A mass conserving level set method for detailed numerical simulation of liquid atomization
Luo, Kun; Shao, Changxiao; Yang, Yue; Fan, Jianren
2015-10-01
An improved mass conserving level set method for detailed numerical simulations of liquid atomization is developed to address the issue of mass loss in the existing level set method. This method introduces a mass remedy procedure based on the local curvature at the interface, and in principle, can ensure the absolute mass conservation of the liquid phase in the computational domain. Three benchmark cases, including Zalesak's disk, a drop deforming in a vortex field, and the binary drop head-on collision, are simulated to validate the present method, and the excellent agreement with exact solutions or experimental results is achieved. It is shown that the present method is able to capture the complex interface with second-order accuracy and negligible additional computational cost. The present method is then applied to study more complex flows, such as a drop impacting on a liquid film and the swirling liquid sheet atomization, which again, demonstrates the advantages of mass conservation and the capability to represent the interface accurately.
NASA Astrophysics Data System (ADS)
Mittal, R. C.; Jiwari, Ram
2011-01-01
In this paper, a rapid, convergent and accurate differential quadrature method (DQM) is employed for numerical study of a two-dimensional reaction-diffusion Brusselator system. In the Brusselator system the reaction terms arise from the mathematical modeling of chemical systems such as in enzymatic reactions, and in plasma and laser physics in multiple coupling between modes. By employing DQM, accurate results can be obtained using fewer grid points in spatial domain for a large value of T = 50. We also found that Chebyshev-Gauss-Lobatto grid points give excellent results in comparison to other grid points such as uniform grid points. Three examples are solved to illustrate the accuracy and efficiency of the DQM. Convergence and stability of the method is also examined.
NASA Technical Reports Server (NTRS)
Cohn, S. E.
1982-01-01
Numerical weather prediction (NWP) is an initial-value problem for a system of nonlinear differential equations, in which initial values are known incompletely and inaccurately. Observational data available at the initial time must therefore be supplemented by data available prior to the initial time, a problem known as meteorological data assimilation. A further complication in NWP is that solutions of the governing equations evolve on two different time scales, a fast one and a slow one, whereas fast scale motions in the atmosphere are not reliably observed. This leads to the so called initialization problem: initial values must be constrained to result in a slowly evolving forecast. The theory of estimation of stochastic dynamic systems provides a natural approach to such problems. For linear stochastic dynamic models, the Kalman-Bucy (KB) sequential filter is the optimal data assimilation method, for linear models, the optimal combined data assimilation-initialization method is a modified version of the KB filter.
NASA Astrophysics Data System (ADS)
Zhou, Q.; Joseph, P. F.
2005-05-01
An approach combining finite element with boundary element methods is proposed to calculate the elastic vibration and acoustic field radiated from an underwater structure. The FEM software NASTRAN is employed for computation of the structural vibration. An uncoupled boundary element method, based on the potential decomposition technique, is described to determine the acoustic added mass and damping coefficients that result due to fluid loading effects. The acoustic matrices of added mass and damping coefficients are then added to the structural mass and damping matrices, respectively, by the DMAP modules of NASTRAN. Numerical results are shown to be in good agreement with experimental data. The complex eigenvalue analyses of underwater structure are obtained by NASTRAN solution sequence SOL107. Results obtained from this study suggest that the natural frequencies of underwater structures are only weakly dependent on the acoustic frequency if the acoustic wavelength is roughly twice as large as the maximum structural dimension.
Phase-Shifted Based Numerical Method for Modeling Frequency-Dependent Effects on Seismic Reflections
NASA Astrophysics Data System (ADS)
Chen, Xuehua; Qi, Yingkai; He, Xilei; He, Zhenhua; Chen, Hui
2016-08-01
The significant velocity dispersion and attenuation has often been observed when seismic waves propagate in fluid-saturated porous rocks. Both the magnitude and variation features of the velocity dispersion and attenuation are frequency-dependent and related closely to the physical properties of the fluid-saturated porous rocks. To explore the effects of frequency-dependent dispersion and attenuation on the seismic responses, in this work, we present a numerical method for seismic data modeling based on the diffusive and viscous wave equation (DVWE), which introduces the poroelastic theory and takes into account diffusive and viscous attenuation in diffusive-viscous-theory. We derive a phase-shift wave extrapolation algorithm in frequencywavenumber domain for implementing the DVWE-based simulation method that can handle the simultaneous lateral variations in velocity, diffusive coefficient and viscosity. Then, we design a distributary channels model in which a hydrocarbon-saturated sand reservoir is embedded in one of the channels. Next, we calculated the synthetic seismic data to analytically and comparatively illustrate the seismic frequency-dependent behaviors related to the hydrocarbon-saturated reservoir, by employing DVWE-based and conventional acoustic wave equation (AWE) based method, respectively. The results of the synthetic seismic data delineate the intrinsic energy loss, phase delay, lower instantaneous dominant frequency and narrower bandwidth due to the frequency-dependent dispersion and attenuation when seismic wave travels through the hydrocarbon-saturated reservoir. The numerical modeling method is expected to contribute to improve the understanding of the features and mechanism of the seismic frequency-dependent effects resulted from the hydrocarbon-saturated porous rocks.
NASA Astrophysics Data System (ADS)
Muthuvalu, Mohana Sundaram; Aruchunan, Elayaraja; Akhir, Mohd Kamalrulzaman Md; Sulaiman, Jumat; Karim, Samsul Ariffin Abdul
2014-10-01
In this paper, application of the Half-Sweep Successive Over-Relaxation (HSSOR) iterative method is extended by solving second order composite closed Newton-Cotes quadrature (2-CCNC) system. The performance of HSSOR method in solving 2-CCNC system is comparatively studied by their application on linear Fredholm integral equations of the second kind. The derivation and implementation of the method are discussed. In addition, numerical results by solving two test problems are included and compared with the standard Gauss-Seidel (GS) and Successive Over-Relaxation (SOR) methods. Numerical results demonstrate that HSSOR method is an efficient method among the tested methods.
Deterministic methods for numerical simulation of high-energy runaway electron avalanches
Babich, L. P. Bochkov, E. I.
2011-03-15
The possibilities of two deterministic methods for describing the kinetics of high-energy runaway electrons (REs) are analyzed as alternatives to stochastic methods requiring unrealistically large computing resources in problems of numerical simulation of electric discharges in dense gases involving REs. One of the methods being developed in recent years is based on multigroup equations for the moments of the electron distribution function, while the second method, which is conventionally used to solve problems in gas discharges, is based on the diffusion-drift equation. The modern method of multigroup equations allows one to calculate the RE energy distribution and the spatial RE distribution along the electric force, which are close to these distributions obtained by the Monte Carlo method if the number N of energy groups is chosen properly. The diffusion-drift equation does not give the energy distribution, but its advantage is the possibility of obtaining spatial RE distributions using small computing resources not only along but also perpendicular to the electric force, which are close to those calculated by the Monte Carlo method. To simulate discharges by the method of multigroup equations, it is necessary to know a priori the number N of groups providing good accuracy, the characteristic RE multiplication time t{sub e}, and the energy runaway threshold {epsilon}{sub th} as functions of the electric-field overvoltage. The diffusion-drift equation requires the specification, along with t{sub e}, of the directed RE velocity and longitudinal and transverse diffusion coefficients calculated by the Monte Carlo method.
ERIC Educational Resources Information Center
Zheng, Lanqin; Yang, Kaicheng; Huang, Ronghuai
2012-01-01
This study proposes a new method named the IIS-map-based method for analyzing interactions in face-to-face collaborative learning settings. This analysis method is conducted in three steps: firstly, drawing an initial IIS-map according to collaborative tasks; secondly, coding and segmenting information flows into information items of IIS; thirdly,…
Numerical simulation of sloshing with large deforming free surface by MPS-LES method
NASA Astrophysics Data System (ADS)
Pan, Xu-jie; Zhang, Huai-xin; Sun, Xue-yao
2012-12-01
the large impact pressure accurately on rolling tank wall but also can generate all physical phenomena successfully. The good agreement between numerical and experimental results proves that the modified MPS-LES method is a good CFD methodology in free surface flow simulations.
Numerical Analysis of Hydrodynamics for Bionic Oscillating Hydrofoil Based on Panel Method.
Xue, Gang; Liu, Yanjun; Zhang, Muqun; Ding, Hongpeng
2016-01-01
The kinematics model based on the Slender-Body theory is proposed from the bionic movement of real fish. The Panel method is applied to the hydrodynamic performance analysis innovatively, with the Gauss-Seidel method to solve the Navier-Stokes equations additionally, to evaluate the flexible deformation of fish in swimming accurately when satisfying the boundary conditions. A physical prototype to mimic the shape of tuna is developed with the revolutionized technology of rapid prototyping manufacturing. The hydrodynamic performance for rigid oscillating hydrofoil is analyzed with the proposed method, and it shows good coherence with the cases analyzed by the commercial software Fluent and the experimental data from robofish. Furthermore, the hydrodynamic performance of coupled hydrofoil, which consisted of flexible fish body and rigid caudal fin, is analyzed with the proposed method. It shows that the caudal fin has great influence on trailing vortex shedding and the phase angle is the key factor on hydrodynamic performance. It is verified that the shape of trailing vortex is similar to the image of the motion curve at the trailing edge as the assumption of linear vortex plane under the condition of small downwash velocity. The numerical analysis of hydrodynamics for bionic movement based on the Panel method has certain value to reveal the fish swimming mechanism.
Numerical Analysis of Hydrodynamics for Bionic Oscillating Hydrofoil Based on Panel Method.
Xue, Gang; Liu, Yanjun; Zhang, Muqun; Ding, Hongpeng
2016-01-01
The kinematics model based on the Slender-Body theory is proposed from the bionic movement of real fish. The Panel method is applied to the hydrodynamic performance analysis innovatively, with the Gauss-Seidel method to solve the Navier-Stokes equations additionally, to evaluate the flexible deformation of fish in swimming accurately when satisfying the boundary conditions. A physical prototype to mimic the shape of tuna is developed with the revolutionized technology of rapid prototyping manufacturing. The hydrodynamic performance for rigid oscillating hydrofoil is analyzed with the proposed method, and it shows good coherence with the cases analyzed by the commercial software Fluent and the experimental data from robofish. Furthermore, the hydrodynamic performance of coupled hydrofoil, which consisted of flexible fish body and rigid caudal fin, is analyzed with the proposed method. It shows that the caudal fin has great influence on trailing vortex shedding and the phase angle is the key factor on hydrodynamic performance. It is verified that the shape of trailing vortex is similar to the image of the motion curve at the trailing edge as the assumption of linear vortex plane under the condition of small downwash velocity. The numerical analysis of hydrodynamics for bionic movement based on the Panel method has certain value to reveal the fish swimming mechanism. PMID:27578959
Numerical simulation of quantum systems using the Particle-In-Cell method
NASA Astrophysics Data System (ADS)
Dirkmann, Sven; Youssef, Ziad; Hemke, Torben; Mussenbrock, Thomas
2014-10-01
The Particle-In-Cell (PIC) method is a very powerful method for studying the dynamics of plasmas. It has been primarily developed for tracking the charged particle trajectories subject to selfconsistent and external electromagnetic fields. Exploiting the power of modern computers, one is able to track the classical paths of tens of millions of particles at the same time. In the late 1980th, it was Dawson (and later Dauger) who had the idea to apply the PIC method to the classical part in the semiclassical approach to quantum systems via path integral methods. One could estimate that if a thousands of classical paths are sufficient to describe the dynamics of one quantum particle, then millions classical paths could describe the dynamics of a quantum particle system. A PIC code in the frame of a semiclassical approach would therefore enable the investigation of a number of quantum phenomena, e.g., optical properties, electrical properties, and, ultimately, chemical reactions. In this contribution we explain the use of the PIC code yapic (developed by the authors) in the frame of the path integral method and discuss the numerical results for simple quantum phenomena, i.e., the quantum harmonic oscillator and quantum tunneling. This work is supported by the German Research Foundation in the frame of FOR 2093.
Numerical Analysis of Hydrodynamics for Bionic Oscillating Hydrofoil Based on Panel Method
2016-01-01
The kinematics model based on the Slender-Body theory is proposed from the bionic movement of real fish. The Panel method is applied to the hydrodynamic performance analysis innovatively, with the Gauss-Seidel method to solve the Navier-Stokes equations additionally, to evaluate the flexible deformation of fish in swimming accurately when satisfying the boundary conditions. A physical prototype to mimic the shape of tuna is developed with the revolutionized technology of rapid prototyping manufacturing. The hydrodynamic performance for rigid oscillating hydrofoil is analyzed with the proposed method, and it shows good coherence with the cases analyzed by the commercial software Fluent and the experimental data from robofish. Furthermore, the hydrodynamic performance of coupled hydrofoil, which consisted of flexible fish body and rigid caudal fin, is analyzed with the proposed method. It shows that the caudal fin has great influence on trailing vortex shedding and the phase angle is the key factor on hydrodynamic performance. It is verified that the shape of trailing vortex is similar to the image of the motion curve at the trailing edge as the assumption of linear vortex plane under the condition of small downwash velocity. The numerical analysis of hydrodynamics for bionic movement based on the Panel method has certain value to reveal the fish swimming mechanism. PMID:27578959
Developing a Brazilian Band Method Book: Phase II.
ERIC Educational Resources Information Center
Barbosa, Joel Luis
1999-01-01
Relates a pilot test of an elementary band method book for group instruction in Brazilian music education. Focused on the amount of content taught within three one-hour classes per week and studied the quality of learning. Concludes that the group covered 17 pages of the book, learned outside material, and performed four concerts. (CMK)
Microwave methods for paving. Final report, Phase II
Jeppson, M.E.
1984-12-07
The purpose of this report is to attempt to identify important highway pavement maintenance and rehabilitation needs and to propose microwave methods and equipment that could be profitably used for this work. As a starting point it is already perceived and accepted that the major emphasis in the US paving indu
River Pollution: Part II. Biological Methods for Assessing Water Quality.
ERIC Educational Resources Information Center
Openshaw, Peter
1984-01-01
Discusses methods used in the biological assessment of river quality and such indicators of clean and polluted waters as the Trent Biotic Index, Chandler Score System, and species diversity indexes. Includes a summary of a river classification scheme based on quality criteria related to water use. (JN)
Mathematical and numerical analysis of non-planer static mode-II crack in a two-layered medium
NASA Astrophysics Data System (ADS)
Hirano, S.; Yamashita, T.
2009-12-01
A crack in an infinite homogeneous medium is widely assumed as a model for earthquake fault. It is, however, well known that the earth's crust is heterogeneous and its structure is approximated well by a layered medium. Hence, such structure should be taken into account to model earthquake fault reasonably. We mathematically analyze the behavior of a 2-D static mode-II non-planar crack in a two-layered elastic medium in order to understand the effect of layer boundary on earthquake faulting. Although Rani and Singh (1993) and Rivalta et al.(2002) studied similar problems, focuses of their studies were quite narrow probably because of inherent mathematical difficulty. Actually the former assumed a planar crack with uniform slip and the latter assumed a planar crack perpendicular to the layer boundary. While a serious difficulty of the analysis of mode-II crack lies in the derivation of stress distribution due to point source as a kernel function, we first overcome the difficulty by writing its expression in a sequence of complex functions in the real (not the Fourier) domain. A very important characteristic in the sequence is that it has recursive property, which makes possible to derive the kernel function explicitly and to integrate it by parts; the integration by parts is required before the boundary integral equation method (BIEM) is applied. Our kernel function is much easier to treat than the expression given by Rani and Singh (1993). This enables us to analyze arbitrarily oriented non-planar crack in a two-layered medium. Next, we calculate the spatial distribution of stress due to crack that does not intersect the layer boundary using the above derived kernel function. We find in the calculation that the existence of layer boundary amplifies or reduces the stress at the crack tip when the crack is located close to the boundary; the stress is amplified when the crack exists in the layer with lower rigidity. Our method of analysis can easily be applied to the
Numerical methods for a Poisson-Nernst-Planck-Fermi model of biological ion channels.
Liu, Jinn-Liang; Eisenberg, Bob
2015-07-01
Numerical methods are proposed for an advanced Poisson-Nernst-Planck-Fermi (PNPF) model for studying ion transport through biological ion channels. PNPF contains many more correlations than most models and simulations of channels, because it includes water and calculates dielectric properties consistently as outputs. This model accounts for the steric effect of ions and water molecules with different sizes and interstitial voids, the correlation effect of crowded ions with different valences, and the screening effect of polarized water molecules in an inhomogeneous aqueous electrolyte. The steric energy is shown to be comparable to the electrical energy under physiological conditions, demonstrating the crucial role of the excluded volume of particles and the voids in the natural function of channel proteins. Water is shown to play a critical role in both correlation and steric effects in the model. We extend the classical Scharfetter-Gummel (SG) method for semiconductor devices to include the steric potential for ion channels, which is a fundamental physical property not present in semiconductors. Together with a simplified matched interface and boundary (SMIB) method for treating molecular surfaces and singular charges of channel proteins, the extended SG method is shown to exhibit important features in flow simulations such as optimal convergence, efficient nonlinear iterations, and physical conservation. The generalized SG stability condition shows why the standard discretization (without SG exponential fitting) of NP equations may fail and that divalent Ca(2+) may cause more unstable discrete Ca(2+) fluxes than that of monovalent Na(+). Two different methods-called the SMIB and multiscale methods-are proposed for two different types of channels, namely, the gramicidin A channel and an L-type calcium channel, depending on whether water is allowed to pass through the channel. Numerical methods are first validated with constructed models whose exact solutions are
NASA Astrophysics Data System (ADS)
Holtslag, M. C.; Steeneveld, G. J.; Holtslag, A. A. M.
2010-07-01
Fog forecasting is a very challenging task due to the local and small-scale nature of the relevant physical processes and land surface heterogeneities. Despite the many research efforts, numerical models remain to have difficulties with fog forecasting, and forecast skill from direct model output is relatively poor. In order to put the progress of fog forecasting in the last decades into a historical perspective, we compare the fog forecasting skill of a semi-empirical method based on radio sounding observations (developed in the 60s and 70s) with the forecasting skill of a state-of-the-art numerical weather prediction model (MM5) for The Netherlands. The semi-empirical method under investigation, the Fog Stability Index, depends solely on the temperature difference between the surface and 850 hPa, the surface dew point depression and the wind speed at 850 hPa, and a threshold value to indicate the probability of fog in the coming hours. Using the critical success index (CSI) as a criterion for forecast quality, we find that the Fog Stability Index is a rather successful predictor for fog, with similar performance as MM5. The FSI could even been optimized for different observational stations in the Netherlands. Also, it appears that adding the 10 m wind as a predictor did not increase the CSI score for all stations. The results of the current study clearly indicate that the current state of knowledge requires improvement of the physical insight in different physical processes in order to beat simple semi-empirical methods.
NASA Technical Reports Server (NTRS)
Lacasse, James M.
1995-01-01
A multiblock sensitivity analysis method is applied in a numerical aerodynamic shape optimization technique. The Sensitivity Analysis Domain Decomposition (SADD) scheme which is implemented in this study was developed to reduce the computer memory requirements resulting from the aerodynamic sensitivity analysis equations. Discrete sensitivity analysis offers the ability to compute quasi-analytical derivatives in a more efficient manner than traditional finite-difference methods, which tend to be computationally expensive and prone to inaccuracies. The direct optimization procedure couples CFD analysis based on the two-dimensional thin-layer Navier-Stokes equations with a gradient-based numerical optimization technique. The linking mechanism is the sensitivity equation derived from the CFD discretized flow equations, recast in adjoint form, and solved using direct matrix inversion techniques. This investigation is performed to demonstrate an aerodynamic shape optimization technique on a multiblock domain and its applicability to complex geometries. The objectives are accomplished by shape optimizing two aerodynamic configurations. First, the shape optimization of a transonic airfoil is performed to investigate the behavior of the method in highly nonlinear flows and the effect of different grid blocking strategies on the procedure. Secondly, shape optimization of a two-element configuration in subsonic flow is completed. Cases are presented for this configuration to demonstrate the effect of simultaneously reshaping interfering elements. The aerodynamic shape optimization is shown to produce supercritical type airfoils in the transonic flow from an initially symmetric airfoil. Multiblocking effects the path of optimization while providing similar results at the conclusion. Simultaneous reshaping of elements is shown to be more effective than individual element reshaping due to the inclusion of mutual interference effects.
Constructive interference II: Semi-chaotic multigrid methods
Douglas, C.C.
1994-12-31
Parallel computer vendors have mostly decided to move towards multi-user, multi-tasking per node machines. A number of these machines already exist today. Self load balancing on these machines is not an option to the users except when the user can convince someone to boot the entire machine in single user mode, which may have to be done node by node. Chaotic relaxation schemes were considered for situations like this as far back as the middle 1960`s. However, very little convergence theory exists. Further, what exists indicates that this is not really a good method. Besides chaotic relaxation, chaotic conjugate direction and minimum residual methods are explored as smoothers for symmetric and nonsymmetric problems. While having each processor potentially going off in a different direction from the rest is not what one would strive for in a unigrid situation, the change of grid procedures in multigrid provide a natural way of aiming all of the processors in the right direction. The author presents some new results for multigrid methods in which synchronization of the calculations on one or more levels is not assumed. However, he assumes that he knows how far out of synch neighboring subdomains are with respect to each other. Thus the author can show that the combination of a limited chaotic smoother and coarse level corrections produces a better algorithm than would be expected.
Lemesurier, Brenton
2013-09-01
The phenomenon of coherent energetic pulse propagation in exciton-phonon molecular chains such as α-helix protein is studied using an ODE system model of Davydov-Scott type, both with numerical studies using a new unconditionally stable fourth-order accurate energy-momentum conserving time discretization and with analytical explanation of the main numerical observations. Impulsive initial data associated with initial excitation of a single amide-I vibration by the energy released by ATP hydrolysis are used as well as the best current estimates of physical parameter values. In contrast to previous studies based on a proposed long-wave approximation by the nonlinear Schrödinger (NLS) equation and focusing on initial data resembling the soliton solutions of that equation, the results here instead lead to approximation by the third derivative nonlinear Schrödinger equation, giving a far better fit to observed behavior. A good part of the behavior is indeed explained well by the linear part of that equation, the Airy PDE, while other significant features do not fit any PDE approximation but are instead explained well by a linearized analysis of the ODE system. A convenient method is described for construction of the highly stable, accurate conservative time discretizations used, with proof of its desirable properties for a large class of Hamiltonian systems, including a variety of molecular models.
NASA Astrophysics Data System (ADS)
Pendota, Premchand
Many physical phenomena and industrial applications involve multiphase fluid flows and hence it is of high importance to be able to simulate various aspects of these flows accurately. The Dynamic Contact Angles (DCA) and the contact lines at the wall boundaries are a couple of such important aspects. In the past few decades, many mathematical models were developed for predicting the contact angles of the inter-face with the wall boundary under various flow conditions. These models are used to incorporate the physics of DCA and contact line motion in numerical simulations using various interface capturing/tracking techniques. In the current thesis, a simple approach to incorporate the static and dynamic contact angle boundary conditions using the level set method is developed and implemented in multiphase CFD codes, LIT (Level set Interface Tracking) (Herrmann (2008)) and NGA (flow solver) (Desjardins et al (2008)). Various DCA models and associated boundary conditions are reviewed. In addition, numerical aspects such as the occurrence of a stress singularity at the contact lines and grid convergence of macroscopic interface shape are dealt with in the context of the level set approach.
Comparison of Several Numerical Methods for Simulation of Compressible Shear Layers
NASA Technical Reports Server (NTRS)
Kennedy, Christopher A.; Carpenter, Mark H.
1997-01-01
An investigation is conducted on several numerical schemes for use in the computation of two-dimensional, spatially evolving, laminar variable-density compressible shear layers. Schemes with various temporal accuracies and arbitrary spatial accuracy for both inviscid and viscous terms are presented and analyzed. All integration schemes use explicit or compact finite-difference derivative operators. Three classes of schemes are considered: an extension of MacCormack's original second-order temporally accurate method, a new third-order variant of the schemes proposed by Rusanov and by Kutier, Lomax, and Warming (RKLW), and third- and fourth-order Runge-Kutta schemes. In each scheme, stability and formal accuracy are considered for the interior operators on the convection-diffusion equation U(sub t) + aU(sub x) = alpha U(sub xx). Accuracy is also verified on the nonlinear problem, U(sub t) + F(sub x) = 0. Numerical treatments of various orders of accuracy are chosen and evaluated for asymptotic stability. Formally accurate boundary conditions are derived for several sixth- and eighth-order central-difference schemes. Damping of high wave-number data is accomplished with explicit filters of arbitrary order. Several schemes are used to compute variable-density compressible shear layers, where regions of large gradients exist.
NASA Astrophysics Data System (ADS)
Park, Inmyong; Kim, Youngkwon; Park, Jiho; Jeong, Sangkwon
2015-09-01
The design procedure of an active magnetic regenerator (AMR) operating between liquid nitrogen temperature and liquid hydrogen temperature is discussed with the selected magnetic refrigerants. Selected magnetic refrigerants (GdNi2, Dy0.85Er0.15Al2, Dy0.5Er0.5Al2, and Gd0.1Dy0.9Ni2) that have different transition temperatures are layered in an AMR to widen the temperature span. The optimum volume fraction of the layered refrigerants for the maximum COP with minimum volume is designed in a two-stage active magnetic regenerative refrigerator (AMRR) using one dimensional numerical simulation. The entropy generation in each stage of the AMR is calculated by the numerical simulation to optimize the proposed design. The main sources of the entropy generation in the AMR are pressure drop, convection and conduction heat transfers in the AMR. However, the entropy generation by the convective heat transfer is mostly dominant in the optimized cases. In this paper, the design parameters and the operating conditions such as the distribution of the selected refrigerants in the layered AMR, the intermediate temperature between two stages and the mass flow rate of heat transfer fluid are specifically determined to maximize the performance of the AMR. The proposed design method will facilitate the construction of AMR systems with various magnetic refrigerants and conditions such as AMR size, operating temperature range, and magnetic field variation.
Chan, Eugene; Rose, L R Francis; Wang, Chun H
2015-05-01
Existing damage imaging algorithms for detecting and quantifying structural defects, particularly those based on diffraction tomography, assume far-field conditions for the scattered field data. This paper presents a major extension of diffraction tomography that can overcome this limitation and utilises a near-field multi-static data matrix as the input data. This new algorithm, which employs numerical solutions of the dynamic Green's functions, makes it possible to quantitatively image laminar damage even in complex structures for which the dynamic Green's functions are not available analytically. To validate this new method, the numerical Green's functions and the multi-static data matrix for laminar damage in flat and stiffened isotropic plates are first determined using finite element models. Next, these results are time-gated to remove boundary reflections, followed by discrete Fourier transform to obtain the amplitude and phase information for both the baseline (damage-free) and the scattered wave fields. Using these computationally generated results and experimental verification, it is shown that the new imaging algorithm is capable of accurately determining the damage geometry, size and severity for a variety of damage sizes and shapes, including multi-site damage. Some aspects of minimal sensors requirement pertinent to image quality and practical implementation are also briefly discussed. PMID:25661053
NASA Astrophysics Data System (ADS)
Hospital-Bravo, Raúl; Sarrate, Josep; Díez, Pedro
2016-05-01
A new 2D numerical model to predict the underwater acoustic propagation is obtained by exploring the potential of the Partition of Unity Method (PUM) enriched with plane waves. The aim of the work is to obtain sound pressure level distributions when multiple operational noise sources are present, in order to assess the acoustic impact over the marine fauna. The model takes advantage of the suitability of the PUM for solving the Helmholtz equation, especially for the practical case of large domains and medium frequencies. The seawater acoustic absorption and the acoustic reflectance of the sea surface and sea bottom are explicitly considered, and perfectly matched layers (PML) are placed at the lateral artificial boundaries to avoid spurious reflexions. The model includes semi-analytical integration rules which are adapted to highly oscillatory integrands with the aim of reducing the computational cost of the integration step. In addition, we develop a novel strategy to mitigate the ill-conditioning of the elemental and global system matrices. Specifically, we compute a low-rank approximation of the local space of solutions, which in turn reduces the number of degrees of freedom, the CPU time and the memory footprint. Numerical examples are presented to illustrate the capabilities of the model and to assess its accuracy.
Robust numerical method for integration of point-vortex trajectories in two dimensions.
Smith, Spencer A; Boghosian, Bruce M
2011-05-01
The venerable two-dimensional (2D) point-vortex model plays an important role as a simplified version of many disparate physical systems, including superfluids, Bose-Einstein condensates, certain plasma configurations, and inviscid turbulence. This system is also a veritable mathematical playground, touching upon many different disciplines from topology to dynamic systems theory. Point-vortex dynamics are described by a relatively simple system of nonlinear ordinary differential equations which can easily be integrated numerically using an appropriate adaptive time stepping method. As the separation between a pair of vortices relative to all other intervortex length scales decreases, however, the computational time required diverges. Accuracy is usually the most discouraging casualty when trying to account for such vortex motion, though the varying energy of this ostensibly Hamiltonian system is a potentially more serious problem. We solve these problems by a series of coordinate transformations: We first transform to action-angle coordinates, which, to lowest order, treat the close pair as a single vortex amongst all others with an internal degree of freedom. We next, and most importantly, apply Lie transform perturbation theory to remove the higher-order correction terms in succession. The overall transformation drastically increases the numerical efficiency and ensures that the total energy remains constant to high accuracy.
Design check of an S-Lay offshore pipeline launching using numerical methods
NASA Astrophysics Data System (ADS)
Stan, L. C.; Călimănescu, I.; Velcea, D. D.
2016-08-01
The production of oil and gas from offshore oil fields is, nowadays, more and more important. As a result of the increasing demand of oil, and being the shallow water reserves not enough, the industry is pushed forward to develop and exploit more difficult fields in deeper waters. The purpose of this paper is to determine the optimum launching parameters of a subsea pipeline in S-Lay system using the software OffPipe. The offshore pipelines designing is an intricate enterprise following very demanding designing codes since at stake is the integrity of multi-million dollars investments in offshore oil and gas exploitation facilities. The case study of this paper is taken on purpose to show how the numeric analysis may help to detect potential problems that might occur during pipe launching with S-Lay method. In the analysed case the launching process is under control since all the launching parameters and stresses are well below the critical ones. In any event the numeric modelling of the process was demonstrated to be a valuable tool in the design engineer hands in order to assess the feasibility of any launching subsea pipe launching.
Numerical solution of an elastic and viscoelastic gravitational models by the finite element method
NASA Astrophysics Data System (ADS)
Arjona Almodóvar, A.; Chacón Rebollo, T.; Gómez Marmol, M.
2014-12-01
Volcanic areas present a lower effective viscosity than usually in the Earth's crust. Both the elastic-gravitational and the viscoelastic-gravitational models allow the computation of gravity, deformation, and gravitational potential changes in order to investigate crustal deformations of Earth (see for instance Battaglia & Segall, 2004; Fernández et al. 1999, 2001; Rundle 1980 and 1983). These models can be represented by a coupled system of linear parabolic (for the elastic deformations), hyperbolic (for the viscoelastic deformations) and elliptic partial differential equations (for gravitational potential changes) (see for instance Arjona et al. 2008 and 2010). The existence and uniqueness of weak solutions for both the elastic-gravitational and viscoelastic-gravitational problem was demonstrated in Arjona et al. (2008 and 2014). The stabilization to solutions of the associated stationary system was proved in Arjona and Díaz (2007). Here we consider the internal source as response to the effect of a pressurized magma reservoir into a multilayered, elastic-gravitational and viscoelastic-gravitational earth model. We introduce the numerical analysis of a simplified steady elastic-gravitational model, solved by means of the finite element method. We also present some numerical tests in realistic situations that confirm the predictions of theoretical order of convergence. Finally, we describe the methodology for both the elastic-gravitational and the viscoelastic-gravitational models using 2D and 3D test examples performed with FreeFEM++.
A Numerical Method for Simulating Non-Newtonian Fluid Flow andDisplacement in Porous Media
Wu, Y.S.; Pruess , K.
1996-02-01
Flow and displacement of non-Newtonian fluids in porousmedia occurs in many subsurface systems, related to underground naturalresource recovery and storage projects, as well as environmentalremediation schemes. A thorough understanding of non-Newtonian fluid flowthrough porous media is of fundamental importance in these engineeringapplications. Considerable progress has been made in our understanding ofsingle-phase porous flow behavior of non-Newtonian fluids through manyquantitative and experimental studies over the past few decades. However,very little research can be found in the literature regarding multi-phasenon-Newtonian fluid flow or numerical modeling approaches for suchanalyses.For non-Newtonian fluid flow through porous media, the governingequations become nonlinear, even under single-phase flow conditions,because effective viscosity for the non-Newtonian fluid is a highlynonlinear function of the shear rate, or the pore velocity. The solutionfor such problems can in general only be obtained by numerical methods.Wehave developed a three-dimensional, fully implicit, integral finitedifference simulator for single- and multi-phase flow of non-Newtonianfluids in porous/fractured media. The methodology, architecture andnumerical scheme of the model are based on a general multi-phase,multi-component fluid and heat flow simulator--TOUGH2. Severalrheological models for power-law and Bingham non-Newtonian fluids havebeen incorporated into the model. In addition, the model predictions onsingle- and multi-phase flow of the power-law and Bingham fluids havebeen verified against the analytical solutions available for theseproblems, and in all the cases the numerical simulations are in goodagreement with the analytical solutions. In this presentation, we willdiscuss the numerical scheme used in the treatment of non-Newtonianproperties, and several benchmark problems for model verification.In aneffort to demonstrate the three-dimensional modeling capability of themodel
A new numerical method for wave propagation through assemblies of cylinders and spheres
NASA Astrophysics Data System (ADS)
Yano, Takeru; Prosperetti, Andrea
2002-05-01
PHYSALIS is a new method for the numerical solution of a variety of problems (potential theory, Navier-Stokes equations, and others) involving cylindrical or spherical internal boundaries [A. Prosperetti and H. N. Oguz, J. Comput. Phys. 167, 196-216 (2001)]. At the heart of the method is the use of an exact analytical solution to transfer the boundary conditions from the surface of the inclusions to the neighboring grid nodes. This step avoids the difficulty deriving from the complex geometrical relationship between the internal boundaries and the underlying regular grid, with the added benefit that fast solvers can be used. In this work the method is adapted to two-dimensional acoustic scattering by cylinders as governed by the Helmholtz equation. As in prior applications, the method reveals itself highly efficient and of a relatively simple implementation. These features are illustrated on several problems. In particular, it is shown that the computational time grows much less than linearly with the number of cylinders, which permits the simulation of complex multiple scattering problems without large computational resources. [Work supported by The Japan Ministry of Education, Culture, Sports, Science and Technology, and by ONR.
A novel model for diffusion based release kinetics using an inverse numerical method.
Mohammadi, Hadi; Herzog, Walter
2011-10-01
We developed and analyzed an inverse numerical model based on Fick's second law on the dynamics of drug release. In contrast to previous models which required two state descriptions of diffusion for long- and short-term release processes, our model is valid for the entire release process. The proposed model may be used for identifying and reducing experimental errors associated with measurements of diffusion based release kinetics. Knowing the initial and boundary conditions, and assuming Fick's second law to be appropriate, we use the methods of Lagrange multiplier along with least-square algorithms to define a cost function which is discretized using finite difference methods and is optimized so as to minimize errors. Our model can describe diffusion based release kinetics for static and dynamic conditions as accurately as finite element methods, but results are obtained in a fraction of CPU time. Our method can be widely used for drug release procedures and for tissue engineering/repair applications where oxygenation of cells residing within a matrix is important.
The Cauchy-Lagrangian method for numerical analysis of Euler flow
NASA Astrophysics Data System (ADS)
Podvigina, O.; Zheligovsky, V.; Frisch, U.
2016-02-01
A novel semi-Lagrangian method is introduced to solve numerically the Euler equation for ideal incompressible flow in arbitrary space dimension. It exploits the time-analyticity of fluid particle trajectories and requires, in principle, only limited spatial smoothness of the initial data. Efficient generation of high-order time-Taylor coefficients is made possible by a recurrence relation that follows from the Cauchy invariants formulation of the Euler equation (Zheligovsky and Frisch, 2014 [44]). Truncated time-Taylor series of very high order allow the use of time steps vastly exceeding the Courant-Friedrichs-Lewy limit, without compromising the accuracy of the solution. Tests performed on the two-dimensional Euler equation indicate that the Cauchy-Lagrangian method is more - and occasionally much more - efficient and less prone to instability than Eulerian Runge-Kutta methods, and less prone to rapid growth of rounding errors than the high-order Eulerian time-Taylor algorithm. We also develop tools of analysis adapted to the Cauchy-Lagrangian method, such as the monitoring of the radius of convergence of the time-Taylor series. Certain other fluid equations can be handled similarly.
Pedler, William H. (Radon Abatement Systems, Inc., Golden, CO); Jepsen, Richard Alan (Sandia National Laboratories, Carlsbad, NM)
2003-08-01
The requirement to accurately measure subsurface groundwater flow at contaminated sites, as part of a time and cost effective remediation program, has spawned a variety of flow evaluation technologies. Validation of the accuracy and knowledge regarding the limitations of these technologies are critical for data quality and application confidence. Leading the way in the effort to validate and better understand these methodologies, the US Army Environmental Center has funded a multi-year program to compare and evaluate all viable horizontal flow measurement technologies. This multi-year program has included a field comparison phase, an application of selected methods as part of an integrated site characterization program phase, and most recently, a laboratory and numerical simulator phase. As part of this most recent phase, numerical modeling predictions and laboratory measurements were made in a simulated fracture borehole set-up within a controlled flow simulator. The scanning colloidal borescope flowmeter (SCBFM) and advanced hydrophysical logging (NxHpL{trademark}) tool were used to measure velocities and flow rate in a simulated fractured borehole in the flow simulator. Particle tracking and mass flux measurements were observed and recorded under a range of flow conditions in the simulator. Numerical models were developed to aid in the design of the flow simulator and predict the flow conditions inside the borehole. Results demonstrated that the flow simulator allowed for predictable, easily controlled, and stable flow rates both inside and outside the well. The measurement tools agreed well with each other over a wide range of flow conditions. The model results demonstrate that the Scanning Colloidal Borescope did not interfere with the flow in the borehole in any of the tests. The model is capable of predicting flow conditions and agreed well with the measurements and observations in the flow simulator and borehole. Both laboratory and model results showed a
Local response dispersion method. II. Generalized multicenter interactions
NASA Astrophysics Data System (ADS)
Sato, Takeshi; Nakai, Hiromi
2010-11-01
Recently introduced local response dispersion method [T. Sato and H. Nakai, J. Chem. Phys. 131, 224104 (2009)], which is a first-principles alternative to empirical dispersion corrections in density functional theory, is implemented with generalized multicenter interactions involving both atomic and atomic pair polarizabilities. The generalization improves the asymptote of intermolecular interactions, reducing the mean absolute percentage error from about 30% to 6% in the molecular C6 coefficients of more than 1000 dimers, compared to experimental values. The method is also applied to calculations of potential energy curves of molecules in the S22 database [P. Jurečka et al., Phys. Chem. Chem. Phys. 8, 1985 (2006)]. The calculated potential energy curves are in a good agreement with reliable benchmarks recently published by Molnar et al. [J. Chem. Phys. 131, 065102 (2009)]. These improvements are achieved at the price of increasing complexity in the implementation, but without losing the computational efficiency of the previous two-center (atom-atom) formulation. A set of different truncations of two-center and three- or four-center interactions is shown to be optimal in the cost-performance balance.
Computational flow development for unsteady viscous flows: Foundation of the numerical method
NASA Technical Reports Server (NTRS)
Bratanow, T.; Spehert, T.
1978-01-01
A procedure is presented for effective consideration of viscous effects in computational development of high Reynolds number flows. The procedure is based on the interpretation of the Navier-Stokes equations as vorticity transport equations. The physics of the flow was represented in a form suitable for numerical analysis. Lighthill's concept for flow development for computational purposes was adapted. The vorticity transport equations were cast in a form convenient for computation. A statement for these equations was written using the method of weighted residuals and applying the Galerkin criterion. An integral representation of the induced velocity was applied on the basis of the Biot-Savart law. Distribution of new vorticity, produced at wing surfaces over small computational time intervals, was assumed to be confined to a thin region around the wing surfaces.
A thermodynamically consistent numerical method for a phase field model of solidification
NASA Astrophysics Data System (ADS)
Gonzalez-Ferreiro, B.; Gomez, H.; Romero, I.
2014-07-01
A discretization is presented for the initial boundary value problem of solidification as described in the phase-field model developed by Penrose and Fife (1990) [1] and Wang et al. (1993) [2]. These are models that are completely derived from the laws of thermodynamics, and the algorithms that we propose are formulated to strictly preserve them. Hence, the discrete solutions obtained can be understood as discrete dynamical systems satisfying discrete versions of the first and second laws of thermodynamics. The proposed methods are based on a finite element discretization in space and a midpoint-type finite-difference discretization in time. By using so-called discrete gradient operators, the conservation/entropic character of the continuum model is inherited in the numerical solution, as well as its Lyapunov stability in pure solid/liquid equilibria.
A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations
NASA Technical Reports Server (NTRS)
Radhakrishnan, K.
1984-01-01
A comparison of the efficiency of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations is presented. The methods examined include two general-purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient than evaluating the temperature by integrating its time-derivative.
An efficient numerical method for evolving microstructures with strong elastic inhomogeneity
NASA Astrophysics Data System (ADS)
Jeong, Darae; Lee, Seunggyu; Kim, Junseok
2015-06-01
In this paper, we consider a fast and efficient numerical method for the modified Cahn-Hilliard equation with a logarithmic free energy for microstructure evolution. Even though it is physically more appropriate to use a logarithmic free energy, a quartic polynomial approximation is typically used for the logarithmic function due to a logarithmic singularity. In order to overcome the singularity problem, we regularize the logarithmic function and then apply an unconditionally stable scheme to the Cahn-Hilliard part in the model. We present computational results highlighting the different dynamic aspects from two different bulk free energy forms. We also demonstrate the robustness of the regularization of the logarithmic free energy, which implies the time-step restriction is based on accuracy and not stability.
Numerical method for computing Maass cusp forms on triply punctured two-sphere
Chan, K. T.; Kamari, H. M.; Zainuddin, H.
2014-03-05
A quantum mechanical system on a punctured surface modeled on hyperbolic space has always been an important subject of research in mathematics and physics. This corresponding quantum system is governed by the Schrödinger equation whose solutions are the Maass waveforms. Spectral studies on these Maass waveforms are known to contain both continuous and discrete eigenvalues. The discrete eigenfunctions are usually called the Maass Cusp Forms (MCF) where their discrete eigenvalues are not known analytically. We introduce a numerical method based on Hejhal and Then algorithm using GridMathematica for computing MCF on a punctured surface with three cusps namely the triply punctured two-sphere. We also report on a pullback algorithm for the punctured surface and a point locater algorithm to facilitate the complete pullback which are essential parts of the main algorithm.
Efficient numerical method for computation of thermohydrodynamics of laminar lubricating films
NASA Technical Reports Server (NTRS)
Elrod, Harold G.
1989-01-01
The purpose of this paper is to describe an accurate, yet economical, method for computing temperature effects in laminar lubricating films in two dimensions. The procedure presented here is a sequel to one presented in Leeds in 1986 that was carried out for the one-dimensional case. Because of the marked dependence of lubricant viscosity on temperature, the effect of viscosity variation both across and along a lubricating film can dwarf other deviations from ideal constant-property lubrication. In practice, a thermohydrodynamics program will involve simultaneous solution of the film lubrication problem, together with heat conduction in a solid, complex structure. The extent of computation required makes economy in numerical processing of utmost importance. In pursuit of such economy, we here use techniques similar to those for Gaussian quadrature. We show that, for many purposes, the use of just two properly positioned temperatures (Lobatto points) characterizes well the transverse temperature distribution.
Numerical analysis of polarization gratings using the finite-difference time-domain method
Oh, Chulwoo; Escuti, Michael J.
2007-10-15
We report the first full numerical analysis of polarization gratings (PGs), and study their most general properties and limits by using the finite-difference time-domain (FDTD) method. In this way, we avoid limiting assumptions on material properties or grating dimensions (e.g., no paraxial approximations) and provide a more complete understanding of PG diffraction behavior. We identify the fundamental delineation between diffraction regimes (thin versus thick) for anisotropic gratings and determine the conditions for {approx_equal}100% diffraction efficiency in the framework of the coupled-wave {rho} and Q parameters. Diffraction characteristics including the efficiency, spectral response, and polarization sensitivity are investigated for the two primary types of PGs with linear and circular birefringence. The angular response and finite-grating behavior (i.e., pixelation) are also examined. Comparisons with previous analytic approximations, where applicable, show good agreement.
Numerical solution of the problem of flame propagation by the use of the random element method
NASA Technical Reports Server (NTRS)
Ghoniem, A. F.; Oppenheim, A. K.
1983-01-01
A numerical, grid-free algorithm is presented for one-dimensional reaction-diffusion model of laminar flame propagation in premixed gases. It is based on the random element method we developed for the analysis of diffusional processes. The effect of combustion is taken into account by applying the principle of fractional steps to separate the process of diffusion, modeled by the random walk of computational elements, from the exothermic effects of chemical reaction, monitoring their strength. The validity of the algorithm is demonstrated by application to flame propagation problems for which exact solutions exist. The flame speed evaluated by its use oscillates around the exact value at a relatively small amplitude, while the temperature and species concentration profiles are self-correcting in their convergence to the exact solution. A satisfactory resolution is obtained by the use of quite a small number of computational elements which automatically adjust their distribution of fit sharp gradients.
Expedient methods of respiratory protection. II. Leakage tests. Final report
Cooper, D.W.; Hinds, W.C.; Price, J.M.; Weker, R.; Yee, H.S.
1983-07-01
The following readily-available materials were tested on a manikin connected to a breathing simulator to determine the fraction of an approximately 2-..mu..m-diameter aerosol that would leak around the seal of the materials to the manikin's face: cotton/polyester shirt material, cotton handkerchief material, toweling (a wash cloth), a surgical mask (Johnson and Johnson Co., model HRI 8137), and a NIOSH-approved disposable face mask (3M, model number 8710). The leakage tests were performed to supplement the measurements of penetration through the materials, conducted as the first phase of this investigation. The leakage tests were performed with the materials held on to the face by three methods, leakage fractions being determined from comparisons with the penetration of the same aerosol for the materials fully taped to the face. At a breathing rate of 37 liters per minute, mean leakages ranged from 0.0 percent to 63 percent. Mean penetrations exclusive of leakage ranged from 0.6 percent to 39 percent. Use of nylon hosiery material (panty hose) to hold the handkerchief material or the disposable face mask to the face was found to be very effective in preventing leakage. Such a combination could be expected to reduce leakage around the handkerchief to about ten percent or less in practice, and around the mask to less than one percent, offering substantial protection from accidentally generated aerosols. The reduction in leakage around the mask provided by the hosiery material suggests the adaptation and use of such an approach in regular industrial hygiene practice. The third and final phase of this investigation is underway, in which the penetration of the materials by particles with diameters between 0.05 and 0.5 ..mu..m is being measured and the effectiveness of the methods for dose reduction in the presence of radioactive aerosols is being modeled.
NASA Astrophysics Data System (ADS)
Piche, Steffanie
Understanding the impact of coastal forests on the propagation of rapidly advancing onshore tsunami bores is difficult due to complexity of this phenomenon and the large amount of parameters which must be considered. The research presented in the thesis focuses on understanding the protective effect of the coastal forest on the forces generated by the tsunami and its ability to reduce the propagation and velocity of the incoming tsunami bore. Concern for this method of protecting the coast from tsunamis is based on the effectiveness of the forest and its ability to withstand the impact forces caused by both the bore and the debris carried along by it. The devastation caused by the tsunami has been investigated in recent examples such as the 2011 Tohoku Tsunami in Japan and the Indian Ocean Tsunami which occurred in 2004. This research examines the reduction of the spatial extent of the tsunami bore inundation and runup due to the presence of the coastal forest, and attempts to quantify the impact forces induced by the tsunami bores and debris impact on the structures. This research work was performed using a numerical model based on the Smoothed Particle Hydrodynamics (SPH) method which is a single-phase three-dimensional model. The simulations performed in this study were separated into three sections. The first section focused on the reduction of the extent of the tsunami inundation and the magnitude of the bore velocity by the coastal forest. This section included the analysis of the hydrodynamic forces acting on the individual trees. The second section involved the numerical modeling of some of the physical laboratory experiments performed by researchers at the University of Ottawa, in cooperation with colleagues from the Ocean, Coastal and River Engineering Lab at the National Research Council, Ottawa, in an attempt to validate the movement and impact forces of floating driftwood on a column. The final section modeled the movement and impact of floating debris
Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H.; Miller, Cass T.
2010-01-01
The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward-difference-formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications. PMID:20577570
A Numerical Investigation of CFRP-Steel Interfacial Failure with Material Point Method
Shen Luming; Faleh, Haydar; Al-Mahaidi, Riadh
2010-05-21
The success of retrofitting steel structures by using the Carbon Fibre Reinforced Polymers (CFRP) significantly depends on the performance and integrity of CFRP-steel joint and the effectiveness of the adhesive used. Many of the previous numerical studies focused on the design and structural performance of the CFRP-steel system and neglected the mechanical responses of adhesive layer, which results in the lack of understanding in how the adhesive layer between the CFRP and steel performs during the loading and failure stages. Based on the recent observation on the failure of CFRP-steel bond in the double lap shear tests, a numerical approach is proposed in this study to simulate the delamination process of CFRP sheet from steel plate using the Material Point Method (MPM). In the proposed approach, an elastoplasticity model with a linear hardening and softening law is used to model the epoxy layer. The MPM, which does not employ fixed mesh-connectivity, is employed as a robust spatial discretization method to accommodate the multi-scale discontinuities involved in the CFRP-steel bond failure process. To demonstrate the potential of the proposed approach, a parametric study is conducted to investigate the effects of bond length and loading rates on the capacity and failure modes of CFRP-steel system. The evolution of the CFRP-steel bond failure and the distribution of stress and strain along bond length direction will be presented. The simulation results not only well match the available experimental data but also provide a better understanding on the physics behind the CFRP sheet delamination process.
A Numerical Investigation of CFRP-Steel Interfacial Failure with Material Point Method
NASA Astrophysics Data System (ADS)
Shen, Luming; Faleh, Haydar; Al-Mahaidi, Riadh
2010-05-01
The success of retrofitting steel structures by using the Carbon Fibre Reinforced Polymers (CFRP) significantly depends on the performance and integrity of CFRP-steel joint and the effectiveness of the adhesive used. Many of the previous numerical studies focused on the design and structural performance of the CFRP-steel system and neglected the mechanical responses of adhesive layer, which results in the lack of understanding in how the adhesive layer between the CFRP and steel performs during the loading and failure stages. Based on the recent observation on the failure of CFRP-steel bond in the double lap shear tests [1], a numerical approach is proposed in this study to simulate the delamination process of CFRP sheet from steel plate using the Material Point Method (MPM). In the proposed approach, an elastoplasticity model with a linear hardening and softening law is used to model the epoxy layer. The MPM [2], which does not employ fixed mesh-connectivity, is employed as a robust spatial discretization method to accommodate the multi-scale discontinuities involved in the CFRP-steel bond failure process. To demonstrate the potential of the proposed approach, a parametric study is conducted to investigate the effects of bond length and loading rates on the capacity and failure modes of CFRP-steel system. The evolution of the CFRP-steel bond failure and the distribution of stress and strain along bond length direction will be presented. The simulation results not only well match the available experimental data but also provide a better understanding on the physics behind the CFRP sheet delamination process.
NASA Astrophysics Data System (ADS)
Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H.; Miller, Cass T.
2010-07-01
The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte-Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward difference formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte-Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.
Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H; Miller, Cass T
2010-07-01
The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward-difference-formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.
A numerical method for investigating crystal settling in convecting magma chambers
NASA Astrophysics Data System (ADS)
Verhoeven, J.; Schmalzl, J.
2009-12-01
Magma chambers can be considered as thermochemically driven convection systems. We present a new numerical method that describes the movement of crystallized minerals in terms of active spherical particles in a convecting magma that is represented by an infinite Prandtl number fluid. The main part focuses on the results we obtained. A finite volume thermochemical convection model for two and three dimensions and a discrete element method, which is used to model granular material, are combined. The new model is validated with floating experiments using particles of different densities and an investigation of single and multiparticle settling velocities. The resulting velocities are compared with theoretical predictions by Stokes's law and a hindered settling function for the multiparticle system. Two fundamental convection regimes are identified in the parameter space that is spanned by the Rayleigh number and the chemical Rayleigh number, which is a measure for the density of the particles. We define the T regime that is dominated by thermal convection. Here the thermal driving force is strong enough to keep all particles in suspension. As the particles get denser, they start settling to the ground, which results in a C regime. The C regime is characterized by the existence of a sediment layer with particle-rich material and a suspension layer with few particles. It is shown that the presence of particles can reduce the vigor of thermal convection. In the frame of a parameter study we discuss the change between the regimes that is systematically investigated. We show that the so-called TC transition fits a power law. Furthermore, we investigate the settling behavior of the particles in vigorous thermal convection, which can be linked to crystal settling in magma chambers. We develop an analytical settling law that describes the number of settled particles against time and show that the results fit the observations from numerical and laboratory experiments.
Numerical methods for a Poisson-Nernst-Planck-Fermi model of biological ion channels
NASA Astrophysics Data System (ADS)
Liu, Jinn-Liang; Eisenberg, Bob
2015-07-01
Numerical methods are proposed for an advanced Poisson-Nernst-Planck-Fermi (PNPF) model for studying ion transport through biological ion channels. PNPF contains many more correlations than most models and simulations of channels, because it includes water and calculates dielectric properties consistently as outputs. This model accounts for the steric effect of ions and water molecules with different sizes and interstitial voids, the correlation effect of crowded ions with different valences, and the screening effect of polarized water molecules in an inhomogeneous aqueous electrolyte. The steric energy is shown to be comparable to the electrical energy under physiological conditions, demonstrating the crucial role of the excluded volume of particles and the voids in the natural function of channel proteins. Water is shown to play a critical role in both correlation and steric effects in the model. We extend the classical Scharfetter-Gummel (SG) method for semiconductor devices to include the steric potential for ion channels, which is a fundamental physical property not present in semiconductors. Together with a simplified matched interface and boundary (SMIB) method for treating molecular surfaces and singular charges of channel proteins, the extended SG method is shown to exhibit important features in flow simulations such as optimal convergence, efficient nonlinear iterations, and physical conservation. The generalized SG stability condition shows why the standard discretization (without SG exponential fitting) of NP equations may fail and that divalent Ca2 + may cause more unstable discrete Ca2 + fluxes than that of monovalent Na+. Two different methods—called the SMIB and multiscale methods—are proposed for two different types of channels, namely, the gramicidin A channel and an L-type calcium channel, depending on whether water is allowed to pass through the channel. Numerical methods are first validated with constructed models whose exact solutions are
A general spectral method for the numerical simulation of one-dimensional interacting fermions
NASA Astrophysics Data System (ADS)
Clason, Christian; von Winckel, Gregory
2012-02-01
This work introduces a general framework for the direct numerical simulation of systems of interacting fermions in one spatial dimension. The approach is based on a specially adapted nodal spectral Galerkin method, where the basis functions are constructed to obey the antisymmetry relations of fermionic wave functions. An efficient MATLAB program for the assembly of the stiffness and potential matrices is presented, which exploits the combinatorial structure of the sparsity pattern arising from this discretization to achieve optimal run-time complexity. This program allows the accurate discretization of systems with multiple fermions subject to arbitrary potentials, e.g., for verifying the accuracy of multi-particle approximations such as Hartree-Fock in the few-particle limit. It can be used for eigenvalue computations or numerical solutions of the time-dependent Schrödinger equation. Program summaryProgram title: assembleFermiMatrix Catalogue identifier: AEKO_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKO_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 102 No. of bytes in distributed program, including test data, etc.: 2294 Distribution format: tar.gz Programming language: MATLAB Computer: Any architecture supported by MATLAB Operating system: Any supported by MATLAB; tested under Linux (x86-64) and Mac OS X (10.6) RAM: Depends on the data Classification: 4.3, 2.2 Nature of problem: The direct numerical solution of the multi-particle one-dimensional Schrödinger equation in a quantum well is challenging due to the exponential growth in the number of degrees of freedom with increasing particles. Solution method: A nodal spectral Galerkin scheme is used where the basis functions are constructed to obey the antisymmetry relations of the fermionic wave
Fully Coupled Simulation of Cosmic Reionization. I. Numerical Methods and Tests
NASA Astrophysics Data System (ADS)
Norman, Michael L.; Reynolds, Daniel R.; So, Geoffrey C.; Harkness, Robert P.; Wise, John H.
2015-01-01
We describe an extension of the Enzo code to enable fully coupled radiation hydrodynamical simulation of inhomogeneous reionization in large ~(100 Mpc)3 cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. We do, however, employ a simple subgrid model for star formation which we calibrate to observations. The numerical method presented is a modification of an earlier method presented in Reynolds et al. differing principally in the operator splitting algorithm we use to advance the system of equations. Radiation transport is done in the gray flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling properties of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. We illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with 32003 Eulerian grid cells and dark matter particles.
Taylor, Diane M; Chow, Fotini K; Delkash, Madjid; Imhoff, Paul T
2016-10-01
Landfills are a significant contributor to anthropogenic methane emissions, but measuring these emissions can be challenging. This work uses numerical simulations to assess the accuracy of the tracer dilution method, which is used to estimate landfill emissions. Atmospheric dispersion simulations with the Weather Research and Forecast model (WRF) are run over Sandtown Landfill in Delaware, USA, using observation data to validate the meteorological model output. A steady landfill methane emissions rate is used in the model, and methane and tracer gas concentrations are collected along various transects downwind from the landfill for use in the tracer dilution method. The calculated methane emissions are compared to the methane emissions rate used in the model to find the percent error of the tracer dilution method for each simulation. The roles of different factors are examined: measurement distance from the landfill, transect angle relative to the wind direction, speed of the transect vehicle, tracer placement relative to the hot spot of methane emissions, complexity of topography, and wind direction. Results show that percent error generally decreases with distance from the landfill, where the tracer and methane plumes become well mixed. Tracer placement has the largest effect on percent error, and topography and wind direction both have significant effects, with measurement errors ranging from -12% to 42% over all simulations. Transect angle and transect speed have small to negligible effects on the accuracy of the tracer dilution method. These tracer dilution method simulations provide insight into measurement errors that might occur in the field, enhance understanding of the method's limitations, and aid interpretation of field data. PMID:27395754
Fully coupled simulation of cosmic reionization. I. numerical methods and tests
Norman, Michael L.; Reynolds, Daniel R.; So, Geoffrey C.; Harkness, Robert P.; Wise, John H.
2015-01-09
Here, we describe an extension of the Enzo code to enable fully coupled radiation hydrodynamical simulation of inhomogeneous reionization in large similar to(100 Mpc)(3) cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. But, we employ a simple subgrid model for star formation which we calibrate to observations. The numerical method presented is a modification of an earlier method presented in Reynolds et al. differing principally in the operator splitting algorithm we use tomore » advance the system of equations. Radiation transport is done in the gray flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling properties of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. Finally, we illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with 3200(3) Eulerian grid cells and dark matter particles.« less
Fully coupled simulation of cosmic reionization. I. numerical methods and tests
Norman, Michael L.; Reynolds, Daniel R.; So, Geoffrey C.; Harkness, Robert P.; Wise, John H.
2015-01-09
Here, we describe an extension of the Enzo code to enable fully coupled radiation hydrodynamical simulation of inhomogeneous reionization in large similar to(100 Mpc)(3) cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. But, we employ a simple subgrid model for star formation which we calibrate to observations. The numerical method presented is a modification of an earlier method presented in Reynolds et al. differing principally in the operator splitting algorithm we use to advance the system of equations. Radiation transport is done in the gray flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling properties of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. Finally, we illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with 3200(3) Eulerian grid cells and dark matter particles.
Taylor, Diane M; Chow, Fotini K; Delkash, Madjid; Imhoff, Paul T
2016-10-01
Landfills are a significant contributor to anthropogenic methane emissions, but measuring these emissions can be challenging. This work uses numerical simulations to assess the accuracy of the tracer dilution method, which is used to estimate landfill emissions. Atmospheric dispersion simulations with the Weather Research and Forecast model (WRF) are run over Sandtown Landfill in Delaware, USA, using observation data to validate the meteorological model output. A steady landfill methane emissions rate is used in the model, and methane and tracer gas concentrations are collected along various transects downwind from the landfill for use in the tracer dilution method. The calculated methane emissions are compared to the methane emissions rate used in the model to find the percent error of the tracer dilution method for each simulation. The roles of different factors are examined: measurement distance from the landfill, transect angle relative to the wind direction, speed of the transect vehicle, tracer placement relative to the hot spot of methane emissions, complexity of topography, and wind direction. Results show that percent error generally decreases with distance from the landfill, where the tracer and methane plumes become well mixed. Tracer placement has the largest effect on percent error, and topography and wind direction both have significant effects, with measurement errors ranging from -12% to 42% over all simulations. Transect angle and transect speed have small to negligible effects on the accuracy of the tracer dilution method. These tracer dilution method simulations provide insight into measurement errors that might occur in the field, enhance understanding of the method's limitations, and aid interpretation of field data.
FULLY COUPLED SIMULATION OF COSMIC REIONIZATION. I. NUMERICAL METHODS AND TESTS
Norman, Michael L.; So, Geoffrey C.; Reynolds, Daniel R.; Harkness, Robert P.; Wise, John H.
2015-01-01
We describe an extension of the Enzo code to enable fully coupled radiation hydrodynamical simulation of inhomogeneous reionization in large ∼(100 Mpc){sup 3} cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. We do, however, employ a simple subgrid model for star formation which we calibrate to observations. The numerical method presented is a modification of an earlier method presented in Reynolds et al. differing principally in the operator splitting algorithm we use to advance the system of equations. Radiation transport is done in the gray flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling properties of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. We illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with 3200{sup 3} Eulerian grid cells and dark matter particles.
Karnaukhov, Alexey V.; Karnaukhova, Elena V.; Williamson, James R.
2007-01-01
A flexible Numerical Matrices Method (NMM) for nonlinear system identification has been developed based on a description of the dynamics of the system in terms of kinetic complexes. A set of related methods are presented that include increasing amounts of prior information about the reaction network structure, resulting in increased accuracy of the reconstructed rate constants. The NMM is based on an analytical least squares solution for a set of linear equations to determine the rate parameters. In the absence of prior information, all possible unimolecular and bimolecular reactions among the species in the system are considered, and the elements of a general kinetic matrix are determined. Inclusion of prior information is facilitated by formulation of the kinetic matrix in terms of a stoichiometry matrix or a more general set of representation matrices. A method for determination of the stoichiometry matrix beginning only with time-dependent concentration data is presented. In addition, we demonstrate that singularities that arise from linear dependencies among the species can be avoided by inclusion of data collected from a number of different initial states. The NMM provides a flexible set of tools for analysis of complex kinetic data, in particular for analysis of chemical and biochemical reaction networks. PMID:17350997
Numerical validation of a suprasystolic brachial cuff-based method for estimating aortic pressure.
Liang, Fuyou
2014-01-01
Central aortic pressures are better predictors of cardiovascular events than peripheral pressures. However, central aortic blood pressures cannot be measured noninvasively; for this reason, estimating aortic pressures from noninvasive measurements of peripheral pressures has been the subject of numerous studies. In the present study, a novel method was proposed to noninvasively estimate aortic pressures from the oscillometric wave of a suprasystolic brachial cuff. The errors of estimation were evaluated in relation to various cardiovascular properties using an integrated cardiovascular-cuff model. Obtained results demonstrated that the estimation errors are affected mainly by aortic stiffness. The estimation errors for aortic systolic pressure, diastolic pressure, pulse pressure and wave shape under the assumed cardiovascular conditions were 5.84 ± 1.58 mmHg, -0.28 ± 0.41 mmHg, 6.12 ± 1.42 mmHg and 1.72 ± 0.57 mmHg, respectively, all of which fell within the error ranges established by existing devices. Since the method is easy to be automated and bases the estimation fully on patient-specific information, its clinical application is promising, although further clinical studies are awaited to validate the method in vivo.
NASA Astrophysics Data System (ADS)
Zhi, Jie; Zhao, Libin; Zhang, Jianyu; Liu, Zhanli
2016-06-01
In this paper, a new numerical method that combines a surface-based cohesive model and extended finite element method (XFEM) without predefining the crack paths is presented to simulate the microscopic damage evolution in composites under uniaxial transverse tension. The proposed method is verified to accurately capture the crack kinking into the matrix after fiber/matrix debonding. A statistical representative volume element (SRVE) under periodic boundary conditions is used to approximate the microstructure of the composites. The interface parameters of the cohesive models are investigated, in which the initial interface stiffness has a great effect on the predictions of the fiber/matrix debonding. The detailed debonding states of SRVE with strong and weak interfaces are compared based on the surface-based and element-based cohesive models. The mechanism of damage in composites under transverse tension is described as the appearance of the interface cracks and their induced matrix micro-cracking, both of which coalesce into transversal macro-cracks. Good agreement is found between the predictions of the model and the in situ experimental observations, demonstrating the efficiency of the presented model for simulating the microscopic damage evolution in composites.
NASA Astrophysics Data System (ADS)
Chung, Sang-Young; Kwon, Deuk-Chul; Song, Mi-Young; Yoon, Jung-Sik
2014-10-01
For reliable plasma simulation an accurate full-set data of collision cross sections between each species participated in the plasma is required. However, the full-set of the reaction data is hard to achieve and estimated data have been used for the missing. To achieve reliable reaction data researchers have tuned the estimated reaction data so that the simulation results with the data agree with experimental results. However, as the number of data to be tuned is increased it becomes very hard work for researchers. In this study, we developed a code to optimize the data numerically based on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm and adopted with a 0-dimensional global simulator for semiconductor processing plasma. BFGS algorithm is a type of a quasi-Newton method. The second derivatives are used for a next estimation like Newton method but are calculated by iterations from first derivatives and previous second derivatives. So the function is called (i.e. the simulator is executed) much smaller times than Newton method. Parallel algorithm was applied to the code to save time. In the serial code the calculation time for each iteration were proportional to the number of unknown variables but it became independent of the number of the variables in the parallel code.
GCR environmental models II: Uncertainty propagation methods for GCR environments
NASA Astrophysics Data System (ADS)
Slaba, Tony C.; Blattnig, Steve R.
2014-04-01
In order to assess the astronaut exposure received within vehicles or habitats, accurate models of the ambient galactic cosmic ray (GCR) environment are required. Many models have been developed and compared to measurements, with uncertainty estimates often stated to be within 15%. However, intercode comparisons can lead to differences in effective dose exceeding 50%. This is the second of three papers focused on resolving this discrepancy. The first paper showed that GCR heavy ions with boundary energies below 500 MeV/n induce less than 5% of the total effective dose behind shielding. Yet, due to limitations on available data, model development and validation are heavily influenced by comparisons to measurements taken below 500 MeV/n. In the current work, the focus is on developing an efficient method for propagating uncertainties in the ambient GCR environment to effective dose values behind shielding. A simple approach utilizing sensitivity results from the first paper is described and shown to be equivalent to a computationally expensive Monte Carlo uncertainty propagation. The simple approach allows a full uncertainty propagation to be performed once GCR uncertainty distributions are established. This rapid analysis capability may be integrated into broader probabilistic radiation shielding analysis and also allows error bars (representing boundary condition uncertainty) to be placed around point estimates of effective dose.
NASA Technical Reports Server (NTRS)
Sidi, A.; Israeli, M.
1986-01-01
High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.
Moridis, G.
1992-03-01
The Laplace Transform Boundary Element (LTBE) method is a recently introduced numerical method, and has been used for the solution of diffusion-type PDEs. It completely eliminates the time dependency of the problem and the need for time discretization, yielding solutions numerical in space and semi-analytical in time. In LTBE solutions are obtained in the Laplace spare, and are then inverted numerically to yield the solution in time. The Stehfest and the DeHoog formulations of LTBE, based on two different inversion algorithms, are investigated. Both formulations produce comparable, extremely accurate solutions.
X. Frank Xu
2010-03-30
Multiscale modeling of stochastic systems, or uncertainty quantization of multiscale modeling is becoming an emerging research frontier, with rapidly growing engineering applications in nanotechnology, biotechnology, advanced materials, and geo-systems, etc. While tremendous efforts have been devoted to either stochastic methods or multiscale methods, little combined work had been done on integration of multiscale and stochastic methods, and there was no method formally available to tackle multiscale problems involving uncertainties. By developing an innovative Multiscale Stochastic Finite Element Method (MSFEM), this research has made a ground-breaking contribution to the emerging field of Multiscale Stochastic Modeling (MSM) (Fig 1). The theory of MSFEM basically decomposes a boundary value problem of random microstructure into a slow scale deterministic problem and a fast scale stochastic one. The slow scale problem corresponds to common engineering modeling practices where fine-scale microstructure is approximated by certain effective constitutive constants, which can be solved by using standard numerical solvers. The fast scale problem evaluates fluctuations of local quantities due to random microstructure, which is important for scale-coupling systems and particularly those involving failure mechanisms. The Green-function-based fast-scale solver developed in this research overcomes the curse-of-dimensionality commonly met in conventional approaches, by proposing a random field-based orthogonal expansion approach. The MSFEM formulated in this project paves the way to deliver the first computational tool/software on uncertainty quantification of multiscale systems. The applications of MSFEM on engineering problems will directly enhance our modeling capability on materials science (composite materials, nanostructures), geophysics (porous media, earthquake), biological systems (biological tissues, bones, protein folding). Continuous development of MSFEM will
Measuring solar reflectance Part II: Review of practical methods
Levinson, Ronnen; Akbari, Hashem; Berdahl, Paul
2010-05-14
A companion article explored how solar reflectance varies with surface orientation and solar position, and found that clear sky air mass 1 global horizontal (AM1GH) solar reflectance is a preferred quantity for estimating solar heat gain. In this study we show that AM1GH solar reflectance R{sub g,0} can be accurately measured with a pyranometer, a solar spectrophotometer, or an updated edition of the Solar Spectrum Reflectometer (version 6). Of primary concern are errors that result from variations in the spectral and angular distributions of incident sunlight. Neglecting shadow, background and instrument errors, the conventional pyranometer technique can measure R{sub g,0} to within 0.01 for surface slopes up to 5:12 [23{sup o}], and to within 0.02 for surface slopes up to 12:12 [45{sup o}]. An alternative pyranometer method minimizes shadow errors and can be used to measure R{sub g,0} of a surface as small as 1 m in diameter. The accuracy with which it can measure R{sub g,0} is otherwise comparable to that of the conventional pyranometer technique. A solar spectrophotometer can be used to determine R*{sub g,0}, a solar reflectance computed by averaging solar spectral reflectance weighted with AM1GH solar spectral irradiance. Neglecting instrument errors, R*{sub g,0} matches R{sub g,0} to within 0.006. The air mass 1.5 solar reflectance measured with version 5 of the Solar Spectrum Reflectometer can differ from R*{sub g,0} by as much as 0.08, but the AM1GH output of version 6 of this instrument matches R*{sub g,0} to within about 0.01.
Measuring solar reflectance - Part II: Review of practical methods
Levinson, Ronnen; Akbari, Hashem; Berdahl, Paul
2010-09-15
A companion article explored how solar reflectance varies with surface orientation and solar position, and found that clear sky air mass 1 global horizontal (AM1GH) solar reflectance is a preferred quantity for estimating solar heat gain. In this study we show that AM1GH solar reflectance R{sub g,0} can be accurately measured with a pyranometer, a solar spectrophotometer, or an updated edition of the Solar Spectrum Reflectometer (version 6). Of primary concern are errors that result from variations in the spectral and angular distributions of incident sunlight. Neglecting shadow, background and instrument errors, the conventional pyranometer technique can measure R{sub g,0} to within 0.01 for surface slopes up to 5:12 [23 ], and to within 0.02 for surface slopes up to 12:12 [45 ]. An alternative pyranometer method minimizes shadow errors and can be used to measure R{sub g,0} of a surface as small as 1 m in diameter. The accuracy with which it can measure R{sub g,0} is otherwise comparable to that of the conventional pyranometer technique. A solar spectrophotometer can be used to determine R{sub g,0}{sup *}, a solar reflectance computed by averaging solar spectral reflectance weighted with AM1GH solar spectral irradiance. Neglecting instrument errors, R{sub g,0}{sup *} matches R{sub g,0} to within 0.006. The air mass 1.5 solar reflectance measured with version 5 of the Solar Spectrum Reflectometer can differ from R{sub g,0}{sup *} by as much as 0.08, but the AM1GH output of version 6 of this instrument matches R{sub g,0}{sup *} to within about 0.01. (author)
Models and numerical methods for the simulation of loss-of-coolant accidents in nuclear reactors
NASA Astrophysics Data System (ADS)
Seguin, Nicolas
2014-05-01
model, this numerical scheme is also efficient in terms of CPU time. Eventually, simpler models can locally replace the more complex model in order to simplify the overall computation, using some appropriate local error indicators developed in [5], without reducing the accuracy. References 1. Ishii, M., Hibiki, T., Thermo-fluid dynamics of two-phase flow, Springer, New-York, 2006. 2. Gallouët, T. and Hérard, J.-M., Seguin, N., Numerical modeling of two-phase flows using the two-fluid two-pressure approach, Math. Models Methods Appl. Sci., Vol. 14, 2004. 3. Seguin, N., Étude d'équations aux dérivées partielles hyperboliques en mécanique des fluides, Habilitation à diriger des recherches, UPMC-Paris 6, 2011. 4. Coquel, F., Hérard, J-M., Saleh, K., Seguin, N., A Robust Entropy-Satisfying Finite Volume Scheme for the Isentropic Baer-Nunziato Model, ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 48, 2013. 5. Mathis, H., Cancès, C., Godlewski, E., Seguin, N., Dynamic model adaptation for multiscale simulation of hyperbolic systems with relaxation, preprint, 2013.
A Hybrid Numerical Method for Turbulent Mixing Layers. Degree awarded by Case Western Reserve Univ.
NASA Technical Reports Server (NTRS)
Georgiadis, Nicholas J.
2001-01-01
A hybrid method has been developed for simulations of compressible turbulent mixing layers. Such mixing layers dominate the flows in exhaust systems of modern day aircraft and also those of hypersonic vehicles currently under development. The method configurations in which a dominant structural feature provides an unsteady mechanism to drive the turbulent development in the mixing layer. The hybrid method uses a Reynolds-averaged Navier-Stokes (RANS) procedure to calculate wall bounded regions entering a mixing section, and a Large Eddy Simulation (LES) procedure to calculate the mixing dominated regions. A numerical technique was developed to enable the use of the hybrid RANS-LES method on stretched, non-Cartesian grids. Closure for the RANS equations was obtained using the Cebeci-Smith algebraic turbulence model in conjunction with the wall-function approach of Ota and Goldberg. The wall-function approach enabled a continuous computational grid from the RANS regions to the LES region. The LES equations were closed using the Smagorinsky subgrid scale model. The hybrid RANS-LES method is applied to a benchmark compressible mixing layer experiment. Preliminary two dimensional calculations are used to investigate the effects of axial grid density and boundary conditions. Vortex shedding from the base region of a splitter plate separating the upstream flows was observed to eventually transition to turbulence. The location of the transition, however, was much further downstream than indicated by experiments. Actual LES calculations, performed in three spatial directions, also indicated vortex shedding, but the transition to turbulence was found to occur much closer to the beginning of the mixing section. which is in agreement with experimental observations. These calculations demonstrated that LES simulations must be performed in three dimensions. Comparisons of time-averaged axial velocities and turbulence intensities indicated reasonable agreement with experimental
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
NASA Astrophysics Data System (ADS)
Lewis, R. W.; Johnson, J. A.; Smith, W. R.
Aspects of heat conduction are discussed, taking into account the numerical solution of steady periodic problems in heat conduction, partially discontinuous boundary elements for heat conduction, the numerical solution of heat conduction in a nonhomogeneous infinite domain by coupling the finite difference method and the boundary element method, and a method for efficiently incorporating radiative boundaries in finite element programs. Other subjects explored are related to phase change, heat and mass transfer in porous bodies, thermal and drying stresses, mathematical and computational techniques, free and forced convection, coupled conduction and convection, turbulent heat transfer, fire and combustion simulation, nuclear waste disposal, solar energy, and industrial and scientific applications. Attention is given to the dynamics of heat exchangers, temperature fields of burnt-up nuclear fuel elements in dry-storage containers, a numerical analysis of solar convective dryers, and a numerical solution by digital computer of optimum thermochemical parameters for the rocket thrust chamber.
Fogelson, A.L.
1984-10-01
The repair of small blood vessels and the pathological growth of internal blood clots involve the formation of platelet aggregates adhering to portions of the vessel wall. Our microscopic model represents blood by a suspension of discrete massless platelets in a viscous incompressible fluid. Platelets are initially noncohesive; however, if stimulated by an above-threshold concentration of the chemical ADP or by contact with the adhesive injured region of the vessel wall, they become cohesive and secrete more ADP into the fluid. Cohesion between platelets and adhesion of a platelet to the injured wall are modeled by creating elastic links. Repulsive forces prevent a platelet from coming too close to another platelet or to the wall. The forces affect the fluid motion in the neighborhood of an aggregate. The platelets and secreted ADP both move by fluid advection and diffusion. The equations of the model are studied numerically in two dimensions. The platelet forces are calculated implicitly by minimizing a nonlinear energy function. Our minimization scheme merges Gill and Murray's (Math. Programming 7 (1974), 311) modified Newton's method with elements of the Yale sparse matix package. The stream-function formulation of the Stokes' equations for the fluid motion under the influence of platelet forces is solved using Bjorstad's biharmonic solver (''Numerical Solution of the Biharmonic Equation,'' Ph.D. Thesis, Stanford University, 1980). The ADP transport equation is solved with an alternating-direction implicit scheme. A linked-list data structure is introduced to keep track of changing platelet states and changing configurations of interplatelet links.
NASA Astrophysics Data System (ADS)
Giacobbi, Dana B.; Rinaldi, Stephanie; Semler, Christian; Païdoussis, Michael P.
2012-04-01
This paper investigates the dynamics of a slender, flexible, aspirating cantilevered pipe, ingesting fluid at its free end and conveying it towards its clamped end. The problem is interesting not only from a fundamental perspective, but also because applications exist, notably in ocean mining. First, the need for the present work is demonstrated through a review of previous research into the topic - spanning many years and yielding often contradictory results - most recently suggesting that the system loses stability by flutter at relatively low flow velocities. In the present paper, that conclusion is refined and expanded upon by exploring the problem in three ways: experimentally, numerically and analytically. First, air-flow experiments were conducted using different elastomer pipes and intake shapes, in which the flow velocity of the fluid was varied and the frequency and amplitude of oscillation of the pipe were measured. Second, a fully coupled Computational Fluid Dynamics (CFD) and Computational Structural Mechanics (CSM) model was developed in ANSYS™ in order to simulate experiments and corroborate experimental results. Finally, using a Newtonian analytical approach, a new linear equation of motion describing the system was derived, and then solved via the Galerkin method in order to determine its stability characteristics. Heavily influenced by the CFD analysis, the proposed analytical model is different from previous ones, most notably because of the inclusion of a two-part fluid depressurisation at the intake. In general, both the actual and numerical experiments suggest a first-mode loss of stability by flutter at flow velocities comparable to those for the discharging case, which agrees with the results from the new analytical model.
Numerical simulations of blast-impact problems using the direct simulation Monte Carlo method
NASA Astrophysics Data System (ADS)
Sharma, Anupam
There is an increasing need to design protective structures that can withstand or mitigate the impulsive loading due to the impact of a blast or a shock wave. A preliminary step in designing such structures is the prediction of the pressure loading on the structure. This is called the "load definition." This thesis is focused on a numerical approach to predict the load definition on arbitrary geometries for a given strength of the incident blast/shock wave. A particle approach, namely the Direct Simulation Monte Carlo (DSMC) method, is used as the numerical model. A three-dimensional, time-accurate DSMC flow solver is developed as a part of this study. Embedded surfaces, modeled as triangulations, are used to represent arbitrary-shaped structures. Several techniques to improve the computational efficiency of the algorithm of particle-structure interaction are presented. The code is designed using the Object Oriented Programming (OOP) paradigm. Domain decomposition with message passing is used to solve large problems in parallel. The solver is extensively validated against analytical results and against experiments. Two kinds of geometries, a box and an I-shaped beam are investigated for blast impact. These simulations are performed in both two- and three-dimensions. A major portion of the thesis is dedicated to studying the uncoupled fluid dynamics problem where the structure is assumed to remain stationary and intact during the simulation. A coupled, fluid-structure dynamics problem is solved in one spatial dimension using a simple, spring-mass-damper system to model the dynamics of the structure. A parametric study, by varying the mass, spring constant, and the damping coefficient, to study their effect on the loading and the displacement of the structure is also performed. Finally, the parallel performance of the solver is reported for three sample-size problems on two Beowulf clusters.
Numerical modeling of surf zone dynamics under weakly plunging breakers with SPH method
NASA Astrophysics Data System (ADS)
Makris, Christos V.; Memos, Constantine D.; Krestenitis, Yannis N.
2016-02-01
The wave breaking of weak plungers over a relatively mild slope is investigated in this paper. Numerical modeling aspects are studied, concerning the propagation and breaking of shore-normal, nonlinear and regular waves. The two-dimensional (2-D) kinematics and dynamics (fluctuating flow features and large 2-D eddies) of the wave-induced flow on a vertical cross-section over the entire surf zone are simulated with the use of Smoothed Particle Hydrodynamics (SPH). The academic 'open source' code SPHysics v.2 is employed and the viscosity treatment is based on a Sub-Particle Scale (SPS) approach, similarly to the Large Eddy Simulations (LES) concept. Thorough analysis of the turbulent flow scales determines the necessary refinement of the spatial resolution. The initial particle discretization reaches down to the demarcation point between integral turbulence length scales and Taylor micro-scales. A convolution-type integration method is implemented for the transformation of scattered Lagrangian particle data to Eulerian values at fixed gauges. A heuristic technique of ensemble-averaging is used for the discrimination of the fluctuating flow components from coherent structures and ordered wave motion. Comparisons between numerical and experimental data give encouraging results for several wave features. The wave-induced mean flows are simulated plausibly, and even the 'streaming' effect near the bed is reproduced. The recurring vorticity patterns are derived, and coherent 2-D structures inside the surf zone are identified. Fourier spectral analysis of velocities reveals isotropy of 2-D fluctuating dynamics up to rather high frequencies in shear intensified regions. The simulated Reynolds stresses follow patterns that define the characteristic mechanism of wave breaking for weak plungers. Persisting discrepancies at the incipient breaking region confirm the need for fine, massively 'parallel' 3-D SPS-SPH simulations.
Comparing models of rapidly rotating relativistic stars constructed by two numerical methods
NASA Astrophysics Data System (ADS)
Stergioulas, Nikolaos; Friedman, John L.
1995-05-01
We present the first direct comparison of codes based on two different numerical methods for constructing rapidly rotating relativistic stars. A code based on the Komatsu-Eriguchi-Hachisu (KEH) method (Komatsu et al. 1989), written by Stergioulas, is compared to the Butterworth-Ipser code (BI), as modified by Friedman, Ipser, & Parker. We compare models obtained by each method and evaluate the accuracy and efficiency of the two codes. The agreement is surprisingly good, and error bars in the published numbers for maximum frequencies based on BI are dominated not by the code inaccuracy but by the number of models used to approximate a continuous sequence of stars. The BI code is faster per iteration, and it converges more rapidly at low density, while KEH converges more rapidly at high density; KEH also converges in regions where BI does not, allowing one to compute some models unstable against collapse that are inaccessible to the BI code. A relatively large discrepancy recently reported (Eriguchi et al. 1994) for models based on Friedman-Pandharipande equation of state is found to arise from the use of two different versions of the equation of state. For two representative equations of state, the two-dimensional space of equilibrium configurations is displayed as a surface in a three-dimensional space of angular momentum, mass, and central density. We find, for a given equation of state, that equilibrium models with maximum values of mass, baryon mass, and angular momentum are (generically) either all unstable to collapse or are all stable. In the first case, the stable model with maximum angular velocity is also the model with maximum mass, baryon mass, and angular momentum. In the second case, the stable models with maximum values of these quantities are all distinct. Our implementation of the KEH method will be available as a public domain program for interested users.
Numerical simulation and fracture evaluation method of dual laterolog in organic shale
NASA Astrophysics Data System (ADS)
Tan, Maojin; Wang, Peng; Li, Jun; Liu, Qiong; Yang, Qinshan
2014-01-01
Fracture identification and parameter evaluation are important for logging interpretation of organic shale, especially fracture evaluation from conventional logs in case the imaging log is not available. It is helpful to study dual laterolog responses of the fractured shale reservoir. First, a physical model is set up according to the property of organic shale, and three-dimensional finite element method (FEM) based on the principle of dual laterolog is introduced and applied to simulate dual laterolog responses in various shale models, which can help identify the fractures in shale formations. Then, through a number of numerical simulations of dual laterolog for various shale models with different base rock resistivities and fracture openings, the corresponding equations of various cases are constructed respectively, and the fracture porosity can be calculated consequently. Finally, we apply this methodology proposed above to a case study of organic shale, and the fracture porosity and fracture opening are calculated. The results are consistent with the fracture parameters processed from Full borehole Micro-resistivity Imaging (FMI). It indicates that the method is applicable for fracture evaluation of organic shale.
Devasenapathy, Deepa; Kannan, Kathiravan
2015-01-01
The traffic in the road network is progressively increasing at a greater extent. Good knowledge of network traffic can minimize congestions using information pertaining to road network obtained with the aid of communal callers, pavement detectors, and so on. Using these methods, low featured information is generated with respect to the user in the road network. Although the existing schemes obtain urban traffic information, they fail to calculate the energy drain rate of nodes and to locate equilibrium between the overhead and quality of the routing protocol that renders a great challenge. Thus, an energy-efficient cluster-based vehicle detection in road network using the intention numeration method (CVDRN-IN) is developed. Initially, sensor nodes that detect a vehicle are grouped into separate clusters. Further, we approximate the strength of the node drain rate for a cluster using polynomial regression function. In addition, the total node energy is estimated by taking the integral over the area. Finally, enhanced data aggregation is performed to reduce the amount of data transmission using digital signature tree. The experimental performance is evaluated with Dodgers loop sensor data set from UCI repository and the performance evaluation outperforms existing work on energy consumption, clustering efficiency, and node drain rate. PMID:25793221
Beronov, Kamen N; Durst, Franz
2005-01-01
A major prerequisite for successful planning and control of the medical treatment of blood vessels with stenoses or aneurysms is the detailed knowledge of the individual situation in the damaged vessels. Modern tomography methods provide good spatial resolution, so that vessel walls as well as prostheses can be easily and rapidly identified. However, the mechanical loads of the walls remain largely unknown. In the past few years, tomography data have been used for spatial and temporal simulations of the blood flow in such vessels and to predict the mechanical loads of the vessel walls. The methodologies used so far, however, involve elaborate grid generation and simulation steps, most often relying on commercial software suited for engineering projects. These require specific knowledge and experience in mechanics and numerical simulation, and are therefore inappropriate for clinical applications. It is now shown, by example of an intracranial aneurysm, that employing a Lattice Boltzmann method for the flow simulation allows to avoid all mentioned drawbacks and to simulate blood flows in a fast and simple way that is also appropriate for clinical use. The practical relevance of such simulations will be enhanced by a better understanding of the correlations between pathology and specific mechanical loads. The paper discusses also some aspects of fluid mechanics that are relevant for the study of aneurysms.
NASA Astrophysics Data System (ADS)
Wang, Chen; Wang, Yabin
2016-08-01
In hard target penetration simulation, the existing researches of the convergence of results are mainly concentrating in the corresponding relationship between penetration depth and mesh scales. However, the influence of the mesh difference on the penetration resistance and acceleration signals are seldom refer to. This paper presents the occurring mechanism and restraining method of numerical noise signal in penetration simulation. First, the concept of the noise signal izs proposed. By taking a 3D penetration simulation as example, the influence of the noise signal on the penetration resistance in different mesh scales and impact velocity is studied. To ensure the convergence of the computational results, the grid scale of the target is encrypted to 1:1:8. In addition, modern spectrum analysis method is introduced to further analyze the penetration resistance signal. The research results presented is useful to improve the computational accuracy of high speed projectile penetration simulation, and provide important reference for carrying out structural design and optimization of fuze system.
A NUMERICAL METHOD FOR STUDYING SUPER-EDDINGTON MASS TRANSFER IN DOUBLE WHITE DWARF BINARIES
Marcello, Dominic C.; Tohline, Joel E. E-mail: tohline@phys.lsu.edu
2012-04-01
We present a numerical method for the study of double white dwarf (DWD) binary systems at the onset of super-Eddington mass transfer. We incorporate the physics of ideal inviscid hydrodynamical flow, Newtonian self-gravity, and radiation transport on a three-dimensional uniformly rotating cylindrical Eulerian grid. Care has been taken to conserve the key physical quantities such as angular momentum and energy. Our new method conserves total energy to a higher degree of accuracy than other codes that are presently being used to model mass transfer in DWD systems. We present the results of verification tests and simulate the first 20 + orbits of a binary system of mass ratio q 0.7 at the onset of dynamically unstable direct impact mass transfer. The mass transfer rate quickly exceeds the critical Eddington limit by many orders of magnitude, and thus we are unable to model a trans-Eddington phase. It appears that radiation pressure does not significantly affect the accretion flow in the highly super-Eddington regime. An optically thick common envelope forms around the binary within a few orbits. Although this envelope quickly exceeds the spatial domain of the computational grid, the fraction of the common envelope that exceeds zero gravitational binding energy is extremely small, suggesting that radiation-driven mass loss is insignificant in this regime. It remains to be seen whether simulations that capture the trans-Eddington phase of such flows will lead to the same conclusion or show that substantial material gets expelled.
Robust numerical methods for conservation laws using a biased averaging procedure
NASA Astrophysics Data System (ADS)
Choi, Hwajeong
In this thesis, we introduce a new biased averaging procedure (BAP) and use it in developing high resolution schemes for conservation laws. Systems of conservation laws arise in variety of physical problems, such as the Euler equation of compressible flows, magnetohydrodynamics, multicomponent flows, the blast waves and the flow of glaciers. Many modern shock capturing schemes are based on solution reconstructions by high order polynomial interpolations, and time evolution by the solutions of Riemann problems. Due to the existence of discontinuities in the solution, the interpolating polynomial has to be carefully constructed to avoid possible oscillations near discontinuities. The BAP is a more general and simpler way to approximate higher order derivatives of given data without introducing oscillations, compared to limiters and the essentially non-oscillatory interpolations. For the solution of a system of conservation laws, we present a finite volume method which employs a flux splitting and uses componentwise reconstruction of the upwind fluxes. A high order piecewise polynomial constructed by using BAP is used to approximate the component of upwind fluxes. This scheme does not require characteristic decomposition nor Riemann solver, offering easy implementation and a relatively small computational cost. More importantly, the BAP is naturally extended for unstructured grids and it will be demonstrated through a cell-centered finite volume method, along with adaptive mesh refinement. A number of numerical experiments from various applications demonstrates the robustness and the accuracy of this approach, and show the potential of this approach for other practical applications.
Numerical simulation of electromagnetic acoustic transducers using distributed point source method.
Eskandarzade, M; Kundu, T; Liebeaux, N; Placko, D; Mobadersani, F
2010-05-01
In spite of many advances in analytical and numerical modeling techniques for solving different engineering problems, an efficient solution technique for wave propagation modeling of an electromagnetic acoustic transducer (EMAT) system is still missing. Distributed point source method (DPSM) is a newly developed semi-analytical technique developed since 2000 by Placko and Kundu (2007) [12] that is very powerful and straightforward for solving various engineering problems, including acoustic and electromagnetic modeling problems. In this study DPSM has been employed to model the Lorentz type EMAT with a meander line and flat spiral type coil. The problem of wave propagation has been solved and eddy currents and Lorentz forces have been calculated. The displacement field has been obtained as well. While modeling the Lorentz force the effect of dynamic magnetic field has been considered that most current analyses ignore. Results from this analysis have been compared with the finite element method (FEM) based predictions. It should be noted that with the current state of knowledge this problem can be solved only by FEM.
NASA Astrophysics Data System (ADS)
Parand, K.; Rad, J. A.; Ahmadi, M.
2016-09-01
Natural convective heat transfer in porous media which is of importance in the design of canisters for nuclear waste disposal has received considerable attention during the past few decades. This paper presents a comparison between two different analytical and numerical methods, i.e. pseudospectral and Adomian decomposition methods. The pseudospectral approach makes use of the orthogonal rational Jacobi functions; this method reduces the solution of the problem to a solution of a system of algebraic equations. Numerical results are compared with each other, showing that the pseudospectral method leads to more accurate results and is applicable on similar problems.
Taylor, G.; Dong, C.; Sun, S.
2010-03-18
A mathematical model for contaminant species passing through fractured porous media is presented. In the numerical model, we combine two locally conservative methods, i.e. mixed finite element (MFE) and the finite volume methods. Adaptive triangle mesh is used for effective treatment of the fractures. A hybrid MFE method is employed to provide an accurate approximation of velocities field for both the fractures and matrix which are crucial to the convection part of the transport equation. The finite volume method and the standard MFE method are used to approximate the convection and dispersion terms respectively. The model is used to investigate the interaction of adsorption with transport and to extract information on effective adsorption distribution coefficients. Numerical examples in different fractured media illustrate the robustness and efficiency of the proposed numerical model.
NASA Astrophysics Data System (ADS)
Jankovic, I.
2002-05-01
Flow and transport in porous formations are analyzed using numerical simulations. Hydraulic conductivity is treated as a spatial random function characterized by a probability density function and a two-point covariance function. Simulations are performed for a multi-indicator conductivity structure developed by Gedeon Dagan (personal communication). This conductivity structure contains inhomogeneities (inclusions) of elliptical and ellipsoidal geometry that are embedded in a homogeneous background. By varying the distribution of sizes and conductivities of inclusions, any probability density function and two-point covariance may be reproduced. The multi-indicator structure is selected since it yields simple approximate transport solutions (Aldo Fiori, personal communication) and accurate numerical solutions (based on the Analytic Element Method). The dispersion is examined for two conceptual models. Both models are based on the multi-indicator conductivity structure. The first model is designed to examine dispersion in aquifers with continuously varying conductivity. The inclusions in this model cover as much area/volume of the porous formation as possible. The second model is designed for aquifers that contain clay/sand/gravel lenses embedded in otherwise homogeneous background. The dispersion in both aquifer types is simulated numerically. Simulation results are compared to those obtained using simple approximate solutions. In order to infer transport statistics that are representative of an infinite domain using the numerical experiments, the inclusions are placed in a domain that was shaped as a large ellipse (2D) and a large spheroid (3D) that were submerged in an unbounded homogeneous medium. On a large scale, the large body of inclusions behaves like a single large inhomogeneity. The analytic solution for a uniform flow past the single inhomogeneity of such geometry yields uniform velocity inside the domain. The velocity differs from that at infinity and
The Theory of Propellers II : Method for Calculating the Axial Interference Velocity
NASA Technical Reports Server (NTRS)
Theodorsen, Theodore
1944-01-01
A technical method is given for calculating the axial interference velocity of a propeller. The method involves the use of certain weight functions p, q, and f. Numerical values for the weight functions are given for two-blade, three-blade, and six-blade propellers.
Numerical Modeling of Spray Combustion with an Unstructured-Grid Method
NASA Technical Reports Server (NTRS)
Shang, H. M.; Chen, Y. S.; Liaw, P.; Shih, M. H.; Wang, T. S.
1996-01-01
The present unstructured-grid method follows strictly the basic finite volume forms of the conservation laws of the governing equations for the entire flow domain. High-order spatially accurate formulation has been employed for the numerical solutions of the Navier-Stokes equations. A two-equation k-epsilon turbulence model is also incorporated in the unstructured-grid solver. The convergence of the resulted linear algebraic equation is accelerated with preconditioned Conjugate Gradient method. A statistical spray combustion model has been incorporated into the present unstructured-grid solver. In this model, spray is represented by discrete particles, rather than by continuous distributions. A finite number of computational particles are used to predict a sample of total population of particles. Particle trajectories are integrated using their momentum and motion equations and particles exchange mass, momentum and energy with the gas within the computational cell in which they are located. The interaction calculations are performed simultaneously and eliminate global iteration for the two-phase momentum exchange. A transient spray flame in a high pressure combustion chamber is predicted and then the solution of liquid-fuel combusting flow with a rotating cup atomizer is presented and compared with the experimental data. The major conclusion of this investigation is that the unstructured-grid method can be employed to study very complicated flow fields of turbulent spray combustion. Grid adaptation can be easily achieved in any flow domain such as droplet evaporation and combustion zone. Future applications of the present model can be found in the full three-dimensional study of flow fields of gas turbine and liquid propulsion engine combustion chambers with multi-injectors.