Mie Light-Scattering Granulometer with an Adaptive Numerical Filtering Method. II. Experiments.
Hespel, L; Delfour, A; Guillame, B
2001-02-20
A nephelometer is presented that theoretically requires no absolute calibration. This instrument is used for determining the particle-size distribution of various scattering media (aerosols, fogs, rocket exhausts, engine plumes, and the like) from angular static light-scattering measurements. An inverse procedure is used, which consists of a least-squares method and a regularization scheme based on numerical filtering. To retrieve the distribution function one matches the experimental data with theoretical patterns derived from Mie theory. The main principles of the inverse method are briefly presented, and the nephelometer is then described with the associated partial calibration procedure. Finally, the whole granulometer system (inverse method and nephelometer) is validated by comparison of measurements of scattering media with calibrated monodisperse or known size distribution functions.
Nonlinear instability and chaos in plasma wave-wave interactions. II. Numerical methods and results
Kueny, C.S.; Morrison, P.J.
1995-05-01
In Part I of this work and Physics of Plasmas, June 1995, the behavior of linearly stable, integrable systems of waves in a simple plasma model was described using a Hamiltonian formulation. It was shown that explosive instability arises from nonlinear coupling between modes of positive and negative energy, with well-defined threshold amplitudes depending on the physical parameters. In this concluding paper, the nonintegrable case is treated numerically. Several sets of waves are considered, comprising systems of two and three degrees of freedom. The time evolution is modelled with an explicit symplectic integration algorithm derived using Lie algebraic methods. When initial wave amplitudes are large enough to support two-wave decay interactions, strongly chaotic motion destroys the separatrix bounding the stable region for explosive triplets. Phase space orbits then experience diffusive growth to amplitudes that are sufficient for explosive instability, thus effectively reducing the threshold amplitude. For initial amplitudes too small to drive decay instability, small perturbations might still grow to arbitrary size via Arnold diffusion. Numerical experiments do not show diffusion in this case, although the actual diffusion rate is probably underestimated due to the simplicity of the model.
NASA Astrophysics Data System (ADS)
Heister, Timo; Dannberg, Juliane; Gassmöller, Rene; Bangerth, Wolfgang
2017-08-01
Computations have helped elucidate the dynamics of Earth's mantle for several decades already. The numerical methods that underlie these simulations have greatly evolved within this time span, and today include dynamically changing and adaptively refined meshes, sophisticated and efficient solvers, and parallelization to large clusters of computers. At the same time, many of the methods - discussed in detail in a previous paper in this series - were developed and tested primarily using model problems that lack many of the complexities that are common to the realistic models our community wants to solve today. With several years of experience solving complex and realistic models, we here revisit some of the algorithm designs of the earlier paper and discuss the incorporation of more complex physics. In particular, we re-consider time stepping and mesh refinement algorithms, evaluate approaches to incorporate compressibility, and discuss dealing with strongly varying material coefficients, latent heat, and how to track chemical compositions and heterogeneities. Taken together and implemented in a high-performance, massively parallel code, the techniques discussed in this paper then allow for high resolution, 3-D, compressible, global mantle convection simulations with phase transitions, strongly temperature dependent viscosity and realistic material properties based on mineral physics data.
Noid, W G; Liu, Pu; Wang, Yanting; Chu, Jhih-Wei; Ayton, Gary S; Izvekov, Sergei; Andersen, Hans C; Voth, Gregory A
2008-06-28
The multiscale coarse-graining (MS-CG) method [S. Izvekov and G. A. Voth, J. Phys. Chem. B 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] employs a variational principle to determine an interaction potential for a CG model from simulations of an atomically detailed model of the same system. The companion paper proved that, if no restrictions regarding the form of the CG interaction potential are introduced and if the equilibrium distribution of the atomistic model has been adequately sampled, then the MS-CG variational principle determines the exact many-body potential of mean force (PMF) governing the equilibrium distribution of CG sites generated by the atomistic model. In practice, though, CG force fields are not completely flexible, but only include particular types of interactions between CG sites, e.g., nonbonded forces between pairs of sites. If the CG force field depends linearly on the force field parameters, then the vector valued functions that relate the CG forces to these parameters determine a set of basis vectors that span a vector subspace of CG force fields. The companion paper introduced a distance metric for the vector space of CG force fields and proved that the MS-CG variational principle determines the CG force force field that is within that vector subspace and that is closest to the force field determined by the many-body PMF. The present paper applies the MS-CG variational principle for parametrizing molecular CG force fields and derives a linear least squares problem for the parameter set determining the optimal approximation to this many-body PMF. Linear systems of equations for these CG force field parameters are derived and analyzed in terms of equilibrium structural correlation functions. Numerical calculations for a one-site CG model of methanol and a molecular CG model of the EMIM(+)NO(3) (-) ionic liquid are provided to illustrate the method.
Introduction to Numerical Methods
Schoonover, Joseph A.
2016-06-14
These are slides for a lecture for the Parallel Computing Summer Research Internship at the National Security Education Center. This gives an introduction to numerical methods. Repetitive algorithms are used to obtain approximate solutions to mathematical problems, using sorting, searching, root finding, optimization, interpolation, extrapolation, least squares regresion, Eigenvalue problems, ordinary differential equations, and partial differential equations. Many equations are shown. Discretizations allow us to approximate solutions to mathematical models of physical systems using a repetitive algorithm and introduce errors that can lead to numerical instabilities if we are not careful.
Sonntag, D; Stachniss-Carp, S; Stachniss, C; Stachniss, V
2006-04-01
The aim of this paper is to present a new method based on numeric calculus to provide data on any type of root canal curvature at any point of the long axis of the canal. Twenty severely curved, simulated root canals were prepared with rotary FlexMaster and Profile instruments in the crown-down technique and manually in the step-back technique. The inner and outer curvatures were registered in a system of coordinates before and after preparation in increments of 0.5 mm. Using an equalising function, the curvatures were first represented in graphic and algebraic form. The maximum and the mean curvature as well as the length of the arc from the apical foramen to the point of maximum curvature were determined mathematically. An increase in maximum curvature was registered for all four shaping systems investigated. The radius of the inner curvature decreased by 0.5-1.2 mm in the manual systems as a result of the preparation. The Profile system displayed the smallest changes in radius (-0.9 mm) even with the outer curvature, and manual preparation with stainless steel files the most pronounced change (-1.8 mm). The point of maximum curvature at the inner curvature was displaced by 1.6 mm to the apical foramen through manual preparation with Ni-Ti files. At the outer curvature, the maximum displacement (1.8 mm) recorded was also the result of preparation with Ni-Ti hand files, while a displacement of only 0.3 mm to the apical foramen was recorded with the other systems. The method offers a means of determining curvatures precisely without random specification of reference points. The method is also capable of registering only minor changes in curvature in the two-dimensional long axis of the canal.
NASA Astrophysics Data System (ADS)
Mehrmann, Volker; Xu, Hongguo
2000-11-01
We study classical control problems like pole assignment, stabilization, linear quadratic control and H[infinity] control from a numerical analysis point of view. We present several examples that show the difficulties with classical approaches and suggest reformulations of the problems in a more general framework. We also discuss some new algorithmic approaches.
Numerical methods in acoustics
NASA Astrophysics Data System (ADS)
Candel, S. M.
This paper presents a survey of some computational techniques applicable to acoustic wave problems. Recent advances in wave extrapolation methods, spectral methods and boundary integral methods are discussed and illustrated by specific calculations.
Numerical Methods for Initial Value Problems.
1980-07-01
of general multistep methods for ordinary differential equations a4 to implement an efficient algorithm for the solution of stiff equations . Still...integral equations II. Roundoff error for variants of Gaussian elimination III. Multistep methods for ordinary differential equations IV. Multi-grid...62 -! Paige III. NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS ....... 63 1. Equivalent Forms of Multistep
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.
A numerical method of regenerator
NASA Astrophysics Data System (ADS)
Zhu, Shaowei; Matsubara, Yoichi
2004-02-01
A numerical method for regenerators is introduced in this paper. It is not only suitable for the regenerators in cryocoolers and Stirling engines, but also suitable for the stacks in acoustic engines and the pulse tubes in pulse tube refrigerators. The numerical model is one dimensional periodic unsteady flow model. The numerical method is based on the control volume concept with the implicitly solve method. The iteration acceleration method, which considers the one-dimensional periodic unsteady problem as the steady two-dimensional problem, is used for decreasing the calculation time. By this method, the regenerator in an inertance tube pulse tube refrigerator was simulated. The result is useful for understanding how the inefficiency of the regenerator changes with the inertance effect.
Numerical Methods for Explosion Plume Predictions
1993-03-12
AD-A262 343 6 NAVSWC TR 91-718 A -22~4..v~w•T ,,-., I II It ill/111111 ti(. NUMERICAL METHODS FOR EXPLOSION PLUME PREDICTIONS BY W.G. SZYMCZAK AND A...METHODS FOR EXPLOSION PLUME PREDICTIONS BY W. G. SZYMCZAK AND A. B. WARDLAW RESEARCH AND TECHNOLOGY DEPARTMENT 12 MARCH 1993 Approved for public release...2 TABLES Table Page 3-1 SHALLOW DEPTH EXPLOSION BUBBLE INITIAL DATA
Numerical relativity and spectral methods
NASA Astrophysics Data System (ADS)
Grandclement, P.
2016-12-01
The term numerical relativity denotes the various techniques that aim at solving Einstein's equations using computers. Those computations can be divided into two families: temporal evolutions on the one hand and stationary or periodic solutions on the other one. After a brief presentation of those two classes of problems, I will introduce a numerical tool designed to solve Einstein's equations: the KADATH library. It is based on the the use of spectral methods that can reach high accuracy with moderate computational resources. I will present some applications about quasicircular orbits of black holes and boson star configurations.
Numerical methods for turbulent flow
NASA Technical Reports Server (NTRS)
Turner, James C., Jr.
1988-01-01
It has generally become accepted that the Navier-Strokes equations predict the dynamic behavior of turbulent as well as laminar flows of a fluid at a point in space away form a discontinuity such as a shock wave. Turbulence is also closely related to the phenomena of non-uniqueness of solutions of the Navier-Strokes equations. These second order, nonlinear partial differential equations can be solved analytically for only a few simple flows. Turbulent flow fields are much to complex to lend themselves to these few analytical methods. Numerical methods, therefore, offer the only possibility of achieving a solution of turbulent flow equations. In spite of recent advances in computer technology, the direct solution, by discrete methods, of the Navier-Strokes equations for turbulent flow fields is today, and in the foreseeable future, impossible. Thus the only economically feasible way to solve practical turbulent flow problems numerically is to use statistically averaged equations governing mean-flow quantities. The objective is to study some recent developments relating to the use of numerical methods to study turbulent flow.
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.
Numerical methods in heat transfer
Lewis, R.W.; Morgan, K.; Schrefler, B.A.
1983-01-01
Topics discussed in this book include modelling the effects of fire, ablation, heat flow in porous rock, thermal stress and dissolving coal. Alternative energy sources such as geothermal reservoirs and solar radiation are also discussed. Includes bibliographies at the end of the papers, a cited author index, and a subject index. Contents, abridged: Exact finite element solutions for linear steady state thermal problems. Steep gradient modelling in diffusion problems. Numerical solution of coupled conduction-convection problems using lumped-parameter methods. The prediction of turbulent heat transfer by the finite element methods. The influence of creep and transformation plasticity in the analysis of stresses due to heat treatment. Heat and moisture movement in wood composite materials during the pressing operation-a simplified model. Index.
NASA Technical Reports Server (NTRS)
Davy, W. C.; Green, M. J.; Lombard, C. K.
1981-01-01
The factored-implicit, gas-dynamic algorithm has been adapted to the numerical simulation of equilibrium reactive flows. Changes required in the perfect gas version of the algorithm are developed, and the method of coupling gas-dynamic and chemistry variables is discussed. A flow-field solution that approximates a Jovian entry case was obtained by this method and compared with the same solution obtained by HYVIS, a computer program much used for the study of planetary entry. Comparison of surface pressure distribution and stagnation line shock-layer profiles indicates that the two solutions agree well.
Spectral Methods for Numerical Relativity.
Grandclément, Philippe; Novak, Jérôme
2009-01-01
Equations arising in general relativity are usually too complicated to be solved analytically and one must rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses on a class called spectral methods in which, typically, the various functions are expanded in sets of orthogonal polynomials or functions. First, a theoretical introduction of spectral expansion is given with a particular emphasis on the fast convergence of the spectral approximation. We then present different approaches to solving partial differential equations, first limiting ourselves to the one-dimensional case, with one or more domains. Generalization to more dimensions is then discussed. In particular, the case of time evolutions is carefully studied and the stability of such evolutions investigated. We then present results obtained by various groups in the field of general relativity by means of spectral methods. Work, which does not involve explicit time-evolutions, is discussed, going from rapidly-rotating strange stars to the computation of black-hole-binary initial data. Finally, the evolution of various systems of astrophysical interest are presented, from supernovae core collapse to black-hole-binary mergers.
Numerical methods used in fusion science numerical modeling
NASA Astrophysics Data System (ADS)
Yagi, M.
2015-04-01
The dynamics of burning plasma is very complicated physics, which is dominated by multi-scale and multi-physics phenomena. To understand such phenomena, numerical simulations are indispensable. Fundamentals of numerical methods used in fusion science numerical modeling are briefly discussed in this paper. In addition, the parallelization technique such as open multi processing (OpenMP) and message passing interface (MPI) parallel programing are introduced and the loop-level parallelization is shown as an example.
NASA Astrophysics Data System (ADS)
Encinas, A. H.; Gayoso-Martínez, V.; Martín Del Rey, A.; Martín-Vaquero, J.; Queiruga-Dios, A.
2016-03-01
In this paper, we discuss the problem of solving nonlinear Klein-Gordon equations (KGEs), which are especially useful to model nonlinear phenomena. In order to obtain more exact solutions, we have derived different fourth- and sixth-order, stable explicit and implicit finite difference schemes for some of the best known nonlinear KGEs. These new higher-order methods allow a reduction in the number of nodes, which is necessary to solve multi-dimensional KGEs. Moreover, we describe how higher-order stable algorithms can be constructed in a similar way following the proposed procedures. For the considered equations, the stability and consistency of the proposed schemes are studied under certain smoothness conditions of the solutions. In addition to that, we present experimental results obtained from numerical methods that illustrate the efficiency of the new algorithms, their stability, and their convergence rate.
Numerical simulation of the Beta II experiment
Shumaker, D.E.; Boyd, J.K.; McNamara, B.; Turner, W.C.
1981-10-01
The transport code FRT which is a 1-1/2-D transport-equilibrium code for an axisymmetric plasma was used to simulate the decay of the plasma and magnetic fields of the Beta II experiment. A comparison is made between the experimentally determined decay times for the magnetic fields and particle confinement times and the computed decay times. It is found that 1% oxygen impurity is enough to clamp the electron temperature below the radiation barrier, which is in agreement with the experiment.
Strong Coupling Unquenched QED. II --- Numerical Study ---
NASA Astrophysics Data System (ADS)
Kondo, K.; Nakatani, H.
1992-10-01
Dynamical chiral-symmetry-breaking in massless QED with N fermion species is studied through the numerical solution of the coupled Schwinger-Dyson (SD) equation. We have taken into account the fermion loop effect (at the 1-loop level) in the SD equation for the photon propagator through the vacuum polarization function Π (k2), with and without the standard approximation: Π((p-q)2) ≍ Π(max(p2, q2)). We have found that the scaling law is unchanged by this approximation and that, irrespective of the fermion flavor N, the dynamical fermion mass and chiral order parameter obey the same mean-field type scaling, while the quenched planar QED without the vacuum polarization (N = 0 limit) obeys the Miransky scaling with the essential singularity.
Collisionless microinstabilities in stellarators. II. Numerical simulations
NASA Astrophysics Data System (ADS)
Proll, J. H. E.; Xanthopoulos, P.; Helander, P.
2013-12-01
Microinstabilities exhibit a rich variety of behavior in stellarators due to the many degrees of freedom in the magnetic geometry. It has recently been found that certain stellarators (quasi-isodynamic ones with maximum-J geometry) are partly resilient to trapped-particle instabilities, because fast-bouncing particles tend to extract energy from these modes near marginal stability. In reality, stellarators are never perfectly quasi-isodynamic, and the question thus arises whether they still benefit from enhanced stability. Here, the stability properties of Wendelstein 7-X and a more quasi-isodynamic configuration, QIPC, are investigated numerically and compared with the National Compact Stellarator Experiment and the DIII-D tokamak. In gyrokinetic simulations, performed with the gyrokinetic code GENE in the electrostatic and collisionless approximation, ion-temperature-gradient modes, trapped-electron modes, and mixed-type instabilities are studied. Wendelstein 7-X and QIPC exhibit significantly reduced growth rates for all simulations that include kinetic electrons, and the latter are indeed found to be stabilizing in the energy budget. These results suggest that imperfectly optimized stellarators can retain most of the stabilizing properties predicted for perfect maximum-J configurations.
Collisionless microinstabilities in stellarators. II. Numerical simulations
Proll, J. H. E.; Xanthopoulos, P.; Helander, P.
2013-12-15
Microinstabilities exhibit a rich variety of behavior in stellarators due to the many degrees of freedom in the magnetic geometry. It has recently been found that certain stellarators (quasi-isodynamic ones with maximum-J geometry) are partly resilient to trapped-particle instabilities, because fast-bouncing particles tend to extract energy from these modes near marginal stability. In reality, stellarators are never perfectly quasi-isodynamic, and the question thus arises whether they still benefit from enhanced stability. Here, the stability properties of Wendelstein 7-X and a more quasi-isodynamic configuration, QIPC, are investigated numerically and compared with the National Compact Stellarator Experiment and the DIII-D tokamak. In gyrokinetic simulations, performed with the gyrokinetic code GENE in the electrostatic and collisionless approximation, ion-temperature-gradient modes, trapped-electron modes, and mixed-type instabilities are studied. Wendelstein 7-X and QIPC exhibit significantly reduced growth rates for all simulations that include kinetic electrons, and the latter are indeed found to be stabilizing in the energy budget. These results suggest that imperfectly optimized stellarators can retain most of the stabilizing properties predicted for perfect maximum-J configurations.
Excel spreadsheet in teaching numerical methods
NASA Astrophysics Data System (ADS)
Djamila, Harimi
2017-09-01
One of the important objectives in teaching numerical methods for undergraduates’ students is to bring into the comprehension of numerical methods algorithms. Although, manual calculation is important in understanding the procedure, it is time consuming and prone to error. This is specifically the case when considering the iteration procedure used in many numerical methods. Currently, many commercial programs are useful in teaching numerical methods such as Matlab, Maple, and Mathematica. These are usually not user-friendly by the uninitiated. Excel spreadsheet offers an initial level of programming, which it can be used either in or off campus. The students will not be distracted with writing codes. It must be emphasized that general commercial software is required to be introduced later to more elaborated questions. This article aims to report on a teaching numerical methods strategy for undergraduates engineering programs. It is directed to students, lecturers and researchers in engineering field.
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.
Implicit Numerical Methods in Meteorology
NASA Technical Reports Server (NTRS)
Augenbaum, J.
1984-01-01
The development of a fully implicit finite-difference model, whose time step is chosen solely to resolve accurately the physical flow of interest is discussed. The method is based on an operator factorization which reduces the dimensionality of the implicit approach: at each time step only (spatially) one-dimensional block-tridiagonal linear systems must be solved. The scheme uses two time levels and is second-order accurate in time. Compact implicit spatial differences are used, yielding fourth-order accuracy both vertically and horizontally. In addition, the development of a fully interactive computer code is discussed. With this code the user will have a choice of models, with various levels of accuracy and sophistication, which are imbedded, as subsets of the fully implicit 3D code.
Numerical Methods For Chemically Reacting Flows
NASA Technical Reports Server (NTRS)
Leveque, R. J.; Yee, H. C.
1990-01-01
Issues related to numerical stability, accuracy, and resolution discussed. Technical memorandum presents issues in numerical solution of hyperbolic conservation laws containing "stiff" (relatively large and rapidly changing) source terms. Such equations often used to represent chemically reacting flows. Usually solved by finite-difference numerical methods. Source terms generally necessitate use of small time and/or space steps to obtain sufficient resolution, especially at discontinuities, where incorrect mathematical modeling results in unphysical solutions.
Perception of numerical methods in rarefied gasdynamics
NASA Technical Reports Server (NTRS)
Bird, G. A.
1989-01-01
The relationships between various numerical methods applied to problems in rarefied gasdynamics are discussed, with emphasis on conflicting viewpoints and computational requirements associated with physical simulation versus the numerical solution of the Boltzmann equation. The basic differences between the molecular dynamics and direct simulation methods are shown to affect their applicability to dense and rarefied flows. Methods for the probabilistic selection of representative collision in the direct simulation Monte Carlo method are reviewed. A method combining the most desirable features of the earlier methods is presented.
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.
Numerical Methods for Nonlinear Hillslope Transport Laws
NASA Astrophysics Data System (ADS)
Perron, J. T.
2008-12-01
The numerical methods used to solve nonlinear sediment transport equations often set restrictive limits on the stability and accuracy of landscape evolution models. This is especially true for hillslope transport laws in which sediment flux increases nonlinearly as the surface slope approaches a limiting value. Standard explicit finite difference methods applied to such laws are subject to fundamental limits on numerical stability that require time steps much shorter than the timescales over which landscapes evolve, creating a heavy computational burden. Methods that rely on cell-to-cell sediment routing schemes can introduce significant errors that may not be obvious unless the numerical solution is compared with a known solution. I present a new, implicit method for nonlinear hillslope transport that builds on a previously proposed approach to modeling alluvial sediment transport but avoids the use of a cell-to-cell sediment routing scheme. Comparisons of numerical solutions with analytic solutions in one and two dimensions show that the new method retains the accuracy of the explicit method while allowing timesteps several orders of magnitude longer than the maximum timesteps permitted by the explicit method. The method can be adapted to any transport law in which the expression for sediment flux is differentiable, including coupled systems in which sediment flux is a function of quantities such as soil depth.
Numerical methods for nonlinear hillslope transport laws
NASA Astrophysics Data System (ADS)
Perron, J. Taylor
2011-06-01
The numerical methods used to solve nonlinear sediment transport equations often set very restrictive limits on the stability and accuracy of landscape evolution models. This is especially true for hillslope transport laws in which sediment flux increases nonlinearly as the surface slope approaches a limiting value. Explicit-time finite difference methods applied to such laws are subject to fundamental limits on numerical stability that require time steps much shorter than the timescales over which landscapes evolve, creating a heavy computational burden. I present an implicit method for nonlinear hillslope transport that builds on a previously proposed approach to modeling alluvial sediment transport and improves stability and accuracy by avoiding the direct calculation of sediment flux. This method can be adapted to any transport law in which the expression for sediment flux is differentiable. Comparisons of numerical solutions with analytic solutions in one and two dimensions show that the implicit method retains the accuracy of a standard explicit method while permitting time steps several orders of magnitude longer than the maximum stable time step for the explicit method. The ability to take long time steps affords a substantial savings in overall computation time, despite the implicit method's higher per-iteration computational cost. Implicit models for hillslope evolution also offer a distinct advantage when modeling the response of hillslopes to incising channels.
Numerical comparison between DHF and RHF methods
NASA Astrophysics Data System (ADS)
Kobus, J.; Jaskolski, W.
1987-10-01
A detailed numerical comparison of the Dirac-Hartree-Fock method and the relativistic Hartree-Fock (RHF) method of Cowan and Griffith (1976) is presented, considering the total energy, the orbital energies, and the one-electron and two-electron integrals. The RHF method is found to yield accurate values of the relativistic transition energies. Using accurate values of the correlation corrections for p-electron and d-electron systems, the usefulness of the RHF method in obtaining relativistic corrections to the differential term energies is demonstrated. Advantages of the method for positron scattering on heavy systems are also pointed out.
Numerical Methods through Open-Ended Projects
ERIC Educational Resources Information Center
Cline, Kelly S.
2005-01-01
We present a design for a junior level numerical methods course that focuses on a series of five open-ended projects in applied mathematics. These projects were deliberately designed to present many of the ambiguities and complexities that appear any time we use mathematics in the real world, and so they offered the students a variety of possible…
Incompatible numerical manifold method for fracture problems
NASA Astrophysics Data System (ADS)
Wei, Gaofeng; Li, Kaitai; Jiang, Haihui
2010-05-01
The incompatible numerical manifold method (INMM) is based on the finite cover approximation theory, which provides a unified framework for problems dealing with continuum and discontinuities. The incompatible numerical manifold method employs two cover systems as follows. The mathematical cover system provides the nodes for forming finite covers of the solution domain and the weighted functions, and the physical cover system describes geometry of the domain and the discontinuous surfaces therein. In INMM, the mathematical finite cover approximation theory is used to model cracks that lead to interior discontinuities in the process of displacement. Therefore, the discontinuity is treated mathematically instead of empirically by the existing methods. However, one cover of a node is divided into two irregular sub-covers when the INMM is used to model the discontinuity. As a result, the method sometimes causes numerical errors at the tip of a crack. To improve the precision of the INMM, the analytical solution is used at the tip of a crack, and thus the cover displacement functions are extended with higher precision and computational efficiency. Some numerical examples are given.
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.
A numerical method for predicting hypersonic flowfields
NASA Technical Reports Server (NTRS)
Maccormack, Robert W.; Candler, Graham V.
1989-01-01
The flow about a body traveling at hypersonic speed is energetic enough to cause the atmospheric gases to chemically react and reach states in thermal nonequilibrium. The prediction of hypersonic flowfields requires a numerical method capable of solving the conservation equations of fluid flow, the chemical rate equations for specie formation and dissociation, and the transfer of energy relations between translational and vibrational temperature states. Because the number of equations to be solved is large, the numerical method should also be as efficient as possible. The proposed paper presents a fully implicit method that fully couples the solution of the fluid flow equations with the gas physics and chemistry relations. The method flux splits the inviscid flow terms, central differences of the viscous terms, preserves element conservation in the strong chemistry source terms, and solves the resulting block matrix equation by Gauss Seidel line relaxation.
A numerical method for predicting hypersonic flowfields
NASA Technical Reports Server (NTRS)
Maccormack, Robert W.; Candler, Graham V.
1989-01-01
The flow about a body traveling at hypersonic speed is energetic enough to cause the atmospheric gases to chemically react and reach states in thermal nonequilibrium. The prediction of hypersonic flowfields requires a numerical method capable of solving the conservation equations of fluid flow, the chemical rate equations for specie formation and dissociation, and the transfer of energy relations between translational and vibrational temperature states. Because the number of equations to be solved is large, the numerical method should also be as efficient as possible. The proposed paper presents a fully implicit method that fully couples the solution of the fluid flow equations with the gas physics and chemistry relations. The method flux splits the inviscid flow terms, central differences of the viscous terms, preserves element conservation in the strong chemistry source terms, and solves the resulting block matrix equation by Gauss Seidel line relaxation.
A hybrid numerical method for orbit correction
White, G.; Himel, T.; Shoaee, H.
1997-09-01
The authors describe a simple hybrid numerical method for beam orbit correction in particle accelerators. The method overcomes both degeneracy in the linear system being solved and respects boundaries on the solution. It uses the Singular Value Decomposition (SVD) to find and remove the null-space in the system, followed by a bounded Linear Least Squares analysis of the remaining recast problem. It was developed for correcting orbit and dispersion in the B-factory rings.
Numerical Simulations of the PEP-II Longitudinal Feedback Kicker.
NASA Astrophysics Data System (ADS)
Li, Zenghai; Lin, Xintian; Ng, Cho-Kuen; Ko, Kwok; Corlett, John; Byrd, John
1997-05-01
The feedback system in PEP-II will employ a drift-tube type kicker to supplement cavity damping in suppressing longitudinal coupled-bunch instabilities. In addition to prototyping, numerical modeling has been used to verify the kicker performance and to study related design issues such as beam impedance and parasitic heating. The simulations have been carried out in the time domain using a realistic MAFIA model that includes the coaxial feedthroughs and the delay lines between the electrodes. The calculated shunt impedance and beam impedance are in good agreement with measurements performed on a prototype.
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.
A numerical method to model excitable cells.
Joyner, R W; Westerfield, M; Moore, J W; Stockbridge, N
1978-01-01
We have extended a fast, stable, and accurate method for the numerical solution of cable equations to include changes in geometry and membrane properties in order to model a single excitable cell realistically. In addition, by including the provision that the radius may be a function of distance along an axis, we have achieved a general and powerful method for simulating a cell with any number of branched processes, any or all of which may be nonuniform in diameter, and with no restriction on the branching pattern. PMID:656539
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.
High accuracy mantle convection simulation through modern numerical methods
NASA Astrophysics Data System (ADS)
Kronbichler, Martin; Heister, Timo; Bangerth, Wolfgang
2012-10-01
Numerical simulation of the processes in the Earth's mantle is a key piece in understanding its dynamics, composition, history and interaction with the lithosphere and the Earth's core. However, doing so presents many practical difficulties related to the numerical methods that can accurately represent these processes at relevant scales. This paper presents an overview of the state of the art in algorithms for high-Rayleigh number flows such as those in the Earth's mantle, and discusses their implementation in the Open Source code ASPECT (Advanced Solver for Problems in Earth's ConvecTion). Specifically, we show how an interconnected set of methods for adaptive mesh refinement (AMR), higher order spatial and temporal discretizations, advection stabilization and efficient linear solvers can provide high accuracy at a numerical cost unachievable with traditional methods, and how these methods can be designed in a way so that they scale to large numbers of processors on compute clusters. ASPECT relies on the numerical software packages DEAL.II and TRILINOS, enabling us to focus on high level code and keeping our implementation compact. We present results from validation tests using widely used benchmarks for our code, as well as scaling results from parallel runs.
Efficient numerical methods for nonlinear Schrodinger equations
NASA Astrophysics Data System (ADS)
Liang, Xiao
The nonlinear Schrodinger equations are widely used to model a number of important physical phenomena, including solitary wave propagations in optical fibers, deep water turbulence, laser beam transmissions, and the Bose-Einstein condensation, just to mention a few. In the field of optics and photonics, the systems of nonlinear Schrodinger equations can be used to model multi-component solitons and the interaction of self-focusing laser beams. In three spatial dimensions, the nonlinear Schrodinger equation is known as the Gross-Pitaevskii equation, which models the soliton in a low-cost graded-index fiber. Recently, research on nonlinear space fractional Schrodinger equations, which capture the self-similarity in the fractional environment, has become prevalent. Our study includes the systems of multi-dimensional nonlinear space fractional Schrodinger equations. To solve the systems of multi-dimensional nonlinear Schrodinger equations efficiently, several novel numerical methods are presented. The central difference and quartic spline approximation based exponential time differencing Crank-Nicolson method is introduced for solving systems of one- and two-dimensional nonlinear Schrodinger equations. A local extrapolation is employed to achieve fourth-order accuracy in time. The numerical examples include the transmission of a self-focusing laser beam. The local discontinuous Galerkin methods combined with the fourth-order exponential time differencing Runge-Kutta time discretization are studied for solving the systems of nonlinear Schrodinger equations with hyperbolic terms, which are critical in modeling optical solitons in the birefringent fibers. The local discontinuous Galerkin method is able to achieve any order of accuracy in space, thanks to the usage of piecewise polynomial spaces. The exponential time differencing methods are employed to deal with the coupled nonlinearities for the reason that there is no need to solve nonlinear systems at every time step
Linearized Implicit Numerical Method for Burgers' Equation
NASA Astrophysics Data System (ADS)
Mukundan, Vijitha; Awasthi, Ashish
2016-12-01
In this work, a novel numerical scheme based on method of lines (MOL) is proposed to solve the nonlinear time dependent Burgers' equation. The Burgers' equation is semi discretized in spatial direction by using MOL to yield system of nonlinear ordinary differential equations in time. The resulting system of nonlinear differential equations is integrated by an implicit finite difference method. We have not used Cole-Hopf transformation which gives less accurate solution for very small values of kinematic viscosity. Also, we have not considered nonlinear solvers that are computationally costlier and take more running time.In the proposed scheme nonlinearity is tackled by Taylor series and the use of fully discretized scheme is easy and practical. The proposed method is unconditionally stable in the linear sense. Furthermore, efficiency of the proposed scheme is demonstrated using three test problems.
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 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 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.
Application of numerical methods to elasticity imaging.
Castaneda, Benjamin; Ormachea, Juvenal; Rodríguez, Paul; Parker, Kevin J
2013-03-01
Elasticity imaging can be understood as the intersection of the study of biomechanical properties, imaging sciences, and physics. It was mainly motivated by the fact that pathological tissue presents an increased stiffness when compared to surrounding normal tissue. In the last two decades, research on elasticity imaging has been an international and interdisciplinary pursuit aiming to map the viscoelastic properties of tissue in order to provide clinically useful information. As a result, several modalities of elasticity imaging, mostly based on ultrasound but also on magnetic resonance imaging and optical coherence tomography, have been proposed and applied to a number of clinical applications: cancer diagnosis (prostate, breast, liver), hepatic cirrhosis, renal disease, thyroiditis, arterial plaque evaluation, wall stiffness in arteries, evaluation of thrombosis in veins, and many others. In this context, numerical methods are applied to solve forward and inverse problems implicit in the algorithms in order to estimate viscoelastic linear and nonlinear parameters, especially for quantitative elasticity imaging modalities. In this work, an introduction to elasticity imaging modalities is presented. The working principle of qualitative modalities (sonoelasticity, strain elastography, acoustic radiation force impulse) and quantitative modalities (Crawling Waves Sonoelastography, Spatially Modulated Ultrasound Radiation Force (SMURF), Supersonic Imaging) will be explained. Subsequently, the areas in which numerical methods can be applied to elasticity imaging are highlighted and discussed. Finally, we present a detailed example of applying total variation and AM-FM techniques to the estimation of elasticity.
Mathematica with a Numerical Methods Course
NASA Astrophysics Data System (ADS)
Varley, Rodney
2003-04-01
An interdisciplinary "Numerical Methods" course has been shared between physics, mathematics and computer science since 1992 at Hunter C. Recently, the lectures and workshops for this course have become formalized and placed on the internet at http://www.ph.hunter.cuny.edu (follow the links "Course Listings and Websites" >> "PHYS385 (Numerical Methods)". Mathematica notebooks for the lectures are available for automatic download (by "double clicking" the lecture icon) for student use in the classroom or at home. AOL (or Netscape/Explorer) can be used provided Mathematica (or the "free" MathReader) has been made a "helper application". Using Mathematica has the virtue that mathematical equations (no LaTex required) can easily be included with the text and Mathematica's graphing is easy to use. Computational cells can be included within the notebook and students may easily modify the calculation to see the result of "what if..." questions. Homework is sent as Mathematica notebooks to the instructor via the internet and the corrected workshops are returned in the same manner. Most exam questions require computational solutions.
Homogenization and Numerical Methods for Hyperbolic Equations
NASA Astrophysics Data System (ADS)
Liu, Jian-Guo
1990-01-01
This dissertation studies three aspects of analysis and numerical methods for partial differential equations with oscillatory solutions. 1. Homogenization theory for certain linear hyperbolic equations is developed. We derive the homogenized convection equations for linear convection problems with rapidly varying velocity in space and time. We find that the oscillatory solutions are very sensitive to the arithmetic properties of certain parameters, such as the corresponding rotation number and the ratio between the components of the mean velocity field in linear convection. We also show that the oscillatory velocity field in two dimensional incompressible flow behaves like shear flows. 2. The homogenization of scalar nonlinear conservation laws in several space variables with oscillatory initial data is also discussed. We prove that the initial oscillations will be eliminated for any positive time when the equations are non-degenerate. This is also true for degenerate equations if there is enough mixing among the initial oscillations in the degenerate direction. Otherwise, the initial oscillation, for which the homogenized equation is obtained, will survive and be propagated. The large-time behavior of conservation laws with several space variables is studied. We show that, under a new nondegenerate condition (the second derivatives of the flux functions are linearly independent in any interval), a piecewise smooth periodic solution with converge strongly to the mean value of initial data. This generalizes Glimm and Lax's result for the one dimensional problem (3). 3. Numerical simulations of the oscillatory solutions are also carried out. We give some error estimate for varepsilon-h resonance ( varepsilon: oscillation wave length, h: numerical step) and prove essential convergence (24) of order alpha < 1 for some numerical schemes. These include upwind schemes and particle methods for linear hyperbolic equations with oscillatory coefficients. A stochastic analysis
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 Investigation of Thermal Counterflow of He II Past Cylinders
NASA Astrophysics Data System (ADS)
Soulaine, Cyprien; Quintard, Michel; Baudouy, Bertrand; Van Weelderen, Rob
2017-02-01
We investigate numerically, for the first time, the thermal counterflow of superfluid helium past a cylinder by solving with a finite volume method the complete so-called two-fluid model. In agreement with existing experimental results, we obtain symmetrical eddies both up- and downstream of the obstacle. The generation of these eddies is a complex transient phenomenon that involves the friction of the normal fluid component with the solid walls and the mutual friction between the superfluid and normal components. Implications for flow in a more realistic porous medium are also investigated.
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
Numerical methods to analyze electromagnetic scattering are presented. The dispersions and attenuations of the normal modes in a circular waveguide coated with lossy material were completely analyzed. The radar cross section (RCS) from a circular waveguide coated with lossy material was calculated. The following is observed: (1) the interior irradiation contributes to the RCS much more than does the rim diffraction; (2) at low frequency, the RCS from the circular waveguide terminated by a perfect electric conductor (PEC) can be reduced more than 13 dB down with a coating thickness less than 1% of the radius using the best lossy material available in a 6 radius-long cylinder; (3) at high frequency, a modal separation between the highly attenuated and the lowly attenuated modes is evident if the coating material is too lossy, however, a large RCS reduction can be achieved for a small incident angle with a thin layer of coating. It is found that the waveguide coated with a lossy magnetic material can be used as a substitute for a corrugated waveguide to produce a circularly polarized radiation yield.
Modeling extracellular electrical stimulation: II. Computational validation and numerical results.
Tahayori, Bahman; Meffin, Hamish; Dokos, Socrates; Burkitt, Anthony N; Grayden, David B
2012-12-01
The validity of approximate equations describing the membrane potential under extracellular electrical stimulation (Meffin et al 2012 J. Neural Eng. 9 065005) is investigated through finite element analysis in this paper. To this end, the finite element method is used to simulate a cylindrical neurite under extracellular stimulation. Laplace's equations with appropriate boundary conditions are solved numerically in three dimensions and the results are compared to the approximate analytic solutions. Simulation results are in agreement with the approximate analytic expressions for longitudinal and transverse modes of stimulation. The range of validity of the equations describing the membrane potential for different values of stimulation and neurite parameters are presented as well. The results indicate that the analytic approach can be used to model extracellular electrical stimulation for realistic physiological parameters with a high level of accuracy.
On a Method of Numerical Differentiation
2000-01-01
the results stated in [4], we have proved Proposition 1. If assumptions i) and ii) of Section 2 hold, we have IJ(n)(x, y) - f(x, y)I = O( 2-j(Fi...be chosen so that 2 -j(5)a is less or of the same order of hm. Proposition 2. If assumptions i), ii) of Section 2 hold, the approximation (6) of the...237. Mira Bozzini Dipartimento di Matematica e Applicazioni Universith di Milano Bicocca via Bicocca degli Arcimboldi 8 20126, Milano Italy
Numerical investigation of blood flow. Part II: In capillaries
NASA Astrophysics Data System (ADS)
Jafari, A.; Zamankhan, P.; Mousavi, S. M.; Kolari, P.
2009-04-01
In order to understand the normal and pathologic behavior of the human vascular system, detailed knowledge of blood flow and the response of blood vessels is required. In fact the ability to predict the flow hydrodynamics at any site in the vessels can lead to a better understanding of the behavior of blood flow. Simulation can play an important role in understanding the hemodynamic forces. The objective of the present attempt was to simulate the behavior of blood flow in microvessels using computational fluid dynamics (CFD). Numerical analysis is performed using a commercially available CFD package Fluent 6.2 which is based on the finite volume method. A continuum approach is proposed in which fluid structure interaction has been taken into account. Based on limitations imposed by computational resources, a more simplified model based on volume of fluid (VOF) approach is suggested to simulate movements of RBCs in capillaries and also to predict RBCs' deformation. Three-dimensional incompressible laminar flow fields are obtained by solving continuity and Navier-Stokes equations computationally. It was found that multiphase CFD simulations may give further insight into the dynamic characteristics of blood flow under complex flow conditions.
Zou, Ling; Zhao, Haihua; Kim, Seung Jun
2016-11-16
In this study, the classical Welander’s oscillatory natural circulation problem is investigated using high-order numerical methods. As originally studied by Welander, the fluid motion in a differentially heated fluid loop can exhibit stable, weakly instable, and strongly instable modes. A theoretical stability map has also been originally derived from the stability analysis. Numerical results obtained in this paper show very good agreement with Welander’s theoretical derivations. For stable cases, numerical results from both the high-order and low-order numerical methods agree well with the non-dimensional flow rate analytically derived. The high-order numerical methods give much less numerical errors compared to themore » low-order methods. For stability analysis, the high-order numerical methods could perfectly predict the stability map, while the low-order numerical methods failed to do so. For all theoretically unstable cases, the low-order methods predicted them to be stable. The result obtained in this paper is a strong evidence to show the benefits of using high-order numerical methods over the low-order ones, when they are applied to simulate natural circulation phenomenon that has already gain increasing interests in many future nuclear reactor designs.« less
Zou, Ling; Zhao, Haihua; Kim, Seung Jun
2016-11-16
In this study, the classical Welander’s oscillatory natural circulation problem is investigated using high-order numerical methods. As originally studied by Welander, the fluid motion in a differentially heated fluid loop can exhibit stable, weakly instable, and strongly instable modes. A theoretical stability map has also been originally derived from the stability analysis. Numerical results obtained in this paper show very good agreement with Welander’s theoretical derivations. For stable cases, numerical results from both the high-order and low-order numerical methods agree well with the non-dimensional flow rate analytically derived. The high-order numerical methods give much less numerical errors compared to the low-order methods. For stability analysis, the high-order numerical methods could perfectly predict the stability map, while the low-order numerical methods failed to do so. For all theoretically unstable cases, the low-order methods predicted them to be stable. The result obtained in this paper is a strong evidence to show the benefits of using high-order numerical methods over the low-order ones, when they are applied to simulate natural circulation phenomenon that has already gain increasing interests in many future nuclear reactor designs.
Numerical analysis of cutting glass by dual CO II-laser beams
NASA Astrophysics Data System (ADS)
Jiao, Junke; Wang, Xinbing; Zhang, Xueling; Tang, Wenlong; Liu, Fujun; Lu, Yanzhao
2008-03-01
Cutting brittle materials such as ceramics and glass by lasers or traditional saw method, costly fractures and associated damage such as chips and cracks can result. In most cases, these problems were caused as a result of the stress was not controlled properly and exceeded the critical value of the fracture. In this study, a dual-laser-beam method was proposed to avoid fractures in glass laser cutting, where an off-focused CO II-laser beam was scanning on the top surface of glass periodically and repeatedly and a preheated-band which has a proper temperature was built. This preheated-band will reduce the temperature gradients when the glass is cut by the focused CO II-laser beam. Under these conditions, glass can be cut with melting method without any fractures. The process of cutting glass by dual CO II-laser beams was simulated numerically with FEA method and the distribution of temperature and thermal stress was investigated. The relationships between the cutting parameters, such as laser beam diameter, laser power, cutting speed, and the profile of the cutting groove were also discussed. The result showed that thermal stress decreased with the increasing width of preheated-banding, and the smaller the diameter of laser beam, the better the quality of the cutting groove was in the same laser power situation.
Numerical Methods for Partial Differential Equations.
1984-01-09
114). The pursuit of a linear-time solution led Brent and Luk to consider Jacobi methods . They have found an implementation using an n/2 xn/2 array...cyclic Jacobi method . It takes 0(n) time to perform a sweep of the method, and 0(log n) sweeps for the method to converge 1 1. Brent and Luk have...Hestenes algorithm that, in real arithmetic, is an exact analogue of their Jacobi method applied to the eigenproblem for ATA. The array requires 0(rnn
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.
Nonlinear dynamics of turbulence driven magnetic islands. II. Numerical simulations
NASA Astrophysics Data System (ADS)
Agullo, O.; Muraglia, M.; Benkadda, S.; Poyé, A.; Dubuit, N.; Garbet, X.; Sen, A.
2017-04-01
The nonlinear dynamics of a turbulence driven magnetic island (TDMI) is investigated numerically in a reduced magnetohydrodynamic fluid model. The significance of identifying a characteristic signature of a TDMI for its experimental observation is discussed. The principal focus of our simulations is on the nature of the pressure profile flattening inside a TDMI, and we show that, in agreement with analytical predictions, a partial flattening occurs when the island size exceeds a critical value that is a function of the small scale interchange dynamics. We also present a model and test it numerically, which links explicitly the interchange turbulence and the island pressure flattening.
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.
Numerical methods for reduction of topside ionograms
NASA Technical Reports Server (NTRS)
Mcculley, L.
1972-01-01
Several alternative methods for solving the group height equation are presented. Three of these are now in operation at Ames Research Center and use data contained in a single ionogram trace. From the data an electron density profile N(h) is computed. If the ionogram also exhibits other traces, reverse ionogram traces are computed, using the N(h) profile, for comparison with the redundant data. When agreement is poor, the initial data trace is reinterpreted, another N(h) profile computed, and the reverse traces generated once again. This process is repeated until a desired degree of consistency is achieved. To reduce the necessity for human intervention and eliminate decision making required in conjunction with the preceding methods, a method is proposed that accepts as input, all data from a single ionogram. In general, no electron density function will satisfy these data exactly, but a best N(h) profile can be computed. Finally, a method is described that eliminates the need to assume that the ionosphere is spherically stratified. Horizontal gradients in electron density are detected and accounted for by processing several ionograms from the same satellite pass simultaneously. This idea is derived as an extension of one of the basic methods.
Fibre reinforced composite dental bridge. Part II: Numerical investigation.
Li, W; Swain, M V; Li, Q; Ironside, J; Steven, G P
2004-09-01
Motivated by the clinical success and limitations on experimental investigation of the fibre-reinforced composite dental bridge, this paper aims at providing a numerical investigation into the bridge structure. The finite element (FE) model adopted here is constructed from computer tomography images of a physical bridge specimen. The stress and strain distributions in the bridge structure especially in the bonding interfaces are analyzed in detail. The peak stresses and their variations with the different bridge designs are evaluated. Due to the lower bond strengths of adhesives and the high stress concentration in the pontic-abutment interface, the likelihood of failure in the interface is predicted by finite element analysis. The validity of the numerical results is established by a good agreement between the FE prediction and the tests in the load-deflection responses, the structural stiffness as well as the failure location of the composite dental bridge.
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 Methods Using B-Splines
NASA Technical Reports Server (NTRS)
Shariff, Karim; Merriam, Marshal (Technical Monitor)
1997-01-01
The seminar will discuss (1) The current range of applications for which B-spline schemes may be appropriate (2) The property of high-resolution and the relationship between B-spline and compact schemes (3) Comparison between finite-element, Hermite finite element and B-spline schemes (4) Mesh embedding using B-splines (5) A method for the incompressible Navier-Stokes equations in curvilinear coordinates using divergence-free expansions.
Modelling asteroid brightness variations. I - Numerical methods
NASA Technical Reports Server (NTRS)
Karttunen, H.
1989-01-01
A method for generating lightcurves of asteroid models is presented. The effects of the shape of the asteroid and the scattering law of a surface element are distinctly separable, being described by chosen functions that can easily be changed. The shape is specified by means of two functions that yield the length of the radius vector and the normal vector of the surface at a given point. The general shape must be convex, but spherical concavities producing macroscopic shadowing can also be modeled.
Efficient Numerical Methods for Stable Distributions
2007-11-02
0 and cutoffs c1 = −128 and c2 = +127 are used, corresponding to the common values used in digital signal processing. Five new functions for discrete...variables using the Chambers- Mallows - Stuck method, rounding them to the nearest integer, and then cutting off if the value is too high or too low...within the common matlab environment they use. We comment briefly on the commercialization of this in the last section. 3 -100 -50 0 50 100 0. 0 0. 01 0
A numerical method for predicting hypersonic flowfields
NASA Technical Reports Server (NTRS)
Maccormack, Robert W.; Candler, Graham V.
1988-01-01
The flow about a body traveling at hypersonic speed is energetic enough to cause the atmospheric gases to react chemically and reach states in thermal nonequilibrium. In this paper, a new procedure based on Gauss-Seidel line relaxation is shown to solve the equations of hypersonic flow fields containing finite reaction rate chemistry and thermal nonequilibrium. The method requires a few hundred time steps and small computer times for axisymmetric flows about simple body shapes. The extension to more complex two-dimensional body geometries appears straightforward.
A numerical method for predicting hypersonic flowfields
NASA Technical Reports Server (NTRS)
Maccormack, Robert W.; Candler, Graham V.
1988-01-01
The flow about a body traveling at hypersonic speed is energetic enough to cause the atmospheric gases to react chemically and reach states in thermal nonequilibrium. In this paper, a new procedure based on Gauss-Seidel line relaxation is shown to solve the equations of hypersonic flow fields containing finite reaction rate chemistry and thermal nonequilibrium. The method requires a few hundred time steps and small computer times for axisymmetric flows about simple body shapes. The extension to more complex two-dimensional body geometries appears straightforward.
Numerical methods for hypersonic boundary layer stability
NASA Technical Reports Server (NTRS)
Malik, M. R.
1990-01-01
Four different schemes for solving compressible boundary layer stability equations are developed and compared, considering both the temporal and spatial stability for a global eigenvalue spectrum and a local eigenvalue search. The discretizations considered encompass: (1) a second-order-staggered finite-difference scheme; (2) a fourth-order accurate, two-point compact scheme; (3) a single-domain Chebychev spectral collocation scheme; and (4) a multidomain spectral collocation scheme. As Mach number increases, the performance of the single-domain collocation scheme deteriorates due to the outward movement of the critical layer; a multidomain spectral method is accordingly designed to furnish superior resolution of the critical layer.
Numerical simulation of the PEP-II beam position monitor
Kurita, N.; Martin, D.; Ng, C.K.; Smith, S.; Weiland, T.
1995-09-01
The authors use MAFIA to analyze the PEP-II button-type beam position monitor (BPM). Employing proper termination of the BPM into a coaxial cable, the output signal at the BPM is determined. Thus the issues of signal sensitivity and power output can be addressed quantitatively, including all transient effects and wakefields. Besides this first quantitative analysis of a true BPM 3D structure, they find that internal resonant modes are a major-source of high value narrow-band impedances. The effects of these resonances on coupled-bunch instabilities are discussed. An estimate of the power dissipation in the ceramic vacuum seal under high current operation is given.
An efficient numerical method for orbit computations
NASA Astrophysics Data System (ADS)
Palacios, M.; Abad, A.; Elipe, A.
1992-08-01
A nonstandard formulation of perturbed Keplerian motion is set forth based on the analysis by Deprit (1975) and incorporating quaternions to integrate the equations of motion. The properties of quaternions are discussed and applied to the portion of the equations of motion describing the rotations between the space frame and the departure frame. Angular momentum is assumed to be constant, and a redundant set of variables is introduced to test the equations of motion for different step sizes. The method is analyzed for the cases of artificial satellites in Keplerian circular orbits, Keplerian elliptical orbits, and zonal harmonics. The present formulation is shown to adequately represent the dynamical behavior while avoiding small inclinations. The rotations described by quaternions require less arithmetic operations and therefore save computation time, and the accuracy of the solutions are improved by at least two significant digits.
Instabilities in astrophysical jets. II - Numerical simulations of slab jets
NASA Technical Reports Server (NTRS)
Zhao, Jun-Hui; Burns, Jack O.; Norman, Michael L.; Sulkanen, Martin E.
1992-01-01
Numerical simulations of an unstable supersonic slab-symmetric jet are described. The instabilities within the jet are characterized by growing internal body waves and their coupled surface waves that are also predicted in linear perturbation theory. The characteristic theory of fluid dynamics is used to help interpret the wave morphologies. It is demonstrated that these waves can be excited by imposing an arbitrary disturbance. From the numerical simulations, it is found that the sound waves propagating against the flow slow down as they propagate outward, and they grow in amplitude. These waves eventually disrupt the jet at a certain length. This disruption length is related to the jet Mach number and the perturbation intensity. Thus, the Mach number of a jet observed with a radio telescope can be estimated by measuring the disruption length and estimating the perturbation intensity. The jet Mach numbers in radio tailed sources determined in this way agree quite well with estimates from ram pressure bending arguments. The wiggles and flares observed in many extragalactic jets, especially in tailed radio sources, appear to be intimately related to instabilities and the jet disruption process.
A Numerical Treatment of the Rf SQUID: II. Noise Temperature
Kleiner, Reinhold; Koelle, Dieter; Clarke, John
2007-01-15
We investigate rf SQUIDs (Superconducting QUantum Interference Devices), coupled to a resonant input circuit, a readout tank circuit and a preamplifier, by numerically solving the corresponding Langevin equations and optimizing model parameters with respect to noise temperature. We also give approximate analytic solutions for the noise temperature, which we reduce to parameters of the SQUID and the tank circuit in the absence of the input circuit. The analytic solutions agree with numerical simulations of the full circuit to within 10%, and are similar to expressions used to calculate the noise temperature of dc SQUIDs. The best device performance is obtained when {beta}{sub L}{prime} {triple_bond} 2{pi}LI{sub 0}/{Phi}{sub 0} is 0.6-0.8; L is the SQUID inductance, I{sub 0} the junction critical current and F{sub 0} the flux quantum. For a tuned input circuit we find an optimal noise temperature T{sub N,opt} {approx} 3Tf/f{sub c}, where T, f and f{sub c} denote temperature, signal frequency and junction characteristic frequency, respectively. This value is only a factor of 2 larger than the optimal noise temperatures obtained by approximate analytic theories carried out previously in the limit {beta}{sub L}{prime} << 1. We study the dependence of the noise temperature on various model parameters, and give examples using realistic device parameters of the extent to which the intrinsic noise temperature can be realized experimentally.
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.
Comparisons of numerical methods with respect to convectively dominated problems
NASA Astrophysics Data System (ADS)
Wang, Yongqi; Hutter, Kolumban
2001-11-01
A series of numerical schemes: first-order upstream, Lax-Friedrichs; second-order upstream, central difference, Lax-Wendroff, Beam-Warming, Fromm; third-order QUICK, QUICKEST and high resolution flux-corrected transport and total variation diminishing (TVD) methods are compared for one-dimensional convection-diffusion problems. Numerical results show that the modified TVD Lax-Friedrichs method is the most competent method for convectively dominated problems with a steep spatial gradient of the variables. Copyright
Scalar gravitation: A laboratory for numerical relativity. II. Disks
Shapiro, S.L.; Teukolsky, S.A. )
1994-02-15
While not a correct physical theory, relativistic scalar gravitation provides a simple test site for developing many of the tools of numerical relativity. Using this theory, we have built a mean-field particle simulation scheme to study the dynamical behavior of collisionless disks. Disks are one-dimensional matter sources of two-dimensional gravitational fields. One-dimensional disk sources can be evolved without excessive computational resources and yet they are able to generate nonspherical gravitational waves. We find that we are able to calculate smooth and accurate wave forms from time-varying disks, despite the stochastic representation of the matter source terms caused by sampling with a finite number of particles. A similar scheme should provide accurate wave forms in general relativity, provided sufficient computer resources are used.
A numerical method for vortex sheet roll-up
NASA Technical Reports Server (NTRS)
Krasny, R.
1986-01-01
The problem of computing vortex sheet roll-up from periodic analytic initial data is studied. Previous theoretical and numerical work is reviewed. Computational difficulties arising from ill posedness and singularity formation are discussed. A desingularization method is proposed to diminish these difficulties. Computations indicate that this approach converges past the time at which previous numerical investigations have failed to converge.
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).
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.
Review of Methods and Approaches for Deriving Numeric ...
EPA will propose numeric criteria for nitrogen/phosphorus pollution to protect estuaries, coastal areas and South Florida inland flowing waters that have been designated Class I, II and III , as well as downstream protective values (DPVs) to protect estuarine and marine waters. In accordance with the formal determination and pursuant to a subsequent consent decree, these numeric criteria are being developed to translate and implement Florida’s existing narrative nutrient criterion, to protect the designated use that Florida has previously set for these waters, at Rule 62-302.530(47)(b), F.A.C. which provides that “In no case shall nutrient concentrations of a body of water be altered so as to cause an imbalance in natural populations of aquatic flora or fauna.” Under the Clean Water Act and EPA’s implementing regulations, these numeric criteria must be based on sound scientific rationale and reflect the best available scientific knowledge. EPA has previously published a series of peer reviewed technical guidance documents to develop numeric criteria to address nitrogen/phosphorus pollution in different water body types. EPA recognizes that available and reliable data sources for use in numeric criteria development vary across estuarine and coastal waters in Florida and flowing waters in South Florida. In addition, scientifically defensible approaches for numeric criteria development have different requirements that must be taken into consider
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.
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.
Some Comments on Numerical Methods for Chaos Problems
NASA Astrophysics Data System (ADS)
Miller, R. H.
1996-03-01
Hamiltonian systems with chaotic regions are particularly slippery to treat numerically. Numerical treatments can introduce nonphysical features. Simple examples illustrate some of the pitfalls. Integer, or discrete, arithmetic is a favorite “workaround.” While it does not cure chaos, it clarifies the interaction of computational methods with the underlying mathematical structure. Be forewarned: I won't give any prescription that is guaranteed to give a good and reliable method to handle chaotic problems numerically. Instead, I'll stress a few of the concerns and describe one or two pitfalls.
A numerical method for phase-change problems
NASA Technical Reports Server (NTRS)
Kim, Charn-Jung; Kaviany, Massoud
1990-01-01
A highly accurate and efficient finite-difference method for phase-change problems with multiple moving boundaries of irregular shape is developed by employing a coordinate transformation that immobilizes moving boundaries and preserves the conservative forms of the original governing equations. The numerical method is first presented for one-dimensional phase-change problems (involving large density variation between phases, heat generation, and multiple moving boundaries) and then extended to solve two-dimensional problems (without change of densities between phases). Numerical solutions are obtained non-iteratively using an explicit treatment of the interfacial mass and energy balances and an implicit treatment of the temperature field equations. The accuracy and flexibility of the present numerical method are verified by solving some phase-change problems and comparing the results with existing analytical, semi-analytical and numerical solutions. Results indicate that one- and two-dimensional phase-change problems can be handled easily with excellent accuracies.
A numerical method for phase-change problems
NASA Technical Reports Server (NTRS)
Kim, Charn-Jung; Kaviany, Massoud
1990-01-01
A highly accurate and efficient finite-difference method for phase-change problems with multiple moving boundaries of irregular shape is developed by employing a coordinate transformation that immobilizes moving boundaries and preserves the conservative forms of the original governing equations. The numerical method is first presented for one-dimensional phase-change problems (involving large density variation between phases, heat generation, and multiple moving boundaries) and then extended to solve two-dimensional problems (without change of densities between phases). Numerical solutions are obtained non-iteratively using an explicit treatment of the interfacial mass and energy balances and an implicit treatment of the temperature field equations. The accuracy and flexibility of the present numerical method are verified by solving some phase-change problems and comparing the results with existing analytical, semi-analytical and numerical solutions. Results indicate that one- and two-dimensional phase-change problems can be handled easily with excellent accuracies.
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.
Effective numerical method of spectral analysis of quantum graphs
NASA Astrophysics Data System (ADS)
Barrera-Figueroa, Víctor; Rabinovich, Vladimir S.
2017-05-01
We present in the paper an effective numerical method for the determination of the spectra of periodic metric graphs equipped by Schrödinger operators with real-valued periodic electric potentials as Hamiltonians and with Kirchhoff and Neumann conditions at the vertices. Our method is based on the spectral parameter power series method, which leads to a series representation of the dispersion equation, which is suitable for both analytical and numerical calculations. Several important examples demonstrate the effectiveness of our method for some periodic graphs of interest that possess potentials usually found in quantum mechanics.
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.
Dynamical modeling of elliptical galaxies. II. numerical prolate models
Lake, G.
1981-01-01
The analytical solutions of Paper I are generalized using the self-consistent field method. These prolate models are constructed using only two integrals of motion, the energy (E) and the angular momentum about the axis of symmetry, (L/sub z/). They are the first models with flattening greater than E4 which possess elliptical isophotes and realistic density profiles. The singularity in the surface brightness which characterized the models of Paper I has been removed by smoothing the extreme suppression of L/sub z/. The new models (like those of Paper I) still show a sharp rise in the velocity dispersion at the center. This feature is due to the strongly anisotropic velocity dispersions, rather than the existence of a supermassive object.
Numerical methods for solving ODEs on the infinity computer
NASA Astrophysics Data System (ADS)
Mazzia, F.; Sergeyev, Ya. D.; Iavernaro, F.; Amodio, P.; Mukhametzhanov, M. S.
2016-10-01
New algorithms for the numerical solution of Ordinary Differential Equations (ODEs) with initial conditions are proposed. They are designed for working on a new kind of a supercomputer - the Infinity Computer - that is able to deal numerically with finite, infinite and infinitesimal numbers. Due to this fact, the Infinity Computer allows one to calculate the exact derivatives of functions using infinitesimal values of the stepsize. As a consequence, the new methods are able to work with the exact values of the derivatives, instead of their approximations. Within this context, variants of one-step multi-point methods closely related to the classical Taylor formulae and to the Obrechkoff methods are considered. To get numerical evidence of the theoretical results, test problems are solved by means of the new methods and the results compared with the performance of classical methods.
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.
Numerical solutions of the GEW equation using MLS collocation method
NASA Astrophysics Data System (ADS)
Kaplan, Ayşe Gül; Dereli, Yılmaz
In this paper, the generalized equal width wave (GEW) equation is solved by using moving least squares collocation (MLSC) method. To test the accuracy of the method some numerical experiments are presented. The motion of single solitary waves, the interaction of two solitary waves and the Maxwellian initial condition problems are chosen as test problems. For the single solitary wave motion whose analytical solution was known L2, L∞ error norms and pointwise rates of convergence were calculated. Also mass, energy and momentum invariants were calculated for every test problems. Obtained numerical results are compared with some earlier works. It is seen that the method is very efficient and reliable due to obtained numerical results are very satisfactorily. Stability analysis of difference equation was done by applying the moving least squares collocation method for GEW equation.
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.
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…
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…
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.
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.
The numerical mirage method for photothermal characterization of materials.
Demko, Michael T; Hostler, Stephen R; Abramson, Alexis R
2008-04-01
Noncontact thermal measurement techniques offer rapid thermal characterization without modification or destruction of the sample being studied. A simple and versatile method has been developed, termed the "numerical mirage method," that utilizes the transient photothermal deflection of a laser beam traversing a modulated temperature gradient. This method expands the range and simplifies the experimental procedure of traditional mirage methods. A numerical solver is used to create accurate deflection profile models and a linear curve fitting routine is developed, from which the thermal diffusivity of a material may be determined. This method allows for rapid modification of sample and heating configurations. Verification of the method is performed on bismuth and fused quartz reference samples, and good agreement with literature is obtained.
Numerical results for extended field method applications. [thin plates
NASA Technical Reports Server (NTRS)
Donaldson, B. K.; Chander, S.
1973-01-01
This paper presents the numerical results obtained when a new method of analysis, called the extended field method, was applied to several thin plate problems including one with non-rectangular geometry, and one problem involving both beams and a plate. The numerical results show that the quality of the single plate solutions was satisfactory for all cases except those involving a freely deflecting plate corner. The results for the beam and plate structure were satisfactory even though the structure had a freely deflecting corner.
Nonlinear vibrations of buckled plates by an asymptotic numerical method
NASA Astrophysics Data System (ADS)
Benchouaf, Lahcen; Boutyour, El Hassan
2016-03-01
This work deals with nonlinear vibrations of a buckled von Karman plate by an asymptotic numerical method and harmonic balance approach. The coupled nonlinear static and dynamic problems are transformed into a sequence of linear ones solved by a finite-element method. The static behavior of the plate is first computed. The fundamental frequency of nonlinear vibrations of the plate, about any equilibrium state, is obtained. To improve the validity range of the power series, Padé approximants are incorporated. A continuation technique is used to get the whole solution. To show the effectiveness of the proposed methodology, numerical tests are presented.
A numerical method for acoustic oscillations in tubes
NASA Technical Reports Server (NTRS)
Gary, John M.
1988-01-01
A numerical method to obtain the neutral curve for the onset of acoustic oscillations in a helium-filled tube is described. Such oscillations can cause a serious heat loss in the plumbing associated with liquid helium dewars. The problem is modelled by a second-order, ordinary differential eigenvalue problem for the pressure perturbation. The numerical method to find the eigenvalues and track the resulting points along the neutral curve is tailored to this problem. The results show that a tube with a uniform temperature gradient along it is much more stable than one where the temperature suddenly jumps from the cold to the hot value in the middle of the tube.
NASA Technical Reports Server (NTRS)
Rodriguez, Ernesto; Kim, Yunjin; Durden, Stephen L.
1992-01-01
A numerical evaluation is presented of the regime of validity for various rough surface scattering theories against numerical results obtained by employing the method of moments. The contribution of each theory is considered up to second order in the perturbation expansion for the surface current. Considering both vertical and horizontal polarizations, the unified perturbation method provides best results among all theories weighed.
Numerical methods for solving terminal optimal control problems
NASA Astrophysics Data System (ADS)
Gornov, A. Yu.; Tyatyushkin, A. I.; Finkelstein, E. A.
2016-02-01
Numerical methods for solving optimal control problems with equality constraints at the right end of the trajectory are discussed. Algorithms for optimal control search are proposed that are based on the multimethod technique for finding an approximate solution of prescribed accuracy that satisfies terminal conditions. High accuracy is achieved by applying a second-order method analogous to Newton's method or Bellman's quasilinearization method. In the solution of problems with direct control constraints, the variation of the control is computed using a finite-dimensional approximation of an auxiliary problem, which is solved by applying linear programming methods.
Numerical methods and calculations for droplet flow, heating and ignition
NASA Technical Reports Server (NTRS)
Dwyer, H. A.; Sanders, B. R.; Dandy, D.
1982-01-01
A numerical method was devised and employed to solve a variety of problems related to liquid droplet combustion. The basic transport equations of mass, momentum and energy were formulated in terms of generalized nonorthogonal coordinates, which allows for adaptive griding and arbitrary particle shape. Example problems are solved for internal droplet heating, droplet ignition and high Reynolds number flow over a droplet.
A numerical method for unsteady aerodynamics via acoustics
NASA Technical Reports Server (NTRS)
Hodge, Steve
1991-01-01
Formal solutions to the wave equation may be conveniently described within the framework of generalized function theory. A generalized function theory is used to yield a formulation and formal solution of a wave equation describing oscillation of a flat plate from which a numerical method may be derived.
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
Comparing Numerical Methods for Isothermal Magnetized Supersonic Turbulence
NASA Astrophysics Data System (ADS)
Kritsuk, Alexei G.; Nordlund, Åke; Collins, David; Padoan, Paolo; Norman, Michael L.; Abel, Tom; Banerjee, Robi; Federrath, Christoph; Flock, Mario; Lee, Dongwook; Li, Pak Shing; Müller, Wolf-Christian; Teyssier, Romain; Ustyugov, Sergey D.; Vogel, Christian; Xu, Hao
2011-08-01
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-Alfvénic 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.
Numerical aperture of multimode fibers by several methods - Resolving differences
NASA Astrophysics Data System (ADS)
Franzen, Douglas L.; Young, Matt; Cherin, Allen H.; Head, E. D.; Hackert, Michael J.
1989-06-01
An industry-wide study among members of the Electronic Industries Association was conducted to document differences among three numerical aperture measurement methods. Results on 12 multimode graded-index fibers indicate systematic differences exist among commonly used far-field and index-profile techniques. Differences can be explained by a wavelength-dependent factor and choice of definitions. Conversion factors can be used to relate the various methods.
Efficient numerical methods for entropy-linear programming problems
NASA Astrophysics Data System (ADS)
Gasnikov, A. V.; Gasnikova, E. B.; Nesterov, Yu. E.; Chernov, A. V.
2016-04-01
Entropy-linear programming (ELP) problems arise in various applications. They are usually written as the maximization of entropy (minimization of minus entropy) under affine constraints. In this work, new numerical methods for solving ELP problems are proposed. Sharp estimates for the convergence rates of the proposed methods are established. The approach described applies to a broader class of minimization problems for strongly convex functionals with affine constraints.
A novel gas-droplet numerical method for spray combustion
NASA Technical Reports Server (NTRS)
Chen, C. P.; Shang, H. M.; Jiang, Y.
1991-01-01
This paper presents a non-iterative numerical technique for computing time-dependent gas-droplet flows. The method is a fully-interacting combination of Eulerian fluid and Lagrangian particle calculation. The interaction calculations between the two phases are formulated on a pressure-velocity coupling procedure based on the operator-splitting technique. This procedure eliminates the global iterations required in the conventional particle-source-in-cell (PSIC) procedure. Turbulent dispersion calculations are treated by a stochastic procedure. Numerical calculations and comparisons with available experimental data, as well as efficiency assessments are given for some sprays typical of spray combustion applications.
Numerical methods and computers used in elastohydrodynamic lubrication
NASA Technical Reports Server (NTRS)
Hamrock, B. J.; Tripp, J. H.
1982-01-01
Some of the methods of obtaining approximate numerical solutions to boundary value problems that arise in elastohydrodynamic lubrication are reviewed. The highlights of four general approaches (direct, inverse, quasi-inverse, and Newton-Raphson) are sketched. Advantages and disadvantages of these approaches are presented along with a flow chart showing some of the details of each. The basic question of numerical stability of the elastohydrodynamic lubrication solutions, especially in the pressure spike region, is considered. Computers used to solve this important class of lubrication problems are briefly described, with emphasis on supercomputers.
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.
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.
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.
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.
A numerical method for interface problems in elastodynamics
NASA Technical Reports Server (NTRS)
Mcghee, D. S.
1984-01-01
The numerical implementation of a formulation for a class of interface problems in elastodynamics is discussed. This formulation combines the use of the finite element and boundary integral methods to represent the interior and the exteriro regions, respectively. In particular, the response of a semicylindrical alluvial valley in a homogeneous halfspace to incident antiplane SH waves is considered to determine the accuracy and convergence of the numerical procedure. Numerical results are obtained from several combinations of the incidence angle, frequency of excitation, and relative stiffness between the inclusion and the surrounding halfspace. The results tend to confirm the theoretical estimates that the convergence is of the order H(2) for the piecewise linear elements used. It was also observed that the accuracy descreases as the frequency of excitation increases or as the relative stiffness of the inclusion decreases.
Numerical methods for solving the Boltzmann equation (a review)
NASA Technical Reports Server (NTRS)
Limar, Y. F.; Shakhov, Y. M.; Shidlovskiy, V. P.
1972-01-01
The methods are reviewed which are utilized in principal attempts to obtain the numerical solution or modeling of the Boltzmann equation over a broad range of Knudsen numbers. The primary methods considered are the Monte Carlo and the discrete velocities methods. The conculsions drawn from the analysis include the following: (1) The Monte Carlo methods are not well suited in the area of small Knudsen numbers. (2) Among the Monte Carlo methods, the Bird method appears to be the most attractive, since it is more directly related to the Boltzmann equation. (3) The deterministic methods, which include the discrete ordinate technique, offer great possibilities but require exceedingly large computer times. (4) The use of approximating equations in combination with the discrete velocities method will possibly improve computation time and reduce the required memory volume.
Numerical simulation of gas discharge CO II lasers with conic tubes
NASA Astrophysics Data System (ADS)
Galeev, Ravil S.; Safiullin, Rafail K.
2006-01-01
The results of numerical simulation for fast-axial-flow gas discharge CO II lasers are presented. Quasi-one-dimensional consideration of the processes for powefil CO II lasers with conic discharge tubes shows that laser operation may be more effective in the case of tubes which are narrowed down fiom anode to cathode provided that gas flow is directed towards the cathode. On the contrary, when tube is narrowed down from cathode to anode, no any advantage in the laser operation may be received. The calculated quantities are in satisfactory agreement with the available experimental data.
Volatile transport on inhomogeneous surfaces: II. Numerical calculations (VT3D)
NASA Astrophysics Data System (ADS)
Young, Leslie A.
2017-03-01
Several distant icy worlds have atmospheres that are in vapor-pressure equilibrium with their surface volatiles, including Pluto, Triton, and, probably, several large KBOs near perihelion. Studies of the volatile and thermal evolution of these have been limited by computational speed, especially for models that treat surfaces that vary with both latitude and longitude. In order to expedite such work, I present a new numerical model for the seasonal behavior of Pluto and Triton which (i) uses initial conditions that improve convergence, (ii) uses an expedient method for handling the transition between global and non-global atmospheres, (iii) includes local conservation of energy and global conservation of mass to partition energy between heating, conduction, and sublimation or condensation, (iv) uses time-stepping algorithms that ensure stability while allowing larger timesteps, and (v) can include longitudinal variability. This model, called VT3D, has been used in Young (2012a, 2012b), Young (2013), Olkin et al. (2015), Young and McKinnon (2013), and French et al. (2015). Many elements of VT3D can be used independently. For example, VT3D can also be used to speed up thermophysical models (Spencer et al., 1989) for bodies without volatiles. Code implementation is included in the supplemental materials and is available from the author.
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
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.
Simple numerical method for solving the steady Euler equations
NASA Technical Reports Server (NTRS)
Von Lavante, E.; Melson, N. Duane
1987-01-01
A numerical method for solving the isenthalpic form of the governing equations for compressible inviscid flows is developed. The method is based on the concept of flux vector splitting in its implicit form and is tested on several demanding configurations. Time marching to steady state is accelerated by the implementation of the multigrid procedure which very effectively increases the rate of convergence. Steady-state results are obtained for various test cases. Only short computational times are required due to the relative efficiency of the basic method.
A Numerical Method for Incompressible Flow with Heat Transfer
NASA Technical Reports Server (NTRS)
Sa, Jong-Youb; Kwak, Dochan
1997-01-01
A numerical method for the convective heat transfer problem is developed for low speed flow at mild temperatures. A simplified energy equation is added to the incompressible Navier-Stokes formulation by using Boussinesq approximation to account for the buoyancy force. A pseudocompressibility method is used to solve the resulting set of equations for steady-state solutions in conjunction with an approximate factorization scheme. A Neumann-type pressure boundary condition is devised to account for the interaction between pressure and temperature terms, especially near a heated or cooled solid boundary. It is shown that the present method is capable of predicting the temperature field in an incompressible flow.
Numerical Method and Analysis of Consistency for Electrodiffusion Problem
NASA Astrophysics Data System (ADS)
Filipek, R.; Szyszkiewicz, K.; Danielewski, M.; Lewenstam, A.
2007-12-01
Numerical procedure based on method of lines for time-dependent electrodiffusion transport is developed. Finite difference space discretization with suitably selected weights based on a non-uniform grid is applied. Consistency of this method and the method put forward by Brumleve and Buck are analyzed and compared. The resulting stiff system of ODEs is effectively solved using the Radau IIa integrator. The applications to selected electrochemical systems: liquid junction, bi-ionic case and fused salts have been tested. Results for ion-selective electrodes are demonstrated.
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.
Automatic numerical integration methods for Feynman integrals through 3-loop
NASA Astrophysics Data System (ADS)
de Doncker, E.; Yuasa, F.; Kato, K.; Ishikawa, T.; Olagbemi, O.
2015-05-01
We give numerical integration results for Feynman loop diagrams through 3-loop such as those covered by Laporta [1]. The methods are based on automatic adaptive integration, using iterated integration and extrapolation with programs from the QUADPACK package, or multivariate techniques from the ParInt package. The Dqags algorithm from QuadPack accommodates boundary singularities of fairly general types. PARINT is a package for multivariate integration layered over MPI (Message Passing Interface), which runs on clusters and incorporates advanced parallel/distributed techniques such as load balancing among processes that may be distributed over a network of nodes. Results are included for 3-loop self-energy diagrams without IR (infra-red) or UV (ultra-violet) singularities. A procedure based on iterated integration and extrapolation yields a novel method of numerical regularization for integrals with UV terms, and is applied to a set of 2-loop self-energy diagrams with UV singularities.
Numerical methods for control optimization in linear systems
NASA Astrophysics Data System (ADS)
Tyatyushkin, A. I.
2015-05-01
Numerical methods are considered for solving optimal control problems in linear systems, namely, terminal control problems with control and phase constraints and time-optimal control problems. Several algorithms with various computer storage requirements are proposed for solving these problems. The algorithms are intended for finding an optimal control in linear systems having certain features, for example, when the reachable set of a system has flat faces.
Fast Numerical Methods for Stochastic Partial Differential Equations
2016-04-15
AFRL-AFOSR-VA-TR-2016-0156 Fast Numerical Methods for Stochastic Partial Differential Equations Hongmei Chi Florida Agricultural and Mechanical...University Tallahassee Final Report 04/15/2016 DISTRIBUTION A: Distribution approved for public release. AF Office Of Scientific Research (AFOSR)/ RTA2...Arlington, Virginia 22203 Air Force Research Laboratory Air Force Materiel Command REPORT DOCUMENTATION PAGE Form ApprovedOMB No. 0704-0188 1. REPORT
[Numerical methods for multi-fluid flows]. Final progress report
Pozrikidis, C.
1998-07-21
The central objective of this research has been to develop efficient numerical methods for computing multi-fluid flows with large interfacial deformations, and apply these methods to study the rheology of suspensions of deformable particles with viscous and non-Newtonian interfacial behavior. The mathematical formulation employs boundary-integral, immersed-boundary, and related numerical methods. Particles of interest include liquid drops with constant surface tension and capsules whose interfaces exhibit viscoelastic and incompressible characteristics. In one family of problems, the author has considered the shear-driven and pressure-driven flow of a suspension of two-dimensional liquid drops with ordered and random structure. In a second series of investigations, the author carried out dynamic simulations of two-dimensional, unbounded, doubly-periodic shear flows with random structure. Another family of problems addresses the deformation of three-dimensional capsules whose interfaces exhibit isotropic surface tension, viscous, elastic, or incompressible behavior, in simple shear flow. The numerical results extend previous asymptotic theories for small deformations and illuminate the mechanism of membrane rupture.
Modeling collisional processes in plasmas using discontinuous numerical methods
NASA Astrophysics Data System (ADS)
Miller, Sean
Fluid-based plasma models are typically applied to parameter regimes where a local thermal equilibrium is assumed. The applicability of this regime is valid for many plasmas, however, it is limited to plasma dynamics dominated by collisional effects. This study attempts to extend the validity of the collisional fluid regime using an anisotropic 13-moment fluid model derived from the Pearson type-IV probability distribution. The model explicitly evolves the heat flux hyperbolically alongside the density, momentum, and energy in order to capture dynamics usually restricted to costly kinetic models. Each particle species is modeled individually and collectively coupled through electromagnetic and collision operators. To remove electromagnetic divergence errors inherent to numerical representations of Maxwell's equations, both hyperbolic and parabolic cleaning methods are presented. The plasma models are implemented using high-order finite volume and discontinuous Galerkin numerical methods designed for unstructured meshes. The unstructured code framework, numerical methods, and plasma models were developed in the University of Washington's WARPXM code for use on heterogeneous accelerated clusters.
The instanton method and its numerical implementation in fluid mechanics
NASA Astrophysics Data System (ADS)
Grafke, Tobias; Grauer, Rainer; Schäfer, Tobias
2015-08-01
A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin-Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler-Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to extract instantons from direct numerical simulations. In the following we present modifications of the algorithms to make them efficient when applied to two- or three-dimensional (2D or 3D) fluid dynamical problems. We illustrate these ideas using the 2D Burgers equation and the 3D Navier-Stokes equations.
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.
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.
An explicit mixed numerical method for mesoscale model
NASA Technical Reports Server (NTRS)
Hsu, H.-M.
1981-01-01
A mixed numerical method has been developed for mesoscale models. The technique consists of a forward difference scheme for time tendency terms, an upstream scheme for advective terms, and a central scheme for the other terms in a physical system. It is shown that the mixed method is conditionally stable and highly accurate for approximating the system of either shallow-water equations in one dimension or primitive equations in three dimensions. Since the technique is explicit and two time level, it conserves computer and programming resources.
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.
New numerical method to study phase transitions and its applications
Lee, Jooyoung; Kosterlitz, J.M.
1991-11-01
We present a powerful method of identifying the nature of transitions by numerical simulation of finite systems. By studying the finite size scaling properties of free energy barrier between competing states, we can identify unambiguously a weak first order transition even when accessible system sizes are L/{xi} < 0.05 as in the five state Potts model in two dimensions. When studying a continuous phase transition we obtain quite accurate estimates of critical exponents by treating it as a field driven first order transition. The method has been successfully applied to various systems.
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.
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.
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.
A Numerical Method for Synthesizing Atmospheric Temperature and Humidity Profiles.
NASA Astrophysics Data System (ADS)
Tatarskaia, Maia S.; Lataitis, Richard J.; Boba Stankov, B.; Tatarskii, Viatcheslav V.
1998-07-01
A numerical technique is described for synthesizing realistic atmospheric temperature and humidity profiles. The method uses an ensemble of radiosonde measurements collected at a site of interest. Erroneous profiles are removed by comparing their likelihood with prevailing meteorological conditions. The remaining profiles are decomposed using the method of empirical orthogonal functions. The corresponding eigenprofiles and the statistics of the expansion coefficients are used to numerically generate synthetic profiles that obey the same statistics (i.e., have the same mean, variability, and vertical correlation) as the initial dataset. The technique was applied to a set of approximately 1000 temperature and humidity soundings made in Denver, Colorado, during the winter months of 1991-95. This dataset was divided into four cloud classification categories and daytime and nighttime launches to better characterize typical profiles for the eight cases considered. It was found that 97% of the variance in the soundings could be accounted for by using only five eigenprofiles in the reconstructions. Ensembles of numerically generated profiles can be used to test the accuracy of various retrieval algorithms under controlled conditions not usually available in practice.
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.
Numerical method for gas dynamics combining characteristic and conservation concepts
NASA Technical Reports Server (NTRS)
Coakley, T. J.
1981-01-01
An efficient implicit numerical method that solves the compressible Navier-Stokes equations in arbitrary curvilinear coordinates by the finite-volume technique is presented. An intrinsically dissipative difference scheme and a fully implicit treatment of boundary conditions, based on characteristic and conservation concepts, are used to improve stability and accuracy. Efficiency is achieved by using a diagonal form of the implicit algorithm and spatially varying time-steps. Comparisons of various schemes and methods are presented for one- and two-dimensional flows, including transonic separated flow past a thick circular-arc airfoil in a channel. The new method is equal to or better than a version of MacCormack's hybrid method in accuracy and it converges to a steady state up to an order of magnitude faster.
Performance analysis of a mirror by numerical iterative method.
Park, Kwijong; Cho, Myung; Lee, Dae-Hee; Moon, Bongkon
2014-12-29
Zernike polynomials are generally used to predict the optical performance of a mirror. However, it can also be done by a numerical iterative method. As piston, tip, tilt, and defocus (P.T.T.F) aberrations can be easily removed by optical alignment, we iteratively used a rotation transformation and a paraboloid graph subtraction for removal of the aberrations from a raw deformation of the optical surface through a Finite Element Method (FEM). The results of a 30 cm concave circular mirror corrected by the iterative method were almost the same as those yielded by Zernike polynomial fitting, and the computational time was fast. In addition, a concave square mirror whose surface area is π was analyzed in order to visualize the deformation maps of a general mirror aperture shape. The iterative method can be applicable efficiently because it does not depend on the mirror aperture shape.
Numerical method for gas dynamics combining characteristic and conservation concepts
NASA Technical Reports Server (NTRS)
Coakley, T. J.
1981-01-01
An efficient implicit numerical method that solves the compressible Navier-Stokes equations in arbitrary curvilinear coordinates by the finite-volume technique is presented. An intrinsically dissipative difference scheme and a fully implicit treatment of boundary conditions, based on characteristic and conservation concepts, are used to improve stability and accuracy. Efficiency is achieved by using a diagonal form of the implicit algorithm and spatially varying time-steps. Comparisons of various schemes and methods are presented for one- and two-dimensional flows, including transonic separated flow past a thick circular-arc airfoil in a channel. The new method is equal to or better than a version of MacCormack's hybrid method in accuracy and it converges to a steady state up to an order of magnitude faster.
Numerical renormalization group method for quantum impurity systems
NASA Astrophysics Data System (ADS)
Bulla, Ralf; Costi, Theo A.; Pruschke, Thomas
2008-04-01
In the early 1970s, Wilson developed the concept of a fully nonperturbative renormalization group transformation. When applied to the Kondo problem, this numerical renormalization group (NRG) method gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin. The NRG method was later generalized to a variety of quantum impurity problems. The purpose of this review is to give a brief introduction to the NRG method, including some guidelines for calculating physical quantities, and to survey the development of the NRG method and its various applications over the last 30 years. These applications include variants of the original Kondo problem such as the non-Fermi-liquid behavior in the two-channel Kondo model, dissipative quantum systems such as the spin-boson model, and lattice systems in the framework of the dynamical mean-field theory.
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
Novel Parallel Numerical Methods for Radiation& Neutron Transport
Brown, P N
2001-03-06
In many of the multiphysics simulations performed at LLNL, transport calculations can take up 30 to 50% of the total run time. If Monte Carlo methods are used, the percentage can be as high as 80%. Thus, a significant core competence in the formulation, software implementation, and solution of the numerical problems arising in transport modeling is essential to Laboratory and DOE research. In this project, we worked on developing scalable solution methods for the equations that model the transport of photons and neutrons through materials. Our goal was to reduce the transport solve time in these simulations by means of more advanced numerical methods and their parallel implementations. These methods must be scalable, that is, the time to solution must remain constant as the problem size grows and additional computer resources are used. For iterative methods, scalability requires that (1) the number of iterations to reach convergence is independent of problem size, and (2) that the computational cost grows linearly with problem size. We focused on deterministic approaches to transport, building on our earlier work in which we performed a new, detailed analysis of some existing transport methods and developed new approaches. The Boltzmann equation (the underlying equation to be solved) and various solution methods have been developed over many years. Consequently, many laboratory codes are based on these methods, which are in some cases decades old. For the transport of x-rays through partially ionized plasmas in local thermodynamic equilibrium, the transport equation is coupled to nonlinear diffusion equations for the electron and ion temperatures via the highly nonlinear Planck function. We investigated the suitability of traditional-solution approaches to transport on terascale architectures and also designed new scalable algorithms; in some cases, we investigated hybrid approaches that combined both.
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 methods and measurement systems for nonlinear magnetic circuits (abstract)
NASA Astrophysics Data System (ADS)
Heitbrink, Axel; Dieter Storzer, Hans; Beyer, Adalbert
1994-05-01
In the past years an increasing interest in calculation methods of circuits containing magnetic nonlinearities could be observed. For this reason a new method was developed which makes it possible to calculate the steady state solution of such circuits by the help of an interactive cad program. The modular concept of the software allows to separate the circuit into nonlinear and linear subnetworks. When regarding nonlinear magnetic elements one can choose between several numerical models for the description of the hysteresis loops or an inbuilt realtime measurement system can be activated to get the dynamic hysteresis loops. The measurement system is also helpful for the parameter extraction for the numerical hysteresis models. A modified harmonic-balance algorithm and a set of iteration schemes is used for solving the network function. The combination of the realtime measurement system and modern numerical methods brings up a productive total concept for the exact calculation of nonlinear magnetic circuits. A special application class will be discussed which is given by earth-leakage circuit breakers. These networks contain a toroidal high permeable NiFe alloy and a relay as nonlinear elements (cells) and some resistors, inductors, and capacitors as linear elements. As input dc signals at the primary winding of the core any curveform must be regarded, especially 135° phasecutted pulses. These signals with extreme higher frequency components make it impossible to use numerical models for the description of the nonlinear behavior of the core and the relays. So for both elements the realtime measurement system must be used during the iteration process. During each iteration step the actual magnetization current is sent to the measurement system, which measures the dynamic hysteresis loop at the probe. These values flow back into the iteration process. A graphic subsystem allows a look at the waveforms of all voltages and current when the iterations take place. One
Comparison of four stable numerical methods for Abel's integral equation
NASA Technical Reports Server (NTRS)
Murio, Diego A.; Mejia, Carlos E.
1991-01-01
The 3-D image reconstruction from cone-beam projections in computerized tomography leads naturally, in the case of radial symmetry, to the study of Abel-type integral equations. If the experimental information is obtained from measured data, on a discrete set of points, special methods are needed in order to restore continuity with respect to the data. A new combined Regularized-Adjoint-Conjugate Gradient algorithm, together with two different implementations of the Mollification Method (one based on a data filtering technique and the other on the mollification of the kernal function) and a regularization by truncation method (initially proposed for 2-D ray sample schemes and more recently extended to 3-D cone-beam image reconstruction) are extensively tested and compared for accuracy and numerical stability as functions of the level of noise in the data.
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
Cho, H.; Venturi, D.; Karniadakis, G.E.
2016-01-15
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.
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.
Numerical Methods for Computing Turbulence-Induced Noise
2005-12-16
consider the finite dimensional subspace Vhl C Vh . Let vhi -= phlu be the optimal representation of u in Vhl and phi : V+_+ Vhl be the appropriate...mapping. We consider the following numerical method which is obtained by replacing h with hi in (2.4). Find uhl E Vhi , such that B(whi, uhl) + M(whUhl, f...the same functional form of the model that leads to the optimal solution on Vh, also leads to the optimal solution on Vhi . Thus, requiring uhl = vh
Simple numerical method for predicting steady compressible flows
NASA Technical Reports Server (NTRS)
Von Lavante, E.; Melson, N. Duane
1987-01-01
The present numerical method for the solution of the isenthalpic form of the governing equations for compressible viscous and inviscid flows has its basis in the concept of flux vector splitting in its implicit form, and has been tested in the cases of several difficult viscous and inviscid configurations. An acceleration of time-marching to steady state is accomplished by implementing a multigrid procedure which effectively increases the convergence rate. The steady state results obtained are largely of good quality, and required only short computational times.
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.
Numerical prediction of interfacial instabilities: Sharp interface method (SIM)
NASA Astrophysics Data System (ADS)
Nourgaliev, R. R.; Liou, M.-S.; Theofanous, T. G.
2008-04-01
We introduce a sharp interface method (SIM) for the direct numerical simulation of unstable fluid-fluid interfaces. The method is based on the level set approach and the structured adaptive mesh refinement technology, endowed with a corridor of irregular, cut-cell grids that resolve the interfacial region to third-order spatial accuracy. Key in that regard are avoidance of numerical mixing, and a least-squares interpolation method that is supported by irregular datasets distinctly on each side of the interface. Results on test problems show our method to be free of the spurious current problem of the continuous surface force method and to converge, on grid refinement, at near-theoretical rates. Simulations of unstable Rayleigh-Taylor and viscous Kelvin-Helmholtz flows are found to converge at near-theoretical rates to the exact results over a wide range of conditions. Further, we show predictions of neutral-stability maps of the viscous Kelvin-Helmholtz flows (Yih instability), as well as self-selection of the most unstable wave-number in multimode simulations of Rayleigh-Taylor instability. All these results were obtained with a simple seeding of random infinitesimal disturbances of interface-shape, as opposed to seeding by a complete eigenmode. For other than elementary flows the latter would normally not be available, and extremely difficult to obtain if at all. Sample comparisons with our code adapted to mimic typical diffuse interface treatments were not satisfactory for shear-dominated flows. On the other hand the sharp dynamics of our method would appear to be compatible and possibly advantageous to any interfacial flow algorithm in which the interface is represented as a discrete Heaviside function.
Numerical methods for large eddy simulation of acoustic combustion instabilities
NASA Astrophysics Data System (ADS)
Wall, Clifton T.
Acoustic combustion instabilities occur when interaction between the combustion process and acoustic modes in a combustor results in periodic oscillations in pressure, velocity, and heat release. If sufficiently large in amplitude, these instabilities can cause operational difficulties or the failure of combustor hardware. In many situations, the dominant instability is the result of the interaction between a low frequency acoustic mode of the combustor and the large scale hydrodynamics. Large eddy simulation (LES), therefore, is a promising tool for the prediction of these instabilities, since both the low frequency acoustic modes and the large scale hydrodynamics are well resolved in LES. Problems with the tractability of such simulations arise, however, due to the difficulty of solving the compressible Navier-Stokes equations efficiently at low Mach number and due to the large number of acoustic periods that are often required for such instabilities to reach limit cycles. An implicit numerical method for the solution of the compressible Navier-Stokes equations has been developed which avoids the acoustic CFL restriction, allowing for significant efficiency gains at low Mach number, while still resolving the low frequency acoustic modes of interest. In the limit of a uniform grid the numerical method causes no artificial damping of acoustic waves. New, non-reflecting boundary conditions have also been developed for use with the characteristic-based approach of Poinsot and Lele (1992). The new boundary conditions are implemented in a manner which allows for significant reduction of the computational domain of an LES by eliminating the need to perform LES in regions where one-dimensional acoustics significantly affect the instability but details of the hydrodynamics do not. These new numerical techniques have been demonstrated in an LES of an experimental combustor. The new techniques are shown to be an efficient means of performing LES of acoustic combustion
Numerical study of the Columbia high-beta device: Torus-II
Izzo, R.
1981-01-01
The ionization, heating and subsequent long-time-scale behavior of the helium plasma in the Columbia fusion device, Torus-II, is studied. The purpose of this work is to perform numerical simulations while maintaining a high level of interaction with experimentalists. The device is operated as a toroidal z-pinch to prepare the gas for heating. This ionization of helium is studied using a zero-dimensional, two-fluid code. It is essentially an energy balance calculation that follows the development of the various charge states of the helium and any impurities (primarily silicon and oxygen) that are present. The code is an atomic physics model of Torus-II. In addition to ionization, we include three-body and radiative recombination processes.
Optimization methods and silicon solar cell numerical models
NASA Technical Reports Server (NTRS)
Girardini, K.
1986-01-01
The goal of this project is the development of an optimization algorithm for use with a solar cell model. It is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junctions depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm has been developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAPID). SCAPID uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the operation of a solar cell. A major obstacle is that the numerical methods used in SCAPID require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the value associated with the maximum efficiency. This problem has been alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution. Adapting SCAPID so that it could be called iteratively by the optimization code provided another means of reducing the cpu time required to complete an optimization. Instead of calculating the entire I-V curve, as is usually done in SCAPID, only the efficiency is calculated (maximum power voltage and current) and the solution from previous calculations is used to initiate the next solution.
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.
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.
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 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.
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.
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.
Examination of Numerical Integration Accuracy and Modeling for GRACE-FO and GRACE-II
NASA Astrophysics Data System (ADS)
McCullough, C.; Bettadpur, S.
2012-12-01
As technological advances throughout the field of satellite geodesy improve the accuracy of satellite measurements, numerical methods and algorithms must be able to keep pace. Currently, the Gravity Recovery and Climate Experiment's (GRACE) dual one-way microwave ranging system can determine changes in inter-satellite range to a precision of a few microns; however, with the advent of laser measurement systems nanometer precision ranging is a realistic possibility. With this increase in measurement accuracy, a reevaluation of the accuracy inherent in the linear multi-step numerical integration methods is necessary. Two areas where this can be a primary concern are the ability of the numerical integration methods to accurately predict the satellite's state in the presence of numerous small accelerations due to operation of the spacecraft attitude control thrusters, and due to small, point-mass anomalies on the surface of the Earth. This study attempts to quantify and minimize these numerical errors in an effort to improve the accuracy of modeling and propagation of these perturbations; helping to provide further insight into the behavior and evolution of the Earth's gravity field from the more capable gravity missions in the future.
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 numerical simulation method for aircraft infrared imaging
NASA Astrophysics Data System (ADS)
Zhou, Yue; Wang, Qiang; Li, Ting; Hu, Haiyang
2017-06-01
Numerical simulation of infrared (IR) emission from aircraft is of great significance for military and civilian applications. In this paper, the narrow band k-distribution (NBK) model is used to calculate radiative properties of non-gray gases in the hot exhaust plume. With model parameters derived from the high resolution spectral database HITEMP 2010, the NBK model is validated by comparisons with exact line by line (LBL) results and experimental data. Based on the NBK model, a new finite volume and back ray tracing (FVBRT) method is proposed to solve the radiative transfer equations and produce IR imaging. Calculated results by the FVBRT method are compared with experimental data and available results in open references, which shows the FVBRT method can maintain good accuracy while producing IR images with better rendering effects. Finally, the NBK model and FVBRT method are integrated to calculate IR signature of an aircraft. The IR images and spatial distributions of radiative intensity are compared and analyzed in both 3 - 5 μm band and 8 - 12 μm band to provide references for engineering applications.
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.
A Hybrid Numerical Analysis Method for Structural Health Monitoring
NASA Technical Reports Server (NTRS)
Forth, Scott C.; Staroselsky, Alexander
2001-01-01
A new hybrid surface-integral-finite-element numerical scheme has been developed to model a three-dimensional crack propagating through a thin, multi-layered coating. The finite element method was used to model the physical state of the coating (far field), and the surface integral method was used to model the fatigue crack growth. The two formulations are coupled through the need to satisfy boundary conditions on the crack surface and the external boundary. The coupling is sufficiently weak that the surface integral mesh of the crack surface and the finite element mesh of the uncracked volume can be set up independently. Thus when modeling crack growth, the finite element mesh can remain fixed for the duration of the simulation as the crack mesh is advanced. This method was implemented to evaluate the feasibility of fabricating a structural health monitoring system for real-time detection of surface cracks propagating in engine components. In this work, the authors formulate the hybrid surface-integral-finite-element method and discuss the mechanical issues of implementing a structural health monitoring system in an aircraft engine environment.
Numerical Method of Characteristics for One-Dimensional Blood Flow.
Acosta, Sebastian; Puelz, Charles; Riviére, 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.
Numerical Method of Characteristics for One–Dimensional Blood Flow
Puelz, Charles; Riviére, Béatrice; Penny, Daniel J.; Rusin, Craig G.
2015-01-01
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. PMID:25931614
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.
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.
Performance of Several High Order Numerical Methods for Supersonic Combustion
NASA Technical Reports Server (NTRS)
Sjoegreen, Bjoern; Yee, H. C.; Don, Wai Sun; Mansour, Nagi N. (Technical Monitor)
2001-01-01
The performance of two recently developed numerical methods by Yee et al. and Sjoegreen and Yee using postprocessing nonlinear filters is examined for a 2-D multiscale viscous supersonic react-live flow. These nonlinear filters can improve nonlinear instabilities and at the same time can capture shock/shear waves accurately. They do not, belong to the class of TVD, ENO or WENO schemes. Nevertheless, they combine stable behavior at discontinuities and detonation without smearing the smooth parts of the flow field. For the present study, we employ a fourth-order Runge-Kutta in time and a sixth-order non-dissipative spatial base scheme for the convection and viscous terms. We denote the resulting nonlinear filter schemes ACM466-RK4 and WAV66-RK4.
Numerical simulation on snow melting phenomena by CIP method
NASA Astrophysics Data System (ADS)
Mizoe, H.; Yoon, Seong Y.; Josho, M.; Yabe, T.
2001-04-01
A numerical scheme based on the C-CUP method to simulate melting phenomena in snow is proposed. To calculate these complex phenomena we introduce the phase change, elastic-plastic model, porous model, and verify each model by using some simple examples. This scheme is applied to a practical model, such as the snow piled on the insulator of electrical transmission line, in which snow is modeled as a compound material composed of air, water, and ice, and is calculated by elastic-plastic model. The electric field between two electrodes is solved by the Poisson equation giving the Joule heating in the energy conservation that eventually leads to snow melting. Comparison is made by changing the fraction of water in the snow to see its effect on melting process for the cases of applied voltage of 50 and 500 kV on the two electrodes.
Performance of Several High Order Numerical Methods for Supersonic Combustion
NASA Technical Reports Server (NTRS)
Sjoegreen, Bjoern; Yee, H. C.; Don, Wai Sun; Mansour, Nagi N. (Technical Monitor)
2001-01-01
The performance of two recently developed numerical methods by Yee et al. and Sjoegreen and Yee using postprocessing nonlinear filters is examined for a 2-D multiscale viscous supersonic react-live flow. These nonlinear filters can improve nonlinear instabilities and at the same time can capture shock/shear waves accurately. They do not, belong to the class of TVD, ENO or WENO schemes. Nevertheless, they combine stable behavior at discontinuities and detonation without smearing the smooth parts of the flow field. For the present study, we employ a fourth-order Runge-Kutta in time and a sixth-order non-dissipative spatial base scheme for the convection and viscous terms. We denote the resulting nonlinear filter schemes ACM466-RK4 and WAV66-RK4.
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…
Simultaneous source-mask optimization: a numerical combining method
NASA Astrophysics Data System (ADS)
Mülders, Thomas; Domnenko, Vitaliy; Küchler, Bernd; Klimpel, Thomas; Stock, Hans-Jürgen; Poonawala, Amyn A.; Taravade, Kunal N.; Stanton, William A.
2010-09-01
A new method for simultaneous Source-Mask Optimization (SMO) is presented. In order to produce optimum imaging fidelity with respect to exposure lattitude, depth of focus (DoF) and mask error enhancement factor (MEEF) the presented method aims to leverage both, the available degrees of freedom of a pixelated source and those available for the mask layout. The approach described in this paper is designed as to work with dissected mask polygons. The dissection of the mask patterns is to be performed in advance (before SMO) with the Synopsys Proteus OPC engine, providing the available degrees of freedom for mask pattern optimization. This is similar to mask optimization done for optical proximity correction (OPC). Additionally, however, the illumination source will be simultaneously optimized. The SMO approach borrows many of the performance enhancement methods of OPC software for mask correction, but is especially designed as to simultaneously optimize a pixelated source shape as nowadays available in production environments. Designed as a numerical optimization approach the method is able to assess in acceptable times several hundreds of thousands source-mask combinations for small, critical layout snippets. This allows a global optimization scheme to be applied to the SMO problem which is expected to better explore the optimization space and thus to yield an improved solution quality compared to local optimizations methods. The method is applied to an example system for investigating the impact of source constraints on the SMO results. Also, it is investigated how well possibly conflicting goals of low MEEF and large DoF can be balanced.
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.
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
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.
Numerical Comparison of Periodic MoM (Method of Moments) and BMIA (Banded Matrix Iteration Method)
NASA Technical Reports Server (NTRS)
Kim, Y.; Rodriguez, E.; Michel, T.
1995-01-01
The most popular numerical technique in rough surface scattering is the Method of Moments (MoM). Since the scattering patch size is finite, the edge current must be suppressed to obtain accurate scattering cross sections. Two standard ways to minimize the edge current are periodic boundary conditions and incident wave tapering. We compare the accuracy & computational requirements of these methods.
Numerical Comparison of Periodic MoM (Method of Moments) and BMIA (Banded Matrix Iteration Method)
NASA Technical Reports Server (NTRS)
Kim, Y.; Rodriguez, E.; Michel, T.
1995-01-01
The most popular numerical technique in rough surface scattering is the Method of Moments (MoM). Since the scattering patch size is finite, the edge current must be suppressed to obtain accurate scattering cross sections. Two standard ways to minimize the edge current are periodic boundary conditions and incident wave tapering. We compare the accuracy & computational requirements of these methods.
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)
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 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.
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.
A numerical solution method for acoustic radiation from axisymmetric bodies
NASA Technical Reports Server (NTRS)
Caruthers, John E.; Raviprakash, G. K.
1995-01-01
A new and very efficient numerical method for solving equations of the Helmholtz type is specialized for problems having axisymmetric geometry. It is then demonstrated by application to the classical problem of acoustic radiation from a vibrating piston set in a stationary infinite plane. The method utilizes 'Green's Function Discretization', to obtain an accurate resolution of the waves using only 2-3 points per wave. Locally valid free space Green's functions, used in the discretization step, are obtained by quadrature. Results are computed for a range of grid spacing/piston radius ratios at a frequency parameter, omega R/c(sub 0), of 2 pi. In this case, the minimum required grid resolution appears to be fixed by the need to resolve a step boundary condition at the piston edge rather than by the length scale imposed by the wave length of the acoustic radiation. It is also demonstrated that a local near-field radiation boundary procedure allows the domain to be truncated very near the radiating source with little effect on the solution.
Exact and quasi exact numerical methods for giant magnetic molecules
NASA Astrophysics Data System (ADS)
Schnack, Jürgen
2012-02-01
The determination of the energy spectra of large magnetic molecules is a demanding numerical problem. In this contribution we demonstrate that theory has advanced very much in recent years. We first show that it is possible to diagonalize the Heisenberg Hamiltonian by employing the spin-rotational symmetry SU(2) in combination with arbitrary point-group symmetries [1]. This goes far beyond earlier approaches and enables us to evaluate thermodynamic observables such as the magnetization and spectroscopic data for molecules as large as the famous ferric wheel Fe10 with a Hilbert space dimension of more than 60 Millions. Then we explain how the finite-temperature Lanczos method can be applied to magnetic molecules in order to determine thermodynamic functions for Hilbert spaces as large as up to 1 Billion [2]. The new method enables us to discuss the magnetic properties of the highly frustrated Keplerate molecule W72V30 which behaves like a finite size Kagome lattice antiferromagnet. [4pt] [1] R. Schnalle and J. Schnack, Int. Rev. Phys. Chem. 29 (2010) 403; R. Schnalle, J. Schnack, Phys. Rev. B 79 (2009) 104419. [0pt] [2] J. Schnack, O. Wendland, Eur. Phys. J. B 78 (2010) 535-541.
Numerical modelling methods for predicting antenna performance on aircraft
NASA Astrophysics Data System (ADS)
Kubina, S. J.
1983-09-01
Typical case studies that involve the application of Moment Methods to the prediction of the radiation characteristics of antennas in the HF frequency band are examined. The examples consist of the analysis of a shorted transmission line HF antenna on a CHSS-2/Sea King helicopter, wire antennas on the CP-140/Aurora patrol aircraft and a long dipole antenna on the Space Shuttle Orbiter spacecraft. In each of these cases the guidelines for antenna modeling by the use of the program called the Numerical Electromagnetic Code are progressively applied and results are compared to measurements made by the use of scale-model techniques. In complex examples of this type comparisons based on individual radiation patterns are insufficient for the validation of computer models. A volumetric method of radiation pattern comparison is used based on criteria that result from pattern integration and that are related to communication system performance. This is supplemented by hidden-surface displays of an entire set of conical radiation patterns resulting from measurements and computations. Antenna coupling considerations are discussed for the case of the dual HF installation on the CP-140/Aurora aircraft.
Handwritten numeral verification method using distribution maps of structural features
NASA Astrophysics Data System (ADS)
Itoh, Nobuyasu; Takahashi, Hiroyasu
1990-08-01
Character recognition methods can be categorized into two major approaches. One is pattern matching, which is little affected by topological changes such as breaks in strokes. The other is structural analysis, which tolerates distorted characters only if the topological features of their undistorted versions are kept. We developed a new recognition method for hand-written numerals by combining the merits of the two approaches. The recognition process consists of three steps: (1) an input character is recognized by a patternmatching method, which reduces the number of possible categories to 1.5 on the average, (2) the character is yenfled to be true, false, or uncertain by a structural analysis method that we have newly developed, and (3) special heuristic verification logics are applied to uncertain characters. In the second step, the new structural analysis method uses the positions and directions of terminal points extracted from thinned character images as a main feature. The extracted terminal points are labeled according to a structural-feature distribution map prepared for each category. The generated labels are matched with template label sets constructed by statistical analysis. The characteristics of the method are as follows: (1) it copes with distortion of hand-written characters by using distribution maps for the positions and directions of feature points, and (2) distribution maps can be automatically generated from statistical data in learning samples and easily tuned interactively. The merits of combining the two methods are as follows: (1) the advantages of both pattern matching and structural analysis are obtained, (2) the probabilities of steps 2 and 3 needing to be executed are 22% and 9% respectively, which hardly affect the total processing time, and (3) as a result of steps 1 and 2, only a small number of special logics are required. In a test using unconstrained hand-written characters of low quality, the recognition rate and substitution
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.
Improved numerical methods for turbulent viscous recirculating flows
NASA Technical Reports Server (NTRS)
Vandoormaal, J. P.; Turan, A.; Raithby, G. D.
1986-01-01
The objective of the present study is to improve both the accuracy and computational efficiency of existing numerical techniques used to predict viscous recirculating flows in combustors. A review of the status of the study is presented along with some illustrative results. The effort to improve the numerical techniques consists of the following technical tasks: (1) selection of numerical techniques to be evaluated; (2) two dimensional evaluation of selected techniques; and (3) three dimensional evaluation of technique(s) recommended in Task 2.
Numerical methods for incompressible viscous flows with engineering applications
NASA Technical Reports Server (NTRS)
Rose, M. E.; Ash, R. L.
1988-01-01
A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems.
Numerical methods for problems involving the Drazin inverse
NASA Technical Reports Server (NTRS)
Meyer, C. D., Jr.
1979-01-01
The objective was to try to develop a useful numerical algorithm for the Drazin inverse and to analyze the numerical aspects of the applications of the Drazin inverse relating to the study of homogeneous Markov chains and systems of linear differential equations with singular coefficient matrices. It is felt that all objectives were accomplished with a measurable degree of success.
Reduced-complexity numerical method for optimal gate synthesis
NASA Astrophysics Data System (ADS)
Sridharan, Srinivas; Gu, Mile; James, Matthew R.; McEneaney, William M.
2010-10-01
Although quantum computers have the potential to efficiently solve certain problems considered difficult by known classical approaches, the design of a quantum circuit remains computationally difficult. It is known that the optimal gate-design problem is equivalent to the solution of an associated optimal-control problem; the solution to which is also computationally intensive. Hence, in this article, we introduce the application of a class of numerical methods (termed the max-plus curse of dimensionality-free techniques) that determine the optimal control, thereby synthesizing the desired unitary gate. The application of this technique to quantum systems has a growth in complexity that depends on the cardinality of the control-set approximation rather than the much larger growth with respect to spatial dimensions in approaches based on gridding of the space, which is used in previous research. This technique is demonstrated by obtaining an approximate solution for the gate synthesis on SU(4)—a problem that is computationally intractable by grid-based approaches.
Numerical Simulation of Tubular Pumping Systems with Different Regulation Methods
NASA Astrophysics Data System (ADS)
Zhu, Honggeng; Zhang, Rentian; Deng, Dongsheng; Feng, Xusong; Yao, Linbi
2010-06-01
Since the flow in tubular pumping systems is basically along axial direction and passes symmetrically through the impeller, most satisfying the basic hypotheses in the design of impeller and having higher pumping system efficiency in comparison with vertical pumping system, they are being widely applied to low-head pumping engineering. In a pumping station, the fluctuation of water levels in the sump and discharge pool is most common and at most time the pumping system runs under off-design conditions. Hence, the operation of pump has to be flexibly regulated to meet the needs of flow rates, and the selection of regulation method is as important as that of pump to reduce operation cost and achieve economic operation. In this paper, the three dimensional time-averaged Navier-Stokes equations are closed by RNG κ-ɛ turbulent model, and two tubular pumping systems with different regulation methods, equipped with the same pump model but with different designed system structures, are numerically simulated respectively to predict the pumping system performances and analyze the influence of regulation device and help designers make final decision in the selection of design schemes. The computed results indicate that the pumping system with blade-adjusting device needs longer suction box, and the increased hydraulic loss will lower the pumping system efficiency in the order of 1.5%. The pumping system with permanent magnet motor, by means of variable speed regulation, obtains higher system efficiency partly for shorter suction box and partly for different structure design. Nowadays, the varied speed regulation is realized by varied frequency device, the energy consumption of which is about 3˜4% of output power of the motor. Hence, when the efficiency of variable frequency device is considered, the total pumping system efficiency will probably be lower.
Numerical simulation of a low-emission gas turbine combustor using KIVA-II
NASA Technical Reports Server (NTRS)
Yang, S. L.; Chen, R.; Cline, M. C.; Nguyen, H. L.; Micklow, G. J.
1992-01-01
A modified version of the KIVA-II code was used to obtain a multidimensional numerical solution for the turbulent two-phase chemically reacting flows inside a staged turbine combustor (STC). The STC under consideration is equipped with an advanced airblast fuel nozzle and encompasses a fuel nozzle (FN), a rich-burn (RB) zone, a converging connecting pipe, a quick-quench (QQ) zone, a diverging connecting pipe, and a lean-combustion (LC) zone. The STC was divided into two subsystems, namely, FN/RB zone and QQ/LC zones, and the numerical solutions were obtained separately for each subsystem. Preliminary data characterize the major features of the flow and temperature fields inside the STC. Information on velocity, temperature, and some critical species in the FN/RB zone is presented. In the QQ/LC zones, formation of the co- and counter-rotating bulk flow and the sandwiched-ring-shaped temperature field can be clearly seen. The calculations of the mass-weighted standard deviation and the pattern factor of temperature indicated that the mixing performance of the STC is very promising.
NASA Astrophysics Data System (ADS)
Kong, Qingzhao; Fan, Shuli; Mo, Y. L.; Song, Gangbing
2017-09-01
The newly developed spherical smart aggregate (SSA) based on a radially polarized spherical piezoceramic shell element has unique omnidirectional actuating and sensing capabilities that can greatly improve the detection aperture and provide additional functionalities in health monitoring applications in concrete structures. Detailed fabrication procedures and electrical characterization of the SSA have been previously studied (Part I). In this second paper (Part II), the functionalities of the SSA used in both active sensing and passive sensing approaches were investigated in experiments and numerical simulations. One SSA sample was embedded in a 1 ft3 concrete specimen. In the active sensing approach, the SSA was first utilized as an actuator to generate stress waves and six conventional smart aggregates (SA) mounted on the six faces of the concrete cube were utilized as sensors to detect the wave response. Conversely, the embedded SSA was then utilized as a sensor to successively detect the wave response from each SA. The experimentally obtained behavior of the SSA was then compared with the numerical simulation results. Further, a series of impact tests were conducted to verify the performance of the SSA in the detection of the impact events from different directions. Comparison with the wave response associated with different faces of the cube verified the omnidirectional actuating and sensing capabilities of the SSA.
Kamalian, Morteza; Prilepsky, Jaroslaw E; Le, Son Thai; Turitsyn, Sergei K
2016-08-08
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.
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…
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…
NASA Astrophysics Data System (ADS)
Fossum, Kristian; Mannseth, Trond
2014-11-01
We assess and compare parameter sampling capabilities of one sequential and one simultaneous Bayesian, ensemble-based, joint state-parameter (JS) estimation method. In the companion paper, part I (Fossum and Mannseth 2014 Inverse Problems 30 114002), analytical investigations lead us to propose three claims, essentially stating that the sequential method can be expected to outperform the simultaneous method for weakly nonlinear forward models. Here, we assess the reliability and robustness of these claims through statistical analysis of results from a range of numerical experiments. Samples generated by the two approximate JS methods are compared to samples from the posterior distribution generated by a Markov chain Monte Carlo method, using four approximate measures of distance between probability distributions. Forward-model nonlinearity is assessed from a stochastic nonlinearity measure allowing for sufficiently large model dimensions. Both toy models (with low computational complexity, and where the nonlinearity is fairly easy to control) and two-phase porous-media flow models (corresponding to down-scaled versions of problems to which the JS methods have been frequently applied recently) are considered in the numerical experiments. Results from the statistical analysis show strong support of all three claims stated in part I.
A method of numerically controlled machine part programming
NASA Technical Reports Server (NTRS)
1970-01-01
Computer program is designed for automatically programmed tools. Preprocessor computes desired tool path and postprocessor computes actual commands causing machine tool to follow specific path. It is used on a Cincinnati ATC-430 numerically controlled machine tool.
Acoustic tensometry. II - Methods and apparatus /survey/
NASA Astrophysics Data System (ADS)
Bobrenko, V. M.; Kutsenko, A. N.; Sheremetikov, A. S.
1981-08-01
Acoustic methods for determining the stress-strain state of a solid are analyzed; the methods are based on the results obtained in a previous article on acoustic tensometry (Bobrenko et al., 1980), as well as other literature and patent information on the subject. The analysis, relevant to factory conditions, is broken down into a study of three methods: (1) the measurement of absolute propagation times of ultrasonic space waves; (2) the measurement of absolute velocities of Rayleigh waves; and (3) the measurement of acoustic anisotrophy. Features of the acoustic and electronic units, and the demands imposed on the transducers are also considered. Practical recommendations are given for using the acoustic methods, depending on the relative dimensions of the testpieces.
Acoustic tensometry. II - Methods and apparatus /survey/
NASA Astrophysics Data System (ADS)
Bobrenko, V. M.; Kutsenko, A. N.; Sheremetikov, A. S.
1980-12-01
Acoustic methods for determining the stress-strain state of a solid are analyzed; the methods are based on the results obtained in a previous article on acoustic tensometry (Bobrenko et al., 1980), as well as other literature and patent information on the subject. The analysis, relevant to factory conditions, is broken down into a study of three methods: (1) the measurement of absolute propagation times of ultrasonic space waves; (2) the measurement of absolute velocities of Rayleigh waves; and (3) the measurement of acoustic anisotrophy. Features of the acoustic and electronic units, and the demands imposed on the transducers are also considered. Practical recommendations are given for using the acoustic methods, depending on the relative dimensions of the testpieces.
Basic numerical methods. [of unsteady and transonic flow
NASA Technical Reports Server (NTRS)
Steger, Joseph L.; Van Dalsem, William R.
1989-01-01
Some of the basic finite-difference schemes that can be used to solve the nonlinear equations that describe unsteady inviscid and viscous transonic flow are reviewed. Numerical schemes for solving the unsteady Euler and Navier-Stokes, boundary-layer, and nonlinear potential equations are described. Emphasis is given to the elementary ideas used in constructing various numerical procedures, not specific details of any one procedure.
Thamsen, Bente; Blümel, Bastian; Schaller, Jens; Paschereit, Christian O; Affeld, Klaus; Goubergrits, Leonid; Kertzscher, Ulrich
2015-08-01
Implantable left ventricular assist devices (LVADs) became the therapy of choice in treating end-stage heart failure. Although survival improved substantially and is similar in currently clinically implanted LVADs HeartMate II (HM II) and HeartWare HVAD, complications related to blood trauma are frequently observed. The aim of this study was to compare these two pumps regarding their potential blood trauma employing computational fluid dynamics. High-resolution structured grids were generated for the pumps. Newtonian flow was calculated, solving Reynolds-averaged Navier-Stokes equations with a sliding mesh approach and a k-ω shear stress transport turbulence model for the operating point of 4.5 L/min and 80 mm Hg. The pumps were compared in terms of volumes subjected to certain viscous shear stress thresholds, below which no trauma was assumed (von Willebrand factor cleavage: 9 Pa, platelet activation: 50 Pa, and hemolysis: 150 Pa), and associated residence times. Additionally, a hemolysis index was calculated based on a Eulerian transport approach. Twenty-two percent of larger volumes above 9 Pa were observed in the HVAD; above 50 Pa and 150 Pa the differences between the two pumps were marginal. Residence times were higher in the HVAD for all thresholds. The hemolysis index was almost equal for the HM II and HVAD. Besides the gap regions in both pumps, the inlet regions of the rotor and diffuser blades have a high hemolysis production in the HM II, whereas in the HVAD, the volute tongue is an additional site for hemolysis production. Thus, in this study, the comparison of the HM II and the HVAD using numerical methods indicated an overall similar tendency to blood trauma in both pumps. However, influences of turbulent shear stresses were not considered and effects of the pivot bearing in the HM II were not taken into account. Further in vitro investigations are required. Copyright © 2015 International Center for Artificial Organs and Transplantation and
Porcine sperm vitrification II: Spheres method.
Arraztoa, C C; Miragaya, M H; Chaves, M G; Trasorras, V L; Gambarotta, M C; Neild, D M
2016-11-10
Owing to current problems in boar sperm cryopreservation, this study proposes to evaluate vitrification in spheres as an alternative cryopreservation procedure, comparing the use or not of permeable cryoprotectants and two warming methods. Extended (n = 3; r = 4) and raw (n = 5; r = 2) porcine spermatozoa were diluted in media, in the absence or presence of either 4% dimethylformamide or 4% glycerol, to a final concentration of 5 × 10(6) spermatozoa/ml and vitrified using the spheres method. Two warming procedures were evaluated: a rapid method (30 s at 37°C) and an ultrarapid method (7 s at 75°C, followed by 30 s at 37°C). Percentages of total motility (phase contrast), membrane function (hypo-osmotic swelling test), acrosome integrity (phase contrast), sperm viability (6-carboxyfluorescein diacetate and propidium iodide stain), chromatin condensation (toluidine blue stain) and chromatin susceptibility to acid denaturation (acridine orange stain) were evaluated in the samples before and after vitrification. Results, analysed using Friedman's test, suggest that rapid warming of raw porcine spermatozoa vitrified without permeable cryoprotectants may preserve DNA condensation and integrity better than the other processing methods studied in this work. Hence, porcine sperm vitrification using spheres could be used to produce embryos with ICSI to further validate this method.
Numerical tracing of energetic electron microsignatures: methods and applications
NASA Astrophysics Data System (ADS)
Andriopoulou, M.; Roussos, E.; Krupp, N.; Paranicas, C.; Thomsen, M. F.; Krimigis, S. M.; Dougherty, M. K.
2012-12-01
One of the most sensitive methods to measure weak, non-corotational velocity components in Saturn's magnetosphere is the detection and analysis of the energetic electron microsignature locations. Microsignatures are typically very sharp and narrow energetic electron flux dropouts observed in the inner saturnian magnetosphere and at locations that map magnetically close to the orbits of the planet's icy moons. Microsignatures form after the drifting electrons encounter one of these moons and get absorbed. Since the resulting cavities cannot refill within the local, moon-magnetosphere interaction region, they propagate in the magnetosphere with the properties of the pre-depleted energetic electrons. Microsignatures may survive up to 1.5 rotations around the planet, and for that reason they are excellent tools for tracing the shape of the magnetospheric particle drift shells. In all tracing studies up to now, however, calculations were performed assuming a dipole field configuration and corotation-driven azimuthal electric fields. These assumptions allow for straightforward, analytical solutions of the equations of motion. Aspects that are usually neglected are related to the detection of the microsignatures, such as the finite energy width and complex response of the detector channels that record the relevant signals. Furthermore, the role of the weak, non-corotational and/or non-dipolar drift components becomes important as the energy of the electrons increases, since corotation and magnetic drifts tend to cancel out between about 400 keV and few MeV. Neglecting these weak drifts at high energies can be a source of large systematic errors in the tracing procedure. In this study we demonstrate how all these assumptions and simplifications may affect the quality and the outcome of the microsignature analysis. We then show how the use of the correct system of equations and numerical tracing helps to understand all major observational aspects of microsignatures (e
Numerical simulations of multicomponent ecological models with adaptive methods.
Owolabi, Kolade M; Patidar, Kailash C
2016-01-08
The study of dynamic relationship between a multi-species models has gained a huge amount of scientific interest over the years and will continue to maintain its dominance in both ecology and mathematical ecology in the years to come due to its practical relevance and universal existence. Some of its emergence phenomena include spatiotemporal patterns, oscillating solutions, multiple steady states and spatial pattern formation. Many time-dependent partial differential equations are found combining low-order nonlinear with higher-order linear terms. In attempt to obtain a reliable results of such problems, it is desirable to use higher-order methods in both space and time. Most computations heretofore are restricted to second order in time due to some difficulties introduced by the combination of stiffness and nonlinearity. Hence, the dynamics of a reaction-diffusion models considered in this paper permit the use of two classic mathematical ideas. As a result, we introduce higher order finite difference approximation for the spatial discretization, and advance the resulting system of ODE with a family of exponential time differencing schemes. We present the stability properties of these methods along with the extensive numerical simulations for a number of multi-species models. When the diffusivity is small many of the models considered in this paper are found to exhibit a form of localized spatiotemporal patterns. Such patterns are correctly captured in the local analysis of the model equations. An extended 2D results that are in agreement with Turing typical patterns such as stripes and spots, as well as irregular snakelike structures are presented. We finally show that the designed schemes are dynamically consistent. The dynamic complexities of some ecological models are studied by considering their linear stability analysis. Based on the choices of parameters in transforming the system into a dimensionless form, we were able to obtain a well-balanced system that
A Fast Numerical Method for a Nonlinear Black-Scholes Equation
NASA Astrophysics Data System (ADS)
Koleva, Miglena N.; Vulkov, Lubin G.
2009-11-01
In this paper we will present an effective numerical method for the Black-Scholes equation with transaction costs for the limiting price u(s, t;a). The technique combines the Rothe method with a two-grid (coarse-fine) algorithm for computation of numerical solutions to initial boundary-values problems to this equation. Numerical experiments for comparison the accuracy ant the computational cost of the method with other known numerical schemes are discussed.
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.
A numerical analysis method for evaluating rod lenses using the Monte Carlo method.
Yoshida, Shuhei; Horiuchi, Shuma; Ushiyama, Zenta; Yamamoto, Manabu
2010-12-20
We propose a numerical analysis method for evaluating GRIN lenses using the Monte Carlo method. Actual measurements of the modulation transfer function (MTF) of a GRIN lens using this method closely match those made by conventional methods. Experimentally, the MTF is measured using a square wave chart, and is then calculated based on the distribution of output strength on the chart. In contrast, the general method using computers evaluates the MTF based on a spot diagram made by an incident point light source. However the results differ greatly from those from experiments. We therefore developed an evaluation method similar to the experimental system based on the Monte Carlo method and verified that it more closely matches the experimental results than the conventional method.
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
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.
Modeling supersonic combustion using a fully-implicit numerical method
NASA Technical Reports Server (NTRS)
Maccormack, Robert W.; Wilson, Gregory J.
1990-01-01
A fully-implicit finite-volume algorithm for two-dimensional axisymmetric flows has been coupled to a detailed hydrogen-air reaction mechanism (13 species and 33 reactions) so that supersonic combustion phenomena may be investigated. Numerical computations are compared with ballistic-range shadowgraphs of Lehr (1972) that exhibit two discontinuities caused by a blunt body as it passes through a premixed stoichiometric hydrogen-air mixture. The suitability of the numerical procedure for simulating these double-front flows is shown. The requirements for the physical formulation and the numerical modeling of these flowfields are discussed. Finally, the sensitivity of these external flowfields to changes in certain key reaction rate constants is examined.
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.
Application of numerical methods to planetary radiowave scattering
NASA Technical Reports Server (NTRS)
Simpson, Richard A.; Tyler, G. Leonard
1987-01-01
Existing numerical techniques for the solution of scattering problems were investigated to determine those which might be applicable to planetary surface studies, with the goal of improving the interpretation of radar data from Venus, Mars, the Moon, and icy satellites. The general characteristics of the models are described along with computational concerns. In particular, the Numerical Electrogmatics Code (NEC) developed at the Lawrence Livermore Laboratory is discussed. Though not developed for random rough surfaces, the NEC contains elements which may be generalized and which could be valuable in the study of scattering by planetary surfaces.
A numerical method for the nonlinear oscillator problem
NASA Astrophysics Data System (ADS)
Killingbeck, J.; Jolicard, G.
1998-03-01
The treatment of a nonlinear Schrödinger equation with power law potential terms by means of hypervirial perturbation theory (HVPT) is considered. Previous workers have tried to handle the nonlinearity by constructing an HVPT which also contains a nonlinear term. We show that higher numerical accuracy can be obtained by reverting to the usual linear HVPT in combination with a simple numerical procedure. The procedure also works with finite-difference shooting calculations, which would permit the calculations to be extended to handle more general potentials.
Applying multi-resolution numerical methods to geodynamics
NASA Astrophysics Data System (ADS)
Davies, David Rhodri
Computational models yield inaccurate results if the underlying numerical grid fails to provide the necessary resolution to capture a simulation's important features. For the large-scale problems regularly encountered in geodynamics, inadequate grid resolution is a major concern. The majority of models involve multi-scale dynamics, being characterized by fine-scale upwelling and downwelling activity in a more passive, large-scale background flow. Such configurations, when coupled to the complex geometries involved, present a serious challenge for computational methods. Current techniques are unable to resolve localized features and, hence, such models cannot be solved efficiently. This thesis demonstrates, through a series of papers and closely-coupled appendices, how multi-resolution finite-element methods from the forefront of computational engineering can provide a means to address these issues. The problems examined achieve multi-resolution through one of two methods. In two-dimensions (2-D), automatic, unstructured mesh refinement procedures are utilized. Such methods improve the solution quality of convection dominated problems by adapting the grid automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. Thermal and thermo-chemical validation tests illustrate that the technique is robust and highly successful, improving solution accuracy whilst increasing computational efficiency. These points are reinforced when the technique is applied to geophysical simulations of mid-ocean ridge and subduction zone magmatism. To date, successful goal-orientated/error-guided grid adaptation techniques have not been utilized within the field of geodynamics. The work included herein is therefore the first geodynamical application of such methods. In view of the existing three-dimensional (3-D) spherical mantle dynamics codes, which are built upon a quasi-uniform discretization of the sphere and closely coupled
The Design of CAL Packages for Teaching Numerical Methods to Chemistry Students.
ERIC Educational Resources Information Center
Norris, A. C.
1979-01-01
Discusses the design of computational exercises useful for a course in numerical methods for chemists. Some of the exercises make use of available programs while others require the student to write programs incorporating numerical routines. The emphasis throughout is on the use of numerical methods to solve chemical problems. (Author)
Numerical Methods for Analysis of Charged Vacancy Diffusion in Dielectric Solids
2006-12-01
numerical solution dictate the practical choice of t∆ 10 ( Chapra and Canale, 1998). Let /B RD dk θ ξ= , where Rξ is a reference concentration per unit...H. A.; Wilkes, J. O. Applied Numerical Methods; Wiley: New York, 1969. Chapra , S. C.; Canale, R. P. Numerical Methods for Engineers with
Numerical modeling of shallow magma intrusions with finite element method
NASA Astrophysics Data System (ADS)
Chen, Tielin; Cheng, Shaozhen; Fang, Qian; Zhou, Cheng
2017-03-01
A numerical approach for simulation of magma intrusion process, considering the couplings of the stress distribution, the viscous fluid flow of magma, and the fracturing of host rock, has been developed to investigate the mechanisms of fracture initiation and propagation in host rock during magma intrusion without pre-placing a set of fractures. The study focused on the dike intrusions filled with injected viscous magma in shallow sediments. A series of numerical modellings were carried out to simulate the process of magma intrusion in host rocks, with particular attention on the magma propagation processes and the formation of intrusion shapes. The model materials were Mohr-Coulomb materials with tension failure and shear failure. The scenarios of both stochastically heterogeneous host rocks and layered host rocks were analyzed. The injected magma formed intrusions shapes of (a) dyke, (b) sill, (c) cup-shaped intrusion, (d) saucer-shaped intrusion. The numerical results were in agreement with the experimental and field observed results, which confirmed the adequacy and the power of the numerical approach.
Numerical Simulation of Turbulent Combustion Using Vortex Methods
1990-01-08
Electric Co., Schenectady, October 1988. 2. DOD and EPA Tyndall Conference on Halon, the Ozone Layer and Research on Alternative Chemicals, Tyndall...26th Aerospace Sciences Meetin , January 11-14, Reno, Nevada, AIAA-88-0729. 13. Ghoniem A.F., and Ng K.K., Numerical study of a forced shear layet
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
NASA Astrophysics Data System (ADS)
Ying, Teh Yuan; Yaacob, Nazeeruddin
2013-04-01
In this paper, a new implicit Runge-Kutta method which based on a 4-point Gauss-Kronrod-Radau II quadrature formula is developed. The resulting implicit method is a 4-stage sixth order Gauss-Kronrod-Radau IIA method, or in brief as GKRM(4,6)-IIA. GKRM(4,6)-IIA requires four function of evaluations at each integration step and it gives accuracy of order six. In addition, GKRM(4,6)-IIA has stage order four and being L-stable. Numerical experiments compare the accuracy between GKRM(4,6)-IIA and the classical 3-stage sixth order Gauss-Legendre method in solving some test problems. Numerical results reveal that GKRM(4,6)-IIA is more accurate than the 3-stage sixth order Gauss-Legendre method because GKRM(4,6)-IIA has higher stage order.
Numerical Simulation of Turbulent Flames using Vortex Methods.
1987-10-05
0 elemen, *’s isert-: h3.- cntrSu:g’*. , upt tti=J 1 51’ an:e n eltoe- aorc log t,. the coert .. of -s dj.;te for to e toree eiements. A b; ") r Dy...0.0 , opened to form a rectilinear vortex, the waves * 2 4 a ii will like a corkscrew spinning at frequency ). The sense of rotations of the waves Is
Subleading poles in the numerical unitarity method at two loops
NASA Astrophysics Data System (ADS)
Abreu, S.; Febres Cordero, F.; Ita, H.; Jaquier, M.; Page, B.
2017-05-01
We describe the unitarity approach for the numerical computation of two-loop integral coefficients of scattering amplitudes. It is well known that the leading propagator singularities of an amplitude's integrand are related to products of tree amplitudes. At two loops, Feynman diagrams with doubled propagators appear naturally, which lead to subleading pole contributions. In general, it is not known how these contributions can be directly expressed in terms of a product of on-shell tree amplitudes. We present a universal algorithm to extract these subleading pole terms by releasing some of the on-shell conditions. We demonstrate the new approach by numerically computing two-loop four-gluon integral coefficients.
A method for direct numerical integration of the Boltzmann equation
NASA Technical Reports Server (NTRS)
Cheremisin, F. G.
1972-01-01
The principal difficulties in numerical solution of the Boltzmann equation are considered. The study is aimed at formulating a numerical solution in such a manner that it contains a minimum amount of excess information at the distribution function level. It is pointed out that the accurate calculation of the distribution function at each point in phase space requires a tremendous number of operations, due to the necessity of solving five-fold quadratures in the collision integral. This results in the operational memory of the digital computer being insufficient to store all the data on the distribution functions at the necessary points in phase space. An algorithm is constructed involving successive iterations of the Boltzmann equation which does not require storage of each step of the new distribution function.
Some variance reduction methods for numerical stochastic homogenization.
Blanc, X; Le Bris, C; Legoll, F
2016-04-28
We give an overview of a series of recent studies devoted to variance reduction techniques for numerical stochastic homogenization. Numerical homogenization requires that a set of problems is solved at the microscale, the so-called corrector problems. In a random environment, these problems are stochastic and therefore need to be repeatedly solved, for several configurations of the medium considered. An empirical average over all configurations is then performed using the Monte Carlo approach, so as to approximate the effective coefficients necessary to determine the macroscopic behaviour. Variance severely affects the accuracy and the cost of such computations. Variance reduction approaches, borrowed from other contexts in the engineering sciences, can be useful. Some of these variance reduction techniques are presented, studied and tested here.
Variable inertia method: A novel numerical method for mantle convection simulation
NASA Astrophysics Data System (ADS)
Takeyama, Kosuke; Saitoh, Takayuki R.; Makino, Junichiro
2017-01-01
3D numerical simulations have been very useful for the understanding of mantle convection of the earth. In almost all previous simulations of mantle convection, the (extended) Boussinesq approximation has been used. This method is implicit in the sense that buoyancy force and viscosity are balanced, and allows the use of long timesteps that are not limited by the CFL condition. However, the resulting matrix is ill-conditioned, in particular since the viscosity strongly depends on the temperature. It is not well-suited to modern large-scale parallel machines. In this paper, we propose an explicit method which can be used to solve the mantle convection problem. If we can reduce the sound speed without changing the characteristics of the flow, we can increase the timestep and thus can use the explicit method. In order to reduce the sound speed, we multiplied the inertia term of the equation of motion by a large and viscosity-dependent coefficient. Theoretically, we can expect that this modification would not change the flow as long as the Reynolds number and the Mach number are sufficiently smaller than unity. We call this method the variable inertia method (VIM). We have performed an extensive set of numerical tests of the proposed method for thermal convection, and concluded that it works well. In particular, it can handle differences in viscosity of more than five orders of magnitude.
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.
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).
Numerical conformal mapping: Methods, applications, and theory. Final report
DeLillo, T.K.
1995-11-01
Section 1 of this report, briefly summarizes research performed under this grant during the first two years 1992 to 1994 and makes some overall remarks. Section 2, summarizes research performed during the final year from September, 1994 through May 31, 1995, more fully. The main achievement of the last period has been the application of numerical conformed mapping to the solution of the biharmonic equation. Section 3, summarizes travel, meetings, and other expenses supported by this grant during the final year.
Improved numerical methods for turbulent viscous recirculating flows
NASA Technical Reports Server (NTRS)
Turan, A.
1985-01-01
The hybrid-upwind finite difference schemes employed in generally available combustor codes possess excessive numerical diffusion errors which preclude accurate quantative calculations. The present study has as its primary objective the identification and assessment of an improved solution algorithm as well as discretization schemes applicable to analysis of turbulent viscous recirculating flows. The assessment is carried out primarily in two dimensional/axisymetric geometries with a view to identifying an appropriate technique to be incorporated in a three-dimensional code.
Overview: Applications of numerical optimization methods to helicopter design problems
NASA Technical Reports Server (NTRS)
Miura, H.
1984-01-01
There are a number of helicopter design problems that are well suited to applications of numerical design optimization techniques. Adequate implementation of this technology will provide high pay-offs. There are a number of numerical optimization programs available, and there are many excellent response/performance analysis programs developed or being developed. But integration of these programs in a form that is usable in the design phase should be recognized as important. It is also necessary to attract the attention of engineers engaged in the development of analysis capabilities and to make them aware that analysis capabilities are much more powerful if integrated into design oriented codes. Frequently, the shortcoming of analysis capabilities are revealed by coupling them with an optimization code. Most of the published work has addressed problems in preliminary system design, rotor system/blade design or airframe design. Very few published results were found in acoustics, aerodynamics and control system design. Currently major efforts are focused on vibration reduction, and aerodynamics/acoustics applications appear to be growing fast. The development of a computer program system to integrate the multiple disciplines required in helicopter design with numerical optimization technique is needed. Activities in Britain, Germany and Poland are identified, but no published results from France, Italy, the USSR or Japan were found.
Sources of Chaos in Planetary Systems Formed Through Numerical Methods
NASA Astrophysics Data System (ADS)
Clement, Matthew S.
2017-01-01
The formation of the solar system’s terrestrial planets has been numerically modeled in countless works, and many other studies have been devoted to char- acterizing our modern planets’ chaotic dynamical state. However, it is still not known whether our planets fragile chaotic state is an expected outcome of terrestrial planet accretion. We use a large suite of numerical simulations to present a detailed analysis and characterization of the dynamical chaos in 145 different systems produced via terrestrial planet formation in Kaib & Cowan (2015). These systems were created in the presence of a fully formed Jupiter and Saturn, using a variety of different initial conditions. We provide the first analysis of the dynamical states of fully evolved (4.5 Gyr) planetary systems formed using numerical simulations. We find that dynamical chaos is preva- lent in roughly half of the systems, with the largest source of the chaos being perturbations from Jupiter. Chaos is most prevalent in systems that form 4 or 5 terrestrial planets. Additionally, an eccentric Jupiter and Saturn is shown to enhance the prevalence of chaos in systems. Furthermore, systems with a center of mass highly concentrated between 0.8-1.2 AU generally prove to be less chaotic than systems with more exotic mass distributions. Through the process of evolving systems to the current epoch, we show that late instabilities are quite common in our systems. Of greatest interest, many of the sources of chaos observed in our own solar system (such as the secularly driven chaos between Mercury and Jupiter) are shown to be common outcomes of terrestrial planetary formation. Thus, the solar system’s marginally stable, chaotic state may naturally arise from the process of terrestrial planet formation.
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.
Path Integrals and Exotic Options:. Methods and Numerical Results
NASA Astrophysics Data System (ADS)
Bormetti, G.; Montagna, G.; Moreni, N.; Nicrosini, O.
2005-09-01
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price path dependent options on multidimensional and correlated underlying assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the case of Asian call options. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at the money (ATM) and out of the money (OTM) options, path integral exhibits competitive performances.
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.
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.
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).
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.
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. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.
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.
Method for numerical simulation of two-term exponentially correlated colored noise
Yilmaz, B.; Ayik, S.; Abe, Y.; Gokalp, A.; Yilmaz, O.
2006-04-15
A method for numerical simulation of two-term exponentially correlated colored noise is proposed. The method is an extension of traditional method for one-term exponentially correlated colored noise. The validity of the algorithm is tested by comparing numerical simulations with analytical results in two physical applications.
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.
A Fractional PDE Approach to Turbulent Mixing; Part II: Numerical Simulation
NASA Astrophysics Data System (ADS)
Samiee, Mehdi; Zayernouri, Mohsen
2016-11-01
We propose a generalizing fractional order transport model of advection-diffusion kind with fractional time- and space-derivatives, governing the evolution of passive scalar turbulence. This approach allows one to incorporate the nonlocal and memory effects in the underlying anomalous diffusion i.e., sub-to-standard diffusion to model the trapping of particles inside the eddied, and super-diffusion associated with the sudden jumps of particles from one coherent region to another. For this nonlocal model, we develop a high order numerical (spectral) method in addition to a fast solver, examined in the context of some canonical problems. PhD student, Department of Mechanical Engineering, & Department Computational Mathematics, Science, and Engineering.
MODELING COLLISIONAL CASCADES IN DEBRIS DISKS: THE NUMERICAL METHOD
Gaspar, Andras; Psaltis, Dimitrios; Oezel, Feryal; Rieke, George H.; Cooney, Alan E-mail: dpsaltis@as.arizona.edu E-mail: grieke@as.arizona.edu
2012-04-10
We develop a new numerical algorithm to model collisional cascades in debris disks. Because of the large dynamical range in particle masses, we solve the integro-differential equations describing erosive and catastrophic collisions in a particle-in-a-box approach, while treating the orbital dynamics of the particles in an approximate fashion. We employ a new scheme for describing erosive (cratering) collisions that yields a continuous set of outcomes as a function of colliding masses. We demonstrate the stability and convergence characteristics of our algorithm and compare it with other treatments. We show that incorporating the effects of erosive collisions results in a decay of the particle distribution that is significantly faster than with purely catastrophic collisions.
[Numerical flow simulation : A new method for assessing nasal breathing].
Hildebrandt, T; Osman, J; Goubergrits, L
2016-08-01
The current options for objective assessment of nasal breathing are limited. The maximum they can determine is the total nasal resistance. Possibilities to analyze the endonasal airstream are lacking. In contrast, numerical flow simulation is able to provide detailed information of the flow field within the nasal cavity. Thus, it has the potential to analyze the nasal airstream of an individual patient in a comprehensive manner and only a computed tomography (CT) scan of the paranasal sinuses is required. The clinical application is still limited due to the necessary technical and personnel resources. In particular, a statistically based referential characterization of normal nasal breathing does not yet exist in order to be able to compare and classify the simulation results.
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.
A new numerical method for shock wave propagation based on geometrical shock dynamics
NASA Astrophysics Data System (ADS)
Schwendeman, D. W.
1993-05-01
In this paper, a new numerical method for calculating the motion of shock waves in two and three dimensions is presented. The numerical method is based on Whitham's theory of geometrical shock dynamics, which is an approximate theory that determines the motion of the leading shockfront explicitly. The numerical method uses a conservative finite difference discretization of the equations of geometrical shock dynamics. These equations are similar to those for steady supersonic potential flow, and thus the numerical method developed here is similar to ones developed for that context. Numerical results are presented for shock propagation in channels and for converging cylindrical and spherical shocks. The channel problem is used in part to compare this new numerical method with ones developed earlier. Converging cylindrical and spherical shocks arc calculated to analyze their stability.
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.
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)
PROSO II--a new method for protein solubility prediction.
Smialowski, Pawel; Doose, Gero; Torkler, Phillipp; Kaufmann, Stefanie; Frishman, Dmitrij
2012-06-01
Many fields of science and industry depend on efficient production of active protein using heterologous expression in Escherichia coli. The solubility of proteins upon expression is dependent on their amino acid sequence. Prediction of solubility from sequence is therefore highly valuable. We present a novel machine-learning-based model called PROSO II which makes use of new classification methods and growth in experimental data to improve coverage and accuracy of solubility predictions. The classification algorithm is organized as a two-layered structure in which the output of a primary Parzen window model for sequence similarity and a logistic regression classifier of amino acid k-mer composition serve as input for a second-level logistic regression classifier. Compared with previously published research our model is trained on five times more data than used by any other method before (82 000 proteins). When tested on a separate holdout set not used at any point of method development our server attained the best results in comparison with other currently available methods: accuracy 75.4%, Matthew's correlation coefficient 0.39, sensitivity 0.731, specificity 0.759, gain (soluble) 2.263. In summary, due to utilization of cutting edge machine learning technologies combined with the largest currently available experimental data set the PROSO II server constitutes a substantial improvement in protein solubility predictions. PROSO II is available at http://mips.helmholtz-muenchen.de/prosoII. © 2012 The Authors Journal compilation © 2012 FEBS.
A numerical oil spill model based on a hybrid method.
Guo, W J; Wang, Y X
2009-05-01
The purpose of this paper is the development of a hybrid particle tracking/Eulerian-Lagrangian approach for the simulation of spilled oil in coastal areas. Oil discharge from the source is modeled by the release of particles. When the oil slick thickness or the oil concentration reaches a critical value, particles are mapped on slick thickness or node concentrations, and the calculations proceed in the Eulerian-Lagrangian mode. To acquire accurate environment information, the model is coupled with the 3-D free-surface hydrodynamics model (POM) and the third-generation wave model (SWAN). By simulating the oil processes of spreading, advection, turbulent diffusion, evaporation, emulsification, dissolution and shoreline deposition, it has the ability to predict the horizontal movement of surface oil slick, the vertical distribution of oil particles, the concentration in the water column and the mass balance of spilled oil. An accidental oil release near Dalian coastal waters is simulated to validate the developed model. Compared with the satellite images of oil slicks on the surface, the numerical results indicate that the model has a reasonable accuracy.
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.
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.
Hybrid Particle-Continuum Numerical Methods for Aerospace Applications
2011-01-01
solution of the Navier-Stokes equations with modern computational uid dynamics ( CFD ) can be found eciently with very little loss in physical accuracy...lee side. During the skip portion, the CFD simulation method over-predict the measurements by over a factor of two. Based on the reconstructed data...macroscopic methods ( CFD ) on the after-body of the AS-202 ight capsule and comparison with experimental ight data [14] Figure 3: Reconstruction of
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; Strauss, Du Toit 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.
NASA Astrophysics Data System (ADS)
Min, Xiaoyi
This thesis first presents the study of the interaction of electromagnetic waves with three-dimensional heterogeneous, dielectric, magnetic, and lossy bodies by surface integral equation modeling. Based on the equivalence principle, a set of coupled surface integral equations is formulated and then solved numerically by the method of moments. Triangular elements are used to model the interfaces of the heterogeneous body, and vector basis functions are defined to expand the unknown current in the formulation. The validity of this formulation is verified by applying it to concentric spheres for which an exact solution exists. The potential applications of this formulation to a partially coated sphere and a homogeneous human body are discussed. Next, this thesis also introduces an efficient new set of integral equations for treating the scattering problem of a perfectly conducting body coated with a thin magnetically lossy layer. These electric field integral equations and magnetic field integral equations are numerically solved by the method of moments (MoM). To validate the derived integral equations, an alternative method to solve the scattering problem of an infinite circular cylinder coated with a thin magnetic lossy layer has also been developed, based on the eigenmode expansion. Results for the radar cross section and current densities via the MoM and the eigenmode expansion method are compared. The agreement is excellent. The finite difference time domain method is subsequently implemented to solve a metallic object coated with a magnetic thin layer and numerical results are compared with that by the MoM. Finally, this thesis presents an application of the finite-difference time-domain approach to the problem of electromagnetic receiving and scattering by a cavity -backed antenna situated on an infinite conducting plane. This application involves modifications of Yee's model, which applies the difference approximations of field derivatives to differential
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.
NASA Astrophysics Data System (ADS)
Nguyen, Tam H.; Song, Junho; Paulino, Glaucio H.
2008-02-01
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 [2]. 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 (Part I, [1]) 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.
Numeric character recognition method based on fractal dimension
NASA Astrophysics Data System (ADS)
He, Tao; Xie, Yulang; Chen, Jiuyin; Cheng, Longfei; Yuan, Ye
2013-10-01
An image processing method based on fractal dimension is proposed in this paper. This method uses fractal dimension to process the character images firstly, and rises the analysis of each grid to the analysis of interrelation between the grids to eliminate interference. Box-counting method is commonly used for calculating fractal dimension of fractal, which uses small box whose side length is r ,that is the topological dimension of the box is d, to cover up the image. Because there are various levels of cavities and cracks, some small boxes are empty and some small boxes cover a part of fractal image which is called non-empty box (here refers to the average gray of the part that contained in the small box is larger than a certain threshold). We note down the number of non-empty boxes, analyze and calculate them. The method is used to image process the polluted characters, which can remove ink and scratches around the contour of the characters and remain basic contour, then the characters can be recognized by using template matching. In computer simulation experiment for polluted character recognition, this method can recognize the polluted characters quickly, which improve the accuracy of the recognition of the polluted characters.
Solution to the Eddy-Current Problem for Type-II Superconductors by Relaxation Method
NASA Astrophysics Data System (ADS)
Janíková, Edita; Slodička, Marián
2008-09-01
The fast developing industrial applications of superconductors require rigorous mathematical models of their physical behaviour and efficient numerical methods to solve them. We propose and study theoretically a new approximation scheme to solve the 3D eddy-current problem of diffusion of the electric field in type-II superconductors. The method is based on the relaxation principle, where the nonlinear time- and space-dependent partial differential equation (PDE) is split into a linear time-independent PDE coupled with a nonlinear equation involving no partial derivatives.
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.
Zhang, Jie; Draxl, Caroline; Hopson, Thomas; Monache, Luca Delle; Vanvyve, Emilie; Hodge, Bri-Mathias
2015-10-01
Numerical weather prediction (NWP) models have been widely used for wind resource assessment. Model runs with higher spatial resolution are generally more accurate, yet extremely computational expensive. An alternative approach is to use data generated by a low resolution NWP model, in conjunction with statistical methods. In order to analyze the accuracy and computational efficiency of different types of NWP-based wind resource assessment methods, this paper performs a comparison of three deterministic and probabilistic NWP-based wind resource assessment methodologies: (i) a coarse resolution (0.5 degrees x 0.67 degrees) global reanalysis data set, the Modern-Era Retrospective Analysis for Research and Applications (MERRA); (ii) an analog ensemble methodology based on the MERRA, which provides both deterministic and probabilistic predictions; and (iii) a fine resolution (2-km) NWP data set, the Wind Integration National Dataset (WIND) Toolkit, based on the Weather Research and Forecasting model. Results show that: (i) as expected, the analog ensemble and WIND Toolkit perform significantly better than MERRA confirming their ability to downscale coarse estimates; (ii) the analog ensemble provides the best estimate of the multi-year wind distribution at seven of the nine sites, while the WIND Toolkit is the best at one site; (iii) the WIND Toolkit is more accurate in estimating the distribution of hourly wind speed differences, which characterizes the wind variability, at five of the available sites, with the analog ensemble being best at the remaining four locations; and (iv) the analog ensemble computational cost is negligible, whereas the WIND Toolkit requires large computational resources. Future efforts could focus on the combination of the analog ensemble with intermediate resolution (e.g., 10-15 km) NWP estimates, to considerably reduce the computational burden, while providing accurate deterministic estimates and reliable probabilistic assessments.
Numerical method for the stochastic projected Gross-Pitaevskii equation
NASA Astrophysics Data System (ADS)
Rooney, S. J.; Blakie, P. B.; Bradley, A. S.
2014-01-01
We present a method for solving the stochastic projected Gross-Pitaevskii equation (SPGPE) for a three-dimensional weakly interacting Bose gas in a harmonic-oscillator trapping potential. The SPGPE contains the challenge of both accurately evolving all modes in the low-energy classical region of the system, and evaluating terms from the number-conserving scattering reservoir process. We give an accurate and efficient procedure for evaluating the scattering terms using a Hermite-polynomial based spectral-Galerkin representation, which allows us to precisely implement the low-energy mode restriction. Stochastic integration is performed using the weak semi-implicit Euler method. We extensively characterize the accuracy of our method, finding a faster-than-expected rate of stochastic convergence. Physical consistency of the algorithm is demonstrated by considering thermalization of initially random states.
Validation of a Numerical Method for Determining Liner Impedance
NASA Technical Reports Server (NTRS)
Watson, Willie R.; Jones, Michael G.; Tanner, Sharon E.; Parrott, Tony L.
1996-01-01
This paper reports the initial results of a test series to evaluate a method for determining the normal incidence impedance of a locally reacting acoustically absorbing liner, located on the lower wall of a duct in a grazing incidence, multi-modal, non-progressive acoustic wave environment without flow. This initial evaluation is accomplished by testing the methods' ability to converge to the known normal incidence impedance of a solid steel plate, and to the normal incidence impedance of an absorbing test specimen whose impedance was measured in a conventional normal incidence tube. The method is shown to converge to the normal incident impedance values and thus to be an adequate tool for determining the impedance of specimens in a grazing incidence, multi-modal, nonprogressive acoustic wave environment for a broad range of source frequencies.
Numerical method for the stochastic projected Gross-Pitaevskii equation.
Rooney, S J; Blakie, P B; Bradley, A S
2014-01-01
We present a method for solving the stochastic projected Gross-Pitaevskii equation (SPGPE) for a three-dimensional weakly interacting Bose gas in a harmonic-oscillator trapping potential. The SPGPE contains the challenge of both accurately evolving all modes in the low-energy classical region of the system, and evaluating terms from the number-conserving scattering reservoir process. We give an accurate and efficient procedure for evaluating the scattering terms using a Hermite-polynomial based spectral-Galerkin representation, which allows us to precisely implement the low-energy mode restriction. Stochastic integration is performed using the weak semi-implicit Euler method. We extensively characterize the accuracy of our method, finding a faster-than-expected rate of stochastic convergence. Physical consistency of the algorithm is demonstrated by considering thermalization of initially random states.
Numerical continuation methods for large-scale dissipative dynamical systems
NASA Astrophysics Data System (ADS)
Umbría, Juan Sánchez; Net, Marta
2016-11-01
A tutorial on continuation and bifurcation methods for the analysis of truncated dissipative partial differential equations is presented. It focuses on the computation of equilibria, periodic orbits, their loci of codimension-one bifurcations, and invariant tori. To make it more self-contained, it includes some definitions of basic concepts of dynamical systems, and some preliminaries on the general underlying techniques used to solve non-linear systems of equations by inexact Newton methods, and eigenvalue problems by means of subspace or Arnoldi iterations.
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
Svetov, Ivan; Maltseva, Svetlana; Polyakova, Anna
2016-08-10
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 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 simulation for the Gross-Pitaevskii equation based on the lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Wang, Huimin
2017-09-01
A lattice Boltzmann model for the Gross-Pitaevskii equation is proposed in this paper. Some numerical tests for one- and two-dimensional Gross-Pitaevskii equation have been conducted. The waves of the Gross-Pitaevskii equation are simulated. Numerical results show that the lattice Boltzmann method is an effective method for the wave of the Gross-Pitaevskii equation.
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.
On numerical methods for Hamiltonian PDEs and a collocation method for the Vlasov-Maxwell equations
Holloway, J.P.
1996-11-01
Hamiltonian partial differential equations often have implicit conservation laws-constants of the motion-embedded within them. It is not, in general, possible to preserve these conservation laws simply by discretization in conservative form because there is frequently only one explicit conservation law. However, by using weighted residual methods and exploiting the Hamiltonian structure of the equations it is shown that at least some of the conservation laws are preserved in a method of lines (continuous in time). In particular, the Hamiltonian can always be exactly preserved as a constant of the motion. Other conservation laws, in particular linear and quadratic Casimirs and momenta, can sometimes be conserved too, depending on the details of the equations under consideration and the form of discretization employed. Collocation methods also offer automatic conservation of linear and quadratic Casimirs. Some standard discretization methods, when applied to Hamiltonian problems are shown to be derived from a numerical approximation to the exact Poisson bracket of the system. A method for the Vlasov-Maxwell equations based on Legendre-Gauss-Lobatto collocation is presented as an example of these ideas. 22 refs.
Ye, Jingfei; Wang, Wei; Gao, Zhishan; Liu, Zhiying; Wang, Shuai; Benítez, Pablo; Miñano, Juan C; Yuan, Qun
2015-10-05
Wavefront estimation from the slope-based sensing metrologies zis important in modern optical testing. A numerical orthogonal transformation method is proposed for deriving the numerical orthogonal gradient polynomials as numerical orthogonal basis functions for directly fitting the measured slope data and then converting to the wavefront in a straightforward way in the modal approach. The presented method can be employed in the wavefront estimation from its slopes over the general shaped aperture. Moreover, the numerical orthogonal transformation method could be applied to the wavefront estimation from its slope measurements over the dynamic varying aperture. The performance of the numerical orthogonal transformation method is discussed, demonstrated and verified by the examples. They indicate that the presented method is valid, accurate and easily implemented for wavefront estimation from its slopes.
Applications of numerical methods to simulate the movement of contaminants in groundwater.
Sun, N Z
1989-01-01
This paper reviews mathematical models and numerical methods that have been extensively used to simulate the movement of contaminants through the subsurface. The major emphasis is placed on the numerical methods of advection-dominated transport problems and inverse problems. Several mathematical models that are commonly used in field problems are listed. A variety of numerical solutions for three-dimensional models are introduced, including the multiple cell balance method that can be considered a variation of the finite element method. The multiple cell balance method is easy to understand and convenient for solving field problems. When the advection transport dominates the dispersion transport, two kinds of numerical difficulties, overshoot and numerical dispersion, are always involved in solving standard, finite difference methods and finite element methods. To overcome these numerical difficulties, various numerical techniques are developed, such as upstream weighting methods and moving point methods. A complete review of these methods is given and we also mention the problems of parameter identification, reliability analysis, and optimal-experiment design that are absolutely necessary for constructing a practical model. PMID:2695327
Globally Convergent Numerical Methods for Coefficient Inverse Problems
2008-09-23
Problems , 18, 209-219, 2002. 50. A.N. Tikhonov and V. Ya. Arsenin , Solutions of Ill - Posed Problems Winston & Sons. Washington...is because solutions of PDEs depend nonlinearly on their coefficients. The ill - posedness is a well known feature of inverse problems . This means that...ut (x, 0)‖L2(Ω) ≤ CK. Theorem 8.5 enables us to prove convergence of our method. Following the Tikhonov concept for ill - posed problems [50], we
Advanced Numerical Methods for Computing Statistical Quantities of Interest
2014-07-10
coefficients , forcing terms, and initial conditions was analyzed. The input data were assumed to depend on a finite number of random variables . Unlike...89, 2012, 1269-1280. We considered the Musiela equation of forward rates; this is a hyperbolic stochastic partial differential equation . A weak...ZHANG AND M. GUNZBURGER, Error analysis of stochastic collocation method for parabolic partial differential equations with random input data; SIAM Journal
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.
Application of Methods of Numerical Analysis to Physical and Engineering Data.
1980-10-15
for tbe estimated fo. Part E extends the method to include an arbitrary signal noise power function. Part F discusses a method for obtaining initial...7 AD-AI02 685 BEDFORD RESEARCH ASSOCIATES MA F/6 4/1APPLICATION OF METHODS OF NUMERICAL ANALYSIS TO PHYSICAL AND EN--ETC(U) OCT 80 R BOUCHER, T...APPLICATION OF METHODS OF NUMERICAL .) ANALYSIS TO PHYSICAL AND! ENGINEERING DATA R. Boucher T. Costello ~ P. Meehan J. Noonan Bedford Research Associates 2
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.
Numerical method for evolving the projected Gross-Pitaevskii equation.
Blakie, P Blair
2008-08-01
In this paper we describe a method for evolving the projected Gross-Pitaevskii equation (PGPE) for a Bose gas in a harmonic oscillator potential. The central difficulty in solving this equation is the requirement that the classical field is restricted to a small set of prescribed modes that constitute the low energy classical region of the system. We present a scheme, using a Hermite-polynomial based spectral representation, that precisely implements this mode restriction and allows an efficient and accurate solution of the PGPE. We show equilibrium and nonequilibrium results from the application of the PGPE to an anisotropic trapped three-dimensional Bose gas.
Riser Feeding Evaluation Method for Metal Castings Using Numerical Analysis
NASA Astrophysics Data System (ADS)
Ahmad, Nadiah
One of the design aspects that continues to create a challenge for casting designers is the optimum design of casting feeders (risers). As liquid metal solidifies, the metal shrinks and forms cavities inside the casting. In order to avoid shrinkage cavities, risers are added to the casting shape to supply additional molten metal when shrinkage occurs during solidification. The shrinkage cavities in the casting are compensated by controlling the cooling rate to promote directional solidification. This control can be achieved by designing the casting such that the cooling begins at the sections that are farthest away from the risers and ends at the risers. Therefore, the risers will solidify last and feed the casting with the molten metal. As a result, the shrinkage cavities formed during solidification are in the risers which are later removed from the casting. Since casting designers have to usually go through iterative processes of validating the casting designs which are very costly due to expensive simulation processes or manual trials and errors on actual casting processes, this study investigates more efficient methods that will help casting designers utilize their casting experiences systematically to develop good initial casting designs. The objective is to reduce the casting design method iterations; therefore, reducing the cost involved in that design processes. The aim of this research aims at finding a method that can help casting designers design effective risers used in sand casting process of aluminum-silicon alloys by utilizing the analysis of solidification simulation. The analysis focuses on studying the significance of pressure distribution of the liquid metal at the early stage of casting solidification, when heat transfer and convective fluid flow are taken into account in the solidification simulation. The mathematical model of casting solidification was solved using the finite volume method (FVM). This study focuses to improve our
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
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.
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
A model and numerical method for compressible flows with capillary effects
NASA Astrophysics Data System (ADS)
Schmidmayer, Kevin; Petitpas, Fabien; Daniel, Eric; Favrie, Nicolas; Gavrilyuk, Sergey
2017-04-01
A new model for interface problems with capillary effects in compressible fluids is presented together with a specific numerical method to treat capillary flows and pressure waves propagation. This new multiphase model is in agreement with physical principles of conservation and respects the second law of thermodynamics. A new numerical method is also proposed where the global system of equations is split into several submodels. Each submodel is hyperbolic or weakly hyperbolic and can be solved with an adequate numerical method. This method is tested and validated thanks to comparisons with analytical solutions (Laplace law) and with experimental results on droplet breakup induced by a shock wave.
An efficient numerical simulation method for a thin film SOI RESURF structure
NASA Astrophysics Data System (ADS)
Liu, Zhan; Gan, Jun-Ying; Gu, Xiao-Feng; Yu, Zong-guang; Yang, Lei
2009-02-01
In this paper, an efficient numerical simulation method, which combines the spline alternating direction implicit (SADI) method and the high-order compact (HOC) finite difference method, is presented to simulate the potential and electric field distributions along the semiconductor surface of thin film silicon-on-insulator (TFSOI) reduced surface field (RESURF) devices. The relative merit of HOC-SADI is compared with three other popular numerical simulation methods, Newton, Gummel and CGS. The numerical results obtained from the proposed scheme are compared to the simulator MEDICI. HOC-SADI is a faster algorithm than Newton, Gummel and CGS as is evident from the CPU times and the number of iterations.
NASA Astrophysics Data System (ADS)
Shen, Fabin; Wang, Anbo
2006-02-01
The numerical calculation of the Rayleigh-Sommerfeld diffraction integral is investigated. The implementation of a fast-Fourier-transform (FFT) based direct integration (FFT-DI) method is presented, and Simpson's rule is used to improve the calculation accuracy. The sampling interval, the size of the computation window, and their influence on numerical accuracy and on computational complexity are discussed for the FFT-DI and the FFT-based angular spectrum (FFT-AS) methods. The performance of the FFT-DI method is verified by numerical simulation and compared with that of the FFT-AS method.
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.
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
Numerical Simulation of Antennas with Improved Integral Equation Method
NASA Astrophysics Data System (ADS)
Ma, Ji; Fang, Guang-You; Lu, Wei
2015-08-01
Simulating antennas around a conducting object is a challenge task in computational electromagnetism, which is concerned with the behaviour of electromagnetic fields. To analyze this model efficiently, an improved integral equation-fast Fourier transform (IE-FFT) algorithm is presented in this paper. The proposed scheme employs two Cartesian grids with different size and location to enclose the antenna and the other object, respectively. On the one hand, IE-FFT technique is used to store matrix in a sparse form and accelerate the matrix-vector multiplication for each sub-domain independently. On the other hand, the mutual interaction between sub-domains is taken as the additional exciting voltage in each matrix equation. By updating integral equations several times, the whole electromagnetic system can achieve a stable status. Finally, the validity of the presented method is verified through the analysis of typical antennas in the presence of a conducting object. Supported by in part China Postdoctoral Science Foundation under Grant No. 2014M550839, and in part by the Key Research Program of the Chinese Academy of Sciences under Grant No. KGZD-EW-603
Numerical Analysis of Maneuvering Rotorcraft Using Moving Overlapped Grid Method
NASA Astrophysics Data System (ADS)
Yang, Choongmo; Aoyama, Takashi
In transient flight, rotor wakes and tip vortex generated by unsteady blade air-loads and blade motions are fully unsteady and 3-dimensionally-aperiodic, giving rise to significant complicity in accurate analysis compared to steady flight. We propose a hybrid approach by splitting the motions of a maneuvering helicopter into translation and rotation. Translation is simulated using a non-inertial moving (translating) coordinate for which new governing equations are derived, and rotations are simulated by moving each grid in the frame. A flow simulation (CFD) code is constructed by using the hybrid approach, then two simple cases (accelerating/decelerating flight and right-turn flight) for maneuvering helicopter are calculated using the moving overlapped grid method, which is now one of the most advanced techniques for tip-vortex capture. The vortex bundling phenomena, which is a main characteristic of right-turn flight, is well captured by the simulation code. The results of the present study provide better understanding of the characteristics for maneuvering rotorcraft, which can be valuable in full helicopter design.
Three-dimensional multispecies nonlinear tumor growth–I. Model and numerical method
Wise, S.M.; Lowengrub, J.S.; Frieboes, H.B.; Cristini, V.
2012-01-01
This is the first paper in a two-part series in which we develop, analyze and simulate a diffuse interface continuum model of multispecies tumor growth and tumor-induced angiogenesis in two and three dimensions. Three dimensional simulations of nonlinear tumor growth and neovascularization using this diffuse interface model were recently presented in Frieboes et al. (2007), but that paper did not describe the details of the model or the numerical algorithm. This is done here. In this diffuse interface approach, sharp interfaces are replaced by narrow transition layers that arise due to differential adhesive forces among the cell-species. Accordingly, a continuum model of adhesion is introduced. The model is thermodynamically consistent, is related to recently developed mixture models, and thus is capable of providing a detailed description of tumor progression. The model is well-posed and consists of fourth-order nonlinear advection-reaction-diffusion equations (of Cahn-Hilliard-type) for the cell-species coupled with reaction-diffusion equations for the substrate components. We demonstrate analytically and numerically that when the diffuse interface thickness tends to zero, the system reduces to a classical sharp interface model. Using a new fully adaptive, nonlinear multigrid/finite difference method the system is simulated efficiently. In this first paper, we present simulations of unstable avascular tumor growth in two and three dimensions and demonstrate that our techniques now make large-scale three dimensional simulations of tumors with complex morphologies computationally feasible. In Part II of this study, we will investigate multispecies tumor invasion, tumor-induced angiogenesis and focus on the morphological instabilities that may underlie invasive phenotypes. PMID:18485374
A numerical method for the study of the circulation of the world ocean
Bryan, K.
1997-08-01
This paper describes a detail computational procedure involving a finite difference numerical schemes to study the circulation models of the world oceans. To obtain an efficient numerical method for low-frequency, large-scale current systems, surfaces gravity-inertial waves are filtered out by the rigid-lid approximation. Special features of the ocean circulation are resolved in the numerical model by allowing for a variable spacing in either the zonal or meridional direction. 20 refs., 5 figs., 1 tab.
NASA Technical Reports Server (NTRS)
Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.
1989-01-01
In response to the tremendous growth in the development of advanced materials, such as fiber-reinforced plastic (FRP) composite materials, a new numerical method is developed to analyze and predict the time-dependent properties of these materials. Basic concepts in viscoelasticity, laminated composites, and previous viscoelastic numerical methods are presented. A stable numerical method, called the nonlinear differential equation method (NDEM), is developed to calculate the in-plane stresses and strains over any time period for a general laminate constructed from nonlinear viscoelastic orthotropic plies. The method is implemented in an in-plane stress analysis computer program, called VCAP, to demonstrate its usefulness and to verify its accuracy. A number of actual experimental test results performed on Kevlar/epoxy composite laminates are compared to predictions calculated from the numerical method.
Barros, R.C. de; Larsen, E.W. )
1991-01-01
A generalization of the one-group Spectral Green's Function (SGF) method is developed for multigroup, slab-geometry discrete ordinates (S{sub N}) problems. The multigroup SGF method is free from spatial truncation errors; it generated numerical values for the cell-edge and cell-average angular fluxes that agree with the analytic solution of the multigroup S{sub N} equations. Numerical results are given to illustrate the method's accuracy.
A numerical method for solving optimal control problems using state parametrization
NASA Astrophysics Data System (ADS)
Mehne, H.; Borzabadi, A.
2006-06-01
A numerical method for solving a special class of optimal control problems is given. The solution is based on state parametrization as a polynomial with unknown coefficients. This converts the problem to a non-linear optimization problem. To facilitate the computation of optimal coefficients, an improved iterative method is suggested. Convergence of this iterative method and its implementation for numerical examples are also given.
NASA Astrophysics Data System (ADS)
Karafyllis, Iasson; Grüne, Lars
2009-09-01
In this work we study the problem of step size selection for numerical schemes, which guarantees that the numerical solution presents the same qualitative behavior as the original system of ordinary differential equations, by means of tools from nonlinear control theory. Lyapunov-based stabilization methods are exploited.
Methods of numerical analysis of 1-dimensional 2-body problem in Wheeler-Feynman electrodynamics
NASA Astrophysics Data System (ADS)
Klimenko, S. V.; Nikitin, I. N.; Urazmetov, W. F.
2000-04-01
Numerical methods for solution of differential equations with deviating arguments describing 1-dimensional ultra-relativistic scattering of 2 identical charged particles in classical electrodynamics with half-retarded/halfadvanced interaction (Wheeler and Feynman, 1949) are developed. A bifurcation of solutions and violation of their reflectional symmetries in the region of velocities v>0.937c are found in numerical analysis.
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)
Xie, Shuisheng; Huang, Guojie; Zhang, Xiaoli; Yang, Haoqiang
2007-05-01
Damper Cooling Tube (DCT) Method to fabricate the semi-solid metal slurry has been studied in this paper. Firstly, numerical simulation is adopted to investigate the flow process in order to optimize the technical parameters. The temperature effects on the rheological properties of the slurries are also considered. The effects of technical parameters on the slurry properties are studied in detail. Then the experiment was carried out with AZ91 magnesium alloy in order to examine the numerical simulation results. The results of numerical simulation are consistent with the experimental results. According to the numerical and experiment results, the DCT device can fabricate fine semisolid slurry with primary globular phase.
Some numerical methods for integrating systems of first-order ordinary differential equations
NASA Technical Reports Server (NTRS)
Clark, N. W.
1969-01-01
Report on numerical methods of integration includes the extrapolation methods of Bulirsch-Stoer and Neville. A comparison is made nith the Runge-Kutta and Adams-Moulton methods, and circumstances are discussed under which the extrapolation method may be preferred.
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.
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.
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.
Rajaraman, Prathish K; Manteuffel, T A; Belohlavek, M; Heys, Jeffrey J
2017-01-01
A new approach has been developed for combining and enhancing the results from an existing computational fluid dynamics model with experimental data using the weighted least-squares finite element method (WLSFEM). Development of the approach was motivated by the existence of both limited experimental blood velocity in the left ventricle and inexact numerical models of the same flow. Limitations of the experimental data include measurement noise and having data only along a two-dimensional plane. Most numerical modeling approaches do not provide the flexibility to assimilate noisy experimental data. We previously developed an approach that could assimilate experimental data into the process of numerically solving the Navier-Stokes equations, but the approach was limited because it required the use of specific finite element methods for solving all model equations and did not support alternative numerical approximation methods. The new approach presented here allows virtually any numerical method to be used for approximately solving the Navier-Stokes equations, and then the WLSFEM is used to combine the experimental data with the numerical solution of the model equations in a final step. The approach dynamically adjusts the influence of the experimental data on the numerical solution so that more accurate data are more closely matched by the final solution and less accurate data are not closely matched. The new approach is demonstrated on different test problems and provides significantly reduced computational costs compared with many previous methods for data assimilation. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
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.
NASA Astrophysics Data System (ADS)
Zamolo, R.; Nobile, E.
2017-01-01
A Least Squares Collocation Meshless Method based on Radial Basis Function (RBF) interpolation is used to solve steady state heat conduction problems on 2D polygonal domains using MATLAB® environment. The point distribution process required by the numerical method can be fully automated, taking account of boundary conditions and geometry of the problem to get higher point distribution density where needed. Several convergence tests have been carried out comparing the numerical results to the corresponding analytical solutions to outline the properties of this numerical approach, considering various combinations of parameters. These tests showed favorable convergence properties in the simple cases considered: along with the geometry flexibility, these features confirm that this peculiar numerical approach can be an effective tool in the numerical simulation of heat conduction problems.
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.
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.
Hindi, Haitham; Prabhakar, Shyam; Fox, John D.; Linscott, Ivan; Teytelman, Dmitri; /SLAC
2011-08-31
We present a technique for the design and verification of efficient bunch-by-bunch controllers for damping longitudinal multibunch instabilities. The controllers attempt to optimize the use of available feedback amplifier power - one of the most expensive components of a feedback system - and define the limits of the closed loop system performance. Our design technique alternates between analytic computation of single bunch optimal controllers and verification on a multibunch numerical simulator. The simulator uses PEP-II parameters and identifies unstable coupled bunch modes, their growth rates and their damping rates with feedback. The results from the simulator are shown to be in reasonable agreement with analytical calculations based on the single bunch model. The technique is then used to evaluate the performance of a variety of controllers proposed for PEP-II.
The numerical method of calculation of two-dimensional stationary electro-gasdynamic internal flows
NASA Astrophysics Data System (ADS)
Zhurin, V. V.; Shipilin, A. V.
The suggested numerical method is meant for computations of two dimensional stationary internal nonviscous gas flows in a presence of a heat supply at expense of Joule heating. Such flows and processes take place in the plasma thrusters and in the working regions of the electro-ionizing lasers. The numerical solution of the Euler equations for subsonic and transonic regimes are considered. For computations of supersonic internal flows the method of characteristics is a very effective method. The method suggested allows an easy connection with the method of characteristics.
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.
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...
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)
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
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.
On Numerical Methods of Solving Some Optimal Path Problems on the Plane
NASA Astrophysics Data System (ADS)
Ushakov, V. N.; Matviychuk, A. R.; Malev, A. G.
Three numerical methods of solution of some time optimal control problems for a system under phase constraints are described in the paper. Two suggested methods are based on transition to the discrete time model, constructing attainability sets and application of the guide construction. The third method is based on the Deikstra algorithm.
NASA Astrophysics Data System (ADS)
Kalogiratou, Z.; Monovasilis, Th.; Simos, T. E.
2016-12-01
In this work we consider trigonometrically fitted two step hybrid methods for the numerical solution of second-order initial value problems. We follow the approach of Simos and derive trigonometrically fitting conditions for methods with five stages. As an example we modify a seventh order method and apply to three well known oscillatory problems.
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)
Barnes, M.; Dorland, W.; Tatsuno, T.; Abel, I. G.; Hammett, G. W.; Ricci, P.; Rogers, B. N.; Schekochihin, A. A.
2009-07-15
A set of key properties for an ideal dissipation scheme in gyrokinetic simulations is proposed, and implementation of a model collision operator satisfying these properties is described. This operator is based on the exact linearized test-particle collision operator, with approximations to the field-particle terms that preserve conservation laws and an H-theorem. It includes energy diffusion, pitch-angle scattering, and finite Larmor radius effects corresponding to classical (real-space) diffusion. The numerical implementation in the continuum gyrokinetic code GS2[Kotschenreuther et al., Comput. Phys. Comm. 88, 128 (1995)] is fully implicit and guarantees exact satisfaction of conservation properties. Numerical results are presented showing that the correct physics is captured over the entire range of collisionalities, from the collisionless to the strongly collisional regimes, without recourse to artificial dissipation.
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.
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.
Application of numerical methods for diffusion-based modeling of skin permeation.
Frasch, H Frederick; Barbero, Ana M
2013-02-01
The application of numerical methods for mechanistic, diffusion-based modeling of skin permeation is reviewed. Methods considered here are finite difference, method of lines, finite element, finite volume, random walk, cellular automata, and smoothed particle hydrodynamics. First the methods are briefly explained with rudimentary mathematical underpinnings. Current state of the art numerical models are described, and then a chronological overview of published models is provided. Key findings and insights of reviewed models are highlighted. Model results support a primarily transcellular pathway with anisotropic lipid transport. Future endeavors would benefit from a fundamental analysis of drug/vehicle/skin interactions.
Method for Numerical Solution of the Stationary Schrödinger Equation
NASA Astrophysics Data System (ADS)
Knyazev, S. Yu.; Shcherbakova, E. E.
2017-02-01
The aim of this work is to describe a method of numerical solution of the stationary Schrödinger equation based on the integral equation that is identical to the Schrödinger equation. The method considered here allows one to find the eigenvalues and eigensolutions for quantum-mechanical problems of different dimensionality. The method is tested by solving problems for one-dimensional and two-dimensional quantum oscillators, and results of these tests are presented. Satisfactory agreement of the results obtained using this numerical method with well-known analytical solutions is demonstrated.
A non-grey analytical model for irradiated atmospheres. II. Analytical vs. numerical solutions
NASA Astrophysics Data System (ADS)
Parmentier, Vivien; Guillot, Tristan; Fortney, Jonathan J.; Marley, Mark S.
2015-02-01
Context. The recent discovery and characterization of the diversity of the atmospheres of exoplanets and brown dwarfs calls for the development of fast and accurate analytical models. Aims: We wish to assess the goodness of the different approximations used to solve the radiative transfer problem in irradiated atmospheres analytically, and we aim to provide a useful tool for a fast computation of analytical temperature profiles that remains correct over a wide range of atmospheric characteristics. Methods: We quantify the accuracy of the analytical solution derived in paper I for an irradiated, non-grey atmosphere by comparing it to a state-of-the-art radiative transfer model. Then, using a grid of numerical models, we calibrate the different coefficients of our analytical model for irradiated solar-composition atmospheres of giant exoplanets and brown dwarfs. Results: We show that the so-called Eddington approximation used to solve the angular dependency of the radiation field leads to relative errors of up to ~5% on the temperature profile. For grey or semi-grey atmospheres (i.e., when the visible and thermal opacities, respectively, can be considered independent of wavelength), we show that the presence of a convective zone has a limited effect on the radiative atmosphere above it and leads to modifications of the radiative temperature profile of approximately ~2%. However, for realistic non-grey planetary atmospheres, the presence of a convective zone that extends to optical depths smaller than unity can lead to changes in the radiative temperature profile on the order of 20% or more. When the convective zone is located at deeper levels (such as for strongly irradiated hot Jupiters), its effect on the radiative atmosphere is again on the same order (~2%) as in the semi-grey case. We show that the temperature inversion induced by a strong absorber in the optical, such as TiO or VO is mainly due to non-grey thermal effects reducing the ability of the upper
NASA Astrophysics Data System (ADS)
Hotokezaka, Kenta; Kyutoku, Koutarou; Okawa, Hirotada; Shibata, Masaru
2015-03-01
We perform new long-term (15-16 orbits) simulations of coalescing binary neutron stars in numerical relativity using an updated Einstein equation solver, employing low-eccentricity initial data, and modeling the neutron stars by a piecewise polytropic equation of state. A convergence study shows that our new results converge more rapidly than the third order, and using the determined convergence order, we construct an extrapolated waveform for which the estimated total phase error should be less than one radian. We then compare the extrapolated waveforms with those calculated by the latest effective-one-body (EOB) formalism in which the so-called tidal deformability, higher post-Newtonian corrections, and gravitational self-force effects are taken into account. We show that for a binary of compact neutron stars with their radius 11.1 km, the waveform by the EOB formalism agrees quite well with the numerical waveform so that the total phase error is smaller than one radian for the total phase of ˜200 radian up to the merger. By contrast, for a binary of less compact neutron stars with their radius 13.6 km, the EOB and numerical waveforms disagree with each other in the last few wave cycles, resulting in the total phase error of approximately three radian.
Numerical solution of DGLAP equations using Laguerre polynomials expansion and Monte Carlo method.
Ghasempour Nesheli, A; Mirjalili, A; Yazdanpanah, M M
2016-01-01
We investigate the numerical solutions of the DGLAP evolution equations at the LO and NLO approximations, using the Laguerre polynomials expansion. The theoretical framework is based on Furmanski et al.'s articles. What makes the content of this paper different from other works, is that all calculations in the whole stages to extract the evolved parton distributions, are done numerically. The employed techniques to do the numerical solutions, based on Monte Carlo method, has this feature that all the results are obtained in a proper wall clock time by computer. The algorithms are implemented in FORTRAN and the employed coding ideas can be used in other numerical computations as well. Our results for the evolved parton densities are in good agreement with some phenomenological models. They also indicate better behavior with respect to the results of similar numerical calculations.
Numerical methods for estimating J integral in models with regular rectangular meshes
NASA Astrophysics Data System (ADS)
Kozłowiec, B.
2017-02-01
Cracks and delaminations are the common structural degradation mechanisms studied recently using numerous methods and techniques. Among them, numerical methods based on FEM analyses are in widespread commercial use. The scope of these methods has focused i.e. on energetic approach to linear elastic fracture mechanics (LEFM) theory, encompassing such quantities as the J-integral and the energy release rate G. This approach enables to introduce damage criteria of analyzed structures without dealing with the details of the physical singularities occurring at the crack tip. In this paper, two numerical methods based on LEFM are used to analyze both isotropic and orthotropic specimens and the results are compared with well-known analytical solutions as well as (in some cases) VCCT results. These methods are optimized for industrial use with simple, rectangular meshes. The verification is made based on two dimensional mode partitioning.
Xiong, Lin; Chen, Cheng; Chen, Qing; Ni, Jinren
2011-05-30
Titanate nanotubes (TNs) with specific surface areas of 272.31 m(2)g(-1) and pore volumes of 1.264 cm(3)g(-1) were synthesized by alkaline hydrothermal method. The TNs were investigated as adsorbents for the removal of Pb(II) and Cd(II) from aqueous solutions. The FT-IR analysis indicated that Pb(II) and Cd(II) adsorption were mainly ascribed to the hydroxyl groups in the TNs. Batch experiments were conducted by varying contact time, pH and adsorbent dosage. It was shown that the initial uptake of each metal ion was very fast in the first 5 min, and adsorption equilibrium was reached after 180 min. The adsorption of Pb(II) and Cd(II) were found to be maximum at pH in the range of 5.0-6.0. The adsorption kinetics of both metal ions followed the pseudo-second-order model. Equilibrium data were best fitted with the Langmuir isotherm model, and the maximum adsorption capacities of Pb(II) and Cd(II) were determined to be 520.83 and 238.61 mg g(-1), respectively. Moreover, more than 80% of Pb(II) and 85% of Cd(II) adsorbed onto TNs can be desorbed with 0.1M HCl after 3h. Thus, TNs were considered to be effective and promising materials for the removal of both Pb(II) and Cd(II) from wastewater.
Application of higher-order numerical methods to the boundary-layer equations
NASA Technical Reports Server (NTRS)
Wornom, S. F.
1978-01-01
A fourth-order method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations for both attached and separated flows. The efficiency of the present method is compared with other higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, the three-point spline methods, and a modified finite-element method. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.
Critical study of higher order numerical methods for solving the boundary-layer equations
NASA Technical Reports Server (NTRS)
Wornom, S. F.
1978-01-01
A fourth order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method, which is the natural extension of the second order box scheme to fourth order, was demonstrated with application to the incompressible, laminar and turbulent, boundary layer equations. The efficiency of the present method is compared with two point and three point higher order methods, namely, the Keller box scheme with Richardson extrapolation, the method of deferred corrections, a three point spline method, and a modified finite element method. For equivalent accuracy, numerical results show the present method to be more efficient than higher order methods for both laminar and turbulent flows.
Kamiya, Tetsu; Toyama, Yoshio; Michiwaki, Yukihiro; Kikuchi, Takahiro
2013-01-01
The aim of the present study was to evaluate the possibility of numerical simulation of the swallowing process using a moving particle simulation (MPS) method, which defined the food bolus as a number of particles in a fluid, a solid, and an elastic body. In order to verify the accuracy of the simulation results, a simple water bolus falling model was solved using the three-dimensional (3D) MPS method. We also examined the simplified swallowing simulation using a two-dimensional (2D) MPS method to confirm the interactions between the liquid, solid, elastic bolus, and organ structure. In a comparison of the 3D MPS simulation and experiments, the falling time of the water bolus and the configuration of the interface between the liquid and air corresponded exactly to the experimental measurements and the visualization images. The results showed that the accuracy of the 3D MPS simulation was qualitatively high for the simple falling model. Based on the results of the simplified swallowing simulation using the 2D MPS method, each bolus, defined as a liquid, solid, and elastic body, exhibited different behavior when the organs were transformed forcedly. This confirmed that the MPS method could be used for coupled simulations of the fluid, the solid, the elastic body, and the organ structures. The results suggested that the MPS method could be used to develop a numerical simulator of the swallowing process.
NASA Technical Reports Server (NTRS)
Thomas, P. D.
1980-01-01
A computer implemented numerical method for predicting the flow in and about an isolated three dimensional jet exhaust nozzle is summarized. The approach is based on an implicit numerical method to solve the unsteady Navier-Stokes equations in a boundary conforming curvilinear coordinate system. Recent improvements to the original numerical algorithm are summarized. Equations are given for evaluating nozzle thrust and discharge coefficient in terms of computed flowfield data. The final formulation of models that are used to simulate flow turbulence effect is presented. Results are presented from numerical experiments to explore the effect of various quantities on the rate of convergence to steady state and on the final flowfield solution. Detailed flowfield predictions for several two and three dimensional nozzle configurations are presented and compared with wind tunnel experimental data.
An improved mixed numerical-experimental method for stress field calculation
NASA Astrophysics Data System (ADS)
Lopes, H. M. R.; Guedes, R. M.; Vaz, M. A.
2007-07-01
In this work a numerical-experimental method is used to study the dynamic behavior of an aluminum plate subjected to a small mass impact. The out-of-plane displacements, due to transient bending wave propagation, were assessed for successive time instants, using double pulse TV-holography, also known as pulsed ESPI. The experimental setup and the image processing methods were improved to allow the calculation of the plate transient stress field. Integral transforms are used to obtain the strain fields from spatial derivatives of displacements noisy data. A numerical simulation of the plate transient response was carried out with FEM Ansys ®. For this purpose a PZT transducer was used to record the impact force history, which was inputted in the numerical model. Finally, the comparisons between numerical and experimental results are presented in order to validate the present methodology.
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.
NASA Technical Reports Server (NTRS)
Chen, Y. S.
1986-01-01
In the present paper, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BEC) systems has been developed and evaluated. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme and a central differencing plus artificial dissipation scheme are used to approximate the convection terms in the governing equations. Effects of these two schemes on the accuracy of numerical predictions are studied. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm, SIMPLE-C. Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present numerical method.
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.
A numerical-perturbation method for the nonlinear analysis of structural vibrations
NASA Technical Reports Server (NTRS)
Nayfeh, A. H.; Mook, D. T.; Lobitz, D. W.
1974-01-01
A numerical-perturbation method is proposed for the determination of the nonlinear forced response of structural elements. Purely analytical techniques are capable of determining the response of structural elements having simple geometries and simple variations in thickness and properties, but they are not applicable to elements with complicated structure and boundaries. Numerical techniques are effective in determining the linear response of complicated structures, but they are not optimal for determining the nonlinear response of even simple elements when modal interactions take place due to the complicated nature of the response. Therefore, the optimum is a combined numerical and perturbation technique. The present technique is applied to beams with varying cross sections.
Numerical solution of a diffusion problem by exponentially fitted finite difference methods.
D'Ambrosio, Raffaele; Paternoster, Beatrice
2014-01-01
This paper is focused on the accurate and efficient solution of partial differential differential equations modelling a diffusion problem by means of exponentially fitted finite difference numerical methods. After constructing and analysing special purpose finite differences for the approximation of second order partial derivatives, we employed them in the numerical solution of a diffusion equation with mixed boundary conditions. Numerical experiments reveal that a special purpose integration, both in space and in time, is more accurate and efficient than that gained by employing a general purpose solver.
A numerical method for reorientation of rotating tidally deformed visco-elastic bodies
NASA Astrophysics Data System (ADS)
Hu, H.; van der Wal, W.; Vermeersen, B. L. A.
2016-12-01
Currently the true polar wander (TPW) of a visco-elastic body is studied with three types of approches: (i) a linear dynamic approach which applies the linearised Liouville equation (e.g. Wu and Peltier [1984]); (ii) a non-linear dynamic approach which is based on the quasi-fluid approximation (e.g. Ricard et al. [1993]); (iii) a long-term limit approach which only considers the fluid limit of a reorientation (e.g. Matsuyama and Nimmo [2007]). Several limitations of these approaches have not been studied: the range for which the linear approach is accurate, the validity of the quasi-fluid approximation, and the dynamic solution for TPW of a tidally deformed rotating body. In order to deal with these isssues, we establish a numerical procedure which is able to determine the large angle reorientation of a visco-elastic celestial body that can be both centrifugally and tidally deformed. We show that the linear approach leads to significant errors for loadings near the poles or the equator. For instance, when the loading is placed at 10 degree colatitude on a model representing the Earth, the maximum allowed TPW is just 0.2 degree for the error of the linear method to remain below 1%. Secondly, we show that slow relaxation modes can have a significant effect on large angle TPW of Earth or other planets and ignoring these modes can lead to large error for the transient response of TPW. Finally, we show that reorientation of a tidally deformed body driven by a positive mass anomaly near the poles has a preference for rotating around the tidal axis instead of towards it. At a tidally deformed body, positive mass anomalies are more likely to be found near the equator and the plane perpendicular to the tidal axis, while negative mass anomalies tend to be near the great circle with longitudes 0 and 180 degree.
Velocity distribution of meteoroids colliding with planets and satellites. II. Numerical results
NASA Astrophysics Data System (ADS)
Kholshevnikov, K. V.; Shor, V. A.
In the first part of the paper we proposed algorithm for describing velocity distribution of meteoroids colliding with planets and satellites. In the present part we show numerical characteristics of the distribution function. Namely, for each of terrestrial planets and their satellites we consider a swarm of encountering particles of asteroidal origin. They form a field of relative collisional velocities v. We consider momenta k (mathematical expectation of vk), k = -1, 1, 2, 3, 4. The data are calculated under two different assumptions: taking into account gravitation of target body or without it. The main results are presented in a series of tables each containing five numbers and several useful functions of them.
NASA Astrophysics Data System (ADS)
Nishino, Ryohei; Namba, Masanobu
The unsteady aerodynamic force and work for contra-rotating annular cascades of oscillating blades are numerically investigated. A comparison among frequency components of unsteady blade loadings on oscillating blades and stationary blades in relative rotational motion is conducted. It is proved that the state of generated acoustic duct mode of the lowest order is a key factor governing the aeroacoustic interaction between the blade rows. The effect of the neighboring blade row on the aerodynamic force and work is never small and will make substantial modifications to the flutter boundaries of an isolated blade row.
Impact of numerical method on a side jets formation in a round jet
NASA Astrophysics Data System (ADS)
Wawrzak, K.; Boguslawski, A.
2016-10-01
Numerical analysis of a formation of side jets in an externally modulated round jet is presented. The research is performed applying Large Eddy Simulation method and high-order codes based on Cartesian and cylindrical coordinates. The main attention is paid to an impact of numerical approach on the formation of the side jets, their number and localisation. The results obtained suggest that on Cartesian meshes the number and directions of the side jets are dependent on the distribution of the mesh nodes.
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 study of the inverse problem for the diffusion-reaction equation using optimization method
NASA Astrophysics Data System (ADS)
Soboleva, O. V.; Brizitskii, R. V.
2016-04-01
The model of transfer of substance with mixed boundary condition is considered. The inverse extremum problem of identification of the main coefficient in a nonstationary diffusion-reaction equation is formulated. The numerical algorithm based on the Newton-method of nonlinear optimization and finite difference discretization for solving this extremum problem is developed and realized on computer. The results of numerical experiments are discussed.
A critical study of higher-order numerical methods for solving the boundary-layer equations
NASA Technical Reports Server (NTRS)
Wornom, S. F.
1977-01-01
A fourth-order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations. The efficiency of the present method is compared with other two-point and three-point higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, and the three-point spline methods. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.
Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems
NASA Technical Reports Server (NTRS)
Cerro, J. A.; Scotti, S. J.
1991-01-01
Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.
Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems
NASA Astrophysics Data System (ADS)
Cerro, J. A.; Scotti, S. J.
1991-07-01
Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.
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.
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.
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.
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.
Numerical analysis of rarefied slit flows. II - Navier-Stokes simulations
NASA Technical Reports Server (NTRS)
Wadsworth, D. C.; Erwin, D. A.
1991-01-01
The model problem of pressure-driven flow of a rarefied monatomic gas through a two-dimensional slit is analyzed via full Navier-Stokes numerical simulation. Parametric solutions are generated for slit-height based Knudsen number ranging from continuum to transitional flow and for reservoir pressure ratios leading to subsonic and supersonic flow. The change in the structure of the flowfield near the slit as a function of pressure ratio and Knudsen number are quantified from a purely continuum standpoint. The choice of numerical domain size, boundary conditions and treatment of the slit are also discussed. As expected, comparison with a Direct Simulation Monte Carlo solution for a highly rarefied case shows large differences in the predicted mass flow. The cause of these differences can be quantified through detailed comparison of the local flowfield properties. For the larger pressure ratio cases qualitative trends with increasing rarefaction are discussed, including the change in the sonic line shape in the slit and the in total mass flow.
NASA Astrophysics Data System (ADS)
Simmel, Martin; Trautmann, Thomas; Tetzlaff, Gerd
The Linear Discrete Method is used to solve the Stochastic Collection Equation (SCE) numerically. Comparisons are made with the Method of Moments, the Berry-Reinhardt model and the Linear Flux Method. Simulations for all numerical methods are shown for the kernel after Golovin [Bull. Acad. Sci. USSR, Geophys. Ser. 5 (1963) 783] and are compared with the analytical solution for two different initial distributions. BRM seems to give the best results and LDM gives good results, too. LFM overestimates the drop growth for the right tail of the distribution and MOM does the same but over the entire drop spectrum. For the hydrodynamic kernel after Long [J. Atmos. Sci. 31 (1974) 1040], simulations are presented using the four numerical methods (LDM, MOM, BRM, LFM). Especially for high resolutions, the solutions of LDM and LFM approach each other very closely. In addition, LDM simulations using the hydrodynamic kernel after Böhm [Atmos. Res. 52 (1999) 167] are presented, which show good correspondence between low- and high-resolution results. Computation efficiency is especially important when numerical schemes are to be included in larger models. Therefore, the computation times of the four methods were compared for the cases with the Golovin kernel. The result is that LDM is the fastest method by far, needing less time than other methods by a factor of 2-7, depending on the case and the bin resolution. For high resolutions, MOM is the slowest. For the lowest resolution, this holds for LFM.
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®.
NASA Astrophysics Data System (ADS)
Ishibashi, N.; Atuko, N.
We have achieved very high accuracy to solve a set of ordinary differential equations with spline functions. It is equivalent with k-th order of implicit differential method. The method is very simple and easy by using de-Boor Cox's recursive formula. We can get very high accuracy numerical results with this method. For example, we have solved trajectories of stars more than 100,000,000 years, and show the usefulness of this method.
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.
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
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)
Numerical simulation of fiber and wire array Z-pinches with Trac-II
Reisman, David B.
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.
Vectorization on the star computer of several numerical methods for a fluid flow problem
NASA Technical Reports Server (NTRS)
Lambiotte, J. J., Jr.; Howser, L. M.
1974-01-01
A reexamination of some numerical methods is considered in light of the new class of computers which use vector streaming to achieve high computation rates. A study has been made of the effect on the relative efficiency of several numerical methods applied to a particular fluid flow problem when they are implemented on a vector computer. The method of Brailovskaya, the alternating direction implicit method, a fully implicit method, and a new method called partial implicitization have been applied to the problem of determining the steady state solution of the two-dimensional flow of a viscous imcompressible fluid in a square cavity driven by a sliding wall. Results are obtained for three mesh sizes and a comparison is made of the methods for serial computation.
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.
NASA Technical Reports Server (NTRS)
Reale, F.; Rosner, R.; Malagoli, A.; Peres, G.; Serio, S.
1991-01-01
The temporal evolution of density perturbations in an initially hydrostatic isothermal atmosphere consisting of an optically thin radiating compressible plasma is studied. Numerical techniques are used to describe the nonlinear evolution of the perturbations, and the relative equilibrium between dynamic and thermal instabilities as governed by three independent control parameters are examined, namely, the initial density contrast of the perturbation, the ratio of the local buoyancy oscillation period to the local radiative cooling time, and the ratio of the perturbation radius to the local scaleheight. Four orders of magnitude of initial density contrasts and ratios of buoyancy and cooling times, and one order of magnitude of the bubble dimensions are explored. Well-defined oscillations were found to occur in a limited parameter range, and thermal instability to occur even within secondary condensations deriving from the bubble fragmentation.
Partial Synchronization in Pulse-Coupled Oscillator Networks II: A Numerical Study
NASA Astrophysics Data System (ADS)
Chen, Bolun; Engelbrecht, Jan R.; Mirollo, Renato
We use high-precision numerical simulations, to compute the dynamics of N identical integrate and fire model neurons coupled in an all-to-all network through α-function pulses. In particular, we determine the discrete evolution of the state of our system from spike to spike. In addition to traditional fully synchronous and splay states, we exhibit multiple competing partially synchronized ordered states, which are fixed points and limit cycles in the phase space. Close examinations reveal the bifurcations among different states. By varying the parameters, we map out the phase diagram of stable fixed points. Our results illustrate the power of dimensional reduction in complex dynamical systems, and shed light on the collective behaviors of neural networks. Work supported by NSF DMS 1413020.
On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs
NASA Astrophysics Data System (ADS)
Bayona, Victor; Flyer, Natasha; Fornberg, Bengt; Barnett, Gregory A.
2017-03-01
RBF-generated finite differences (RBF-FD) have in the last decade emerged as a very powerful and flexible numerical approach for solving a wide range of PDEs. We find in the present study that combining polyharmonic splines (PHS) with multivariate polynomials offers an outstanding combination of simplicity, accuracy, and geometric flexibility when solving elliptic equations in irregular (or regular) regions. In particular, the drawbacks on accuracy and stability due to Runge's phenomenon are overcome once the RBF stencils exceed a certain size due to an underlying minimization property. Test problems include the classical 2-D driven cavity, and also a 3-D global electric circuit problem with the earth's irregular topography as its bottom boundary. The results we find are fully consistent with previous results for data interpolation.
NASA Astrophysics Data System (ADS)
Johnsen, Eric; Larsson, Johan; Bhagatwala, Ankit V.; Cabot, William H.; Moin, Parviz; Olson, Britton J.; Rawat, Pradeep S.; Shankar, Santhosh K.; Sjögreen, Björn; Yee, H. C.; Zhong, Xiaolin; Lele, Sanjiva K.
2010-02-01
Flows in which shock waves and turbulence are present and interact dynamically occur in a wide range of applications, including inertial confinement fusion, supernovae explosion, and scramjet propulsion. Accurate simulations of such problems are challenging because of the contradictory requirements of numerical methods used to simulate turbulence, which must minimize any numerical dissipation that would otherwise overwhelm the small scales, and shock-capturing schemes, which introduce numerical dissipation to stabilize the solution. The objective of the present work is to evaluate the performance of several numerical methods capable of simultaneously handling turbulence and shock waves. A comprehensive range of high-resolution methods (WENO, hybrid WENO/central difference, artificial diffusivity, adaptive characteristic-based filter, and shock fitting) and suite of test cases (Taylor-Green vortex, Shu-Osher problem, shock-vorticity/entropy wave interaction, Noh problem, compressible isotropic turbulence) relevant to problems with shocks and turbulence are considered. The results indicate that the WENO methods provide sharp shock profiles, but overwhelm the physical dissipation. The hybrid method is minimally dissipative and leads to sharp shocks and well-resolved broadband turbulence, but relies on an appropriate shock sensor. Artificial diffusivity methods in which the artificial bulk viscosity is based on the magnitude of the strain-rate tensor resolve vortical structures well but damp dilatational modes in compressible turbulence; dilatation-based artificial bulk viscosity methods significantly improve this behavior. For well-defined shocks, the shock fitting approach yields good results.
Johnsen, Eric Larsson, Johan Bhagatwala, Ankit V.; Cabot, William H.; Moin, Parviz; Olson, Britton J.; Rawat, Pradeep S.; Shankar, Santhosh K.; Sjoegreen, Bjoern; Yee, H.C.; Zhong Xiaolin; Lele, Sanjiva K.
2010-02-20
Flows in which shock waves and turbulence are present and interact dynamically occur in a wide range of applications, including inertial confinement fusion, supernovae explosion, and scramjet propulsion. Accurate simulations of such problems are challenging because of the contradictory requirements of numerical methods used to simulate turbulence, which must minimize any numerical dissipation that would otherwise overwhelm the small scales, and shock-capturing schemes, which introduce numerical dissipation to stabilize the solution. The objective of the present work is to evaluate the performance of several numerical methods capable of simultaneously handling turbulence and shock waves. A comprehensive range of high-resolution methods (WENO, hybrid WENO/central difference, artificial diffusivity, adaptive characteristic-based filter, and shock fitting) and suite of test cases (Taylor-Green vortex, Shu-Osher problem, shock-vorticity/entropy wave interaction, Noh problem, compressible isotropic turbulence) relevant to problems with shocks and turbulence are considered. The results indicate that the WENO methods provide sharp shock profiles, but overwhelm the physical dissipation. The hybrid method is minimally dissipative and leads to sharp shocks and well-resolved broadband turbulence, but relies on an appropriate shock sensor. Artificial diffusivity methods in which the artificial bulk viscosity is based on the magnitude of the strain-rate tensor resolve vortical structures well but damp dilatational modes in compressible turbulence; dilatation-based artificial bulk viscosity methods significantly improve this behavior. For well-defined shocks, the shock fitting approach yields good results.
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
Numerical solution of fluid-structure interaction in piping systems by Glimm's method
NASA Astrophysics Data System (ADS)
Gomes da Rocha, Rogerio; Bastos de Freitas Rachid, Felipe
2012-01-01
This work presents a numerical procedure for obtaining approximated solutions for one-dimensional fluid-structure interaction (FSI) models, which are used in transient analyses of liquid-filled piping systems. The FSI model considered herein is formed by a system of hyperbolic partial differential equations and describes, simultaneously, pressure waves propagating in the liquid as well as axial, shear and bending waves traveling in the pipe walls. By taking advantage of an operator splitting technique, the flux term is split away from the source one, giving rise to a sequence of simpler problems formed by a set of homogeneous hyperbolic differential equations and by a set of ordinary differential equations in time. The numerical procedure is constructed by advancing in time sequentially through these sets of equations by employing Glimm's method and Gear's stiff method, respectively. To implement Glimm's method, analytical solutions for the associated Riemann problems are presented. The boundary conditions are properly accounted for in Glimm's method by formulating and analytically solving suitable (non-classical) Riemann problems for the pipe's ends. The proposed numerical procedure is used to obtain numerical approximations for the well-known eight-equation FSI model for two closed piping systems, in which transients are generated by the impact of a rod onto one of the ends. The obtained numerical results are compared with experimental data available in the literature and very good agreement is found.
A numerical study of the European option by the MLPG method with moving kriging interpolation.
Phaochoo, P; Luadsong, A; Aschariyaphotha, N
2016-01-01
In this paper, the meshless local Petrov-Galerkin (MLPG) method is applied for solving a generalized Black-Scholes equation in financial problems. This equation is a PDE governing the price evolution of a European call or a European put under the Black-Scholes model. The θ-weighted method and MLPG are used for discretizing the governing equation in time variable and option pricing, respectively. We show that the spectral radius of amplification matrix with the discrete operator is less than 1. This ensures that this numerical scheme is stable. Numerical experiments are performed with time varying volatility and the results are compared with the analytical and the numerical results of other methods.
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.
NASA Astrophysics Data System (ADS)
Ivanov, M. F.; Kiverin, A. D.; Pinevich, S. G.; Yakovenko, I. S.
2016-10-01
This paper discusses capabilities of the novel dissipation-free CABARET numerical algorithm to solve the range of complex non-stationary combustion problems. On the basis of detailed analysis of the obtained results and comparison with the data derived with the classic low-order coarse particles method it was shown that reactive flow evolution process may be strongly influenced by the artificial effects introduced by the numerical algorithm, numerical dissipation in particular. Revealed peculiarities of the flame propagation dynamics regimes taking place in considered tests allowed us to propose a number of requirements which should be taken into account when choosing numerical procedure suitable for modelling combustion processes in real technical environment.
NASA Astrophysics Data System (ADS)
Rizvi, Zarghaam Haider; Shrestha, Dinesh; Sattari, Amir S.; Wuttke, Frank
2017-09-01
Macroscopic parameters such as effective thermal conductivity (ETC) is an important parameter which is affected by micro and meso level behaviour of particulate materials, and has been extensively examined in the past decades. In this paper, a new lattice based numerical model is developed to predict the ETC of sand and modified high thermal backfill material for energy transportation used for underground power cables. 2D and 3D simulations are performed to analyse and detect differences resulting from model simplification. The thermal conductivity of the granular mixture is determined numerically considering the volume and the shape of the each constituting portion. The new numerical method is validated with transient needle measurements and the existing theoretical and semi empirical models for thermal conductivity prediction sand and the modified backfill material for dry condition. The numerical prediction and the measured values are in agreement to a large extent.
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.
An analytically based numerical method for computing view factors in real urban environments
NASA Astrophysics Data System (ADS)
Lee, Doo-Il; Woo, Ju-Wan; Lee, Sang-Hyun
2016-11-01
A view factor is an important morphological parameter used in parameterizing in-canyon radiative energy exchange process as well as in characterizing local climate over urban environments. For realistic representation of the in-canyon radiative processes, a complete set of view factors at the horizontal and vertical surfaces of urban facets is required. Various analytical and numerical methods have been suggested to determine the view factors for urban environments, but most of the methods provide only sky-view factor at the ground level of a specific location or assume simplified morphology of complex urban environments. In this study, a numerical method that can determine the sky-view factors (ψ ga and ψ wa ) and wall-view factors (ψ gw and ψ ww ) at the horizontal and vertical surfaces is presented for application to real urban morphology, which are derived from an analytical formulation of the view factor between two blackbody surfaces of arbitrary geometry. The established numerical method is validated against the analytical sky-view factor estimation for ideal street canyon geometries, showing a consolidate confidence in accuracy with errors of less than 0.2 %. Using a three-dimensional building database, the numerical method is also demonstrated to be applicable in determining the sky-view factors at the horizontal (roofs and roads) and vertical (walls) surfaces in real urban environments. The results suggest that the analytically based numerical method can be used for the radiative process parameterization of urban numerical models as well as for the characterization of local urban climate.
Deterministic numerical solutions of the Boltzmann equation using the fast spectral method
NASA Astrophysics Data System (ADS)
Wu, Lei; White, Craig; Scanlon, Thomas J.; Reese, Jason M.; Zhang, Yonghao
2013-10-01
The Boltzmann equation describes the dynamics of rarefied gas flows, but the multidimensional nature of its collision operator poses a real challenge for its numerical solution. In this paper, the fast spectral method [36], originally developed by Mouhot and Pareschi for the numerical approximation of the collision operator, is extended to deal with other collision kernels, such as those corresponding to the soft, Lennard-Jones, and rigid attracting potentials. The accuracy of the fast spectral method is checked by comparing our numerical solutions of the space-homogeneous Boltzmann equation with the exact Bobylev-Krook-Wu solutions for a gas of Maxwell molecules. It is found that the accuracy is improved by replacing the trapezoidal rule with Gauss-Legendre quadrature in the calculation of the kernel mode, and the conservation of momentum and energy are ensured by the Lagrangian multiplier method without loss of spectral accuracy. The relax-to-equilibrium processes of different collision kernels with the same value of shear viscosity are then compared; the numerical results indicate that different forms of the collision kernels can be used as long as the shear viscosity (not only the value, but also its temperature dependence) is recovered. An iteration scheme is employed to obtain stationary solutions of the space-inhomogeneous Boltzmann equation, where the numerical errors decay exponentially. Four classical benchmarking problems are investigated: the normal shock wave, and the planar Fourier/Couette/force-driven Poiseuille flows. For normal shock waves, our numerical results are compared with a finite difference solution of the Boltzmann equation for hard sphere molecules, experimental data, and molecular dynamics simulation of argon using the realistic Lennard-Jones potential. For planar Fourier/Couette/force-driven Poiseuille flows, our results are compared with the direct simulation Monte Carlo method. Excellent agreements are observed in all test cases
NASA Astrophysics Data System (ADS)
Ortleb, Sigrun; Seidel, Christian
2017-07-01
In this second symposium at the limits of experimental and numerical methods, recent research is presented on practically relevant problems. Presentations discuss experimental investigation as well as numerical methods with a strong focus on application. In addition, problems are identified which require a hybrid experimental-numerical approach. Topics include fast explicit diffusion applied to a geothermal energy storage tank, noise in experimental measurements of electrical quantities, thermal fluid structure interaction, tensegrity structures, experimental and numerical methods for Chladni figures, optimized construction of hydroelectric power stations, experimental and numerical limits in the investigation of rain-wind induced vibrations as well as the application of exponential integrators in a domain-based IMEX setting.
Numerical wave tank based on a conserved wave-absorbing method
NASA Astrophysics Data System (ADS)
Hu, Zhe; Tang, Wen-yong; Xue, Hong-xiang; Zhang, Xiao-ying
2016-03-01
Recently the numerical wave tank has become a widely-used tool to study waves as well as wave-structure interactions, and the wave-absorbing method is very important as its effect on the quality of waves generated. The relaxation method and the derived momentum source method are often utilized, however, the damping weight is constant during calculation and repeated trials are required to obtain an acceptable wave-absorbing effect. To address the abovementioned issues, a conserved wave-absorbing method is developed. The damping weight is determined by solving the mass conservation equation of the absorbing region at every time step. Based on this method, a two-dimensional numerical wave tank is established by using the VB language to simulate various waves by which the validation of this method is evaluated.
The Interruption of Alpine Foehn by a Cold Front. Part II: Numerical Simulations
NASA Astrophysics Data System (ADS)
Dautz, E.; Gohm, A.
2010-09-01
In this work the interaction of Alpine foehn winds with a cold front is investigated. Despite the wealth of studies on south foehn in the region of Innsbruck during the last century not much is known about the dynamics of foehn breakdown. In most cases, the interruption of foehn is connected with a cold front, which approaches the Alps from northerly or northwesterly directions. The resulting change of warm and dry southerly winds to a cold and moist airmass may occur within less than an hour. The objective of this study is to receive a better understanding of the dynamical processes connected with the collision of two airflows from opposing directions in an Alpine valley by means of numerical simulations conducted with the Weather Research and Forecasting (WRF) Model, Version 3.1. For this purpose a foehn event at the Special Observing Period (SOP) of the Mesoscale Alpine Programme (MAP) has been chosen. On 6 November 1999 a cold front impinged on the Alps and caused the breakdown of the foehn flow. The investigations are mainly focused on the Austrian Inn- and Wipp Valley, which has been one of the target areas during the MAP SOP. The results from the mesoscale model are compaired against the large available observational data set, including surface station, radiosonde and lidar measurements. Nested model runs provide the ability to investigate a wide range of temporal and spatial scales. The model is able to capture the blocking of moist air south of the Alps during foehn and the deformation of the cold front by the mountain range north of the Alps. To quantitatively describe the exchange of air masses in a given box near Innsbruck a mass budget calculation has been accomplished. The most prominent feature is a sudden increase of the inflow from the west during the cold front passage. The fine-scale structure of the cold front, which shows the nature of a density current, is determined with an additional one-way nested high-resolution simulation in the Wipp
NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION
Liu, F.; Meerschaert, M.M.; McGough, R.J.; Zhuang, P.; Liu, Q.
2013-01-01
In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian. PMID:23772179
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.
A numerical method to solve the Stokes problem with a punctual force in source term
NASA Astrophysics Data System (ADS)
Lacouture, Loïc
2015-03-01
The aim of this note is to present a numerical method to solve the Stokes problem in a bounded domain with a Dirac source term, which preserves optimality for any approximation order by the finite-element method. It is based on the knowledge of a fundamental solution to the associated operator over the whole space. This method is motivated by the modeling of the movement of active thin structures in a viscous fluid.
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.
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.
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.
Detection of Extraterrestrial Life. Method II- Optical Rotatory Dispersion
NASA Technical Reports Server (NTRS)
1963-01-01
The object of this study is to develop polarimetric methods to detect the presence of DNA (deoxyribonucleic acid) or its congeners in soil suspensions, and through these methods determine the existence of life (as known terrestrially) on other planets. The cotton region associated with optically active organic compounds is being used to detect and characterize the compounds above. An apparatus has been designed and assembled which can measure optical rotations in systems which strongly attenuate incident-polarized, monochromatic light. This instrument was used to measure the optical rotatory dispersion spectra of nucleosides, a polynucleotide, and proteins whose optical density at 260 microns approached 1.0. This work is discussed in the final report on Contract NASR-85, Detection of Extraterrestrial Life, Method II: Optical Rotatory Dispersion. Recent work in Melpar laboratories has reaffirmed these rotatory dispersion spectra. Based upon the analysis of the optical components associated with this apparatus, however, these measurements must be considered as qualitative rather than quantitative. The reason for this is discussed in greater detail subsequently in this report. In addition, an evaluation of the theoretical and instrumental aspects of making rotatory-dispersion measurements in the cotton region has resulted in a procedure for measuring optical rotation.
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.
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.
Convection in a rotating magnetic system and taylor's constraint part II, numerical results
NASA Astrophysics Data System (ADS)
Skinner, P. H.; Soward, A. M.
1991-11-01
Results are presented of a numerical study of marginal convection of electrically conducting fluid, permeated by a strong azimuthal magnetic field, contained in a circular cylinder rotating rapidly about its vertical axis of symmetry. To this basic state is added a geostrophic flow UG(s), constant on geostrophic cylinders radius s. Its magnitude is fixed by requiring that the Lorentz forces induced by the convecting mode satisfy Taylor's condition. The nonlinear mathematical problem describing the system was developed in an earlier paper (Skinner and Soward, 1988) and the predictions made there are confirmed here. In particular, for small values of the Roberts number q which measures the ratio of the thermal to magnetic diffusivities, two distinct regions can be recognised within the fluid with the outer region moving rapidly compared to the inner. Otherwise, conditions for the onset of instability via the Taylor state (UG0) do not differ significantly from those appropriate to the static (UG = 0) basic state. The possible disruption of the Taylor states by shear flow instabilities is discussed briefly.
Hindi, H.; Prabhakar, S.; Fox, J.; Teytelman, D.
1997-12-01
The authors present a technique for the design and verification of efficient bunch-by-bunch controllers for damping longitudinal multibunch instabilities. The controllers attempt to optimize the use of available feedback amplifier power--one of the most expensive components of a feedback system--and define the limits of closed loop system performance. The design technique alternates between analytic computation of single bunch optimal controllers and verification on a multibunch numerical simulator. The simulator identifies unstable coupled bunch modes and predicts their growth and damping rates. The results from the simulator are shown to be in reasonable agreement with analytical calculations based on the single bunch model. The technique is then used to evaluate the performance of a variety of controllers proposed for PEP-II.
NASA Astrophysics Data System (ADS)
Alvionita; Sutikno; Suharsono, A.
2017-03-01
Cluster analysis is a technique in multivariate analysis methods that reduces (classifying) data. This analysis has the main purpose to classify the objects of observation into groups based on characteristics. In the process, a cluster analysis is not only used for numerical data or categorical data but also developed for mixed data. There are several methods in analyzing the mixed data as ensemble methods and methods Similarity Weight and Filter Methods (SWFM). There is a lot of research on these methods, but the study did not compare the performance given by both of these methods. Therefore, this paper will be compared the performance between the clustering ensemble ROCK methods and ensemble SWFM methods. These methods will be used in clustering cross citrus accessions based on the characteristics of fruit and leaves that involve variables that are a mixture of numerical and categorical. Clustering methods with the best performance determined by looking at the ratio of standard deviation values within groups (SW) with a standard deviation between groups (SB). Methods with the best performance has the smallest ratio. From the result, we get that the performance of ensemble ROCK methods is better than ensemble SWFM methods.
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.
Numerical solution of the Navier-Stokes equations by discontinuous Galerkin method
NASA Astrophysics Data System (ADS)
Krasnov, M. M.; Kuchugov, P. A.; E Ladonkina, M.; E Lutsky, A.; Tishkin, V. F.
2017-02-01
Detailed unstructured grids and numerical methods of high accuracy are frequently used in the numerical simulation of gasdynamic flows in areas with complex geometry. Galerkin method with discontinuous basis functions or Discontinuous Galerkin Method (DGM) works well in dealing with such problems. This approach offers a number of advantages inherent to both finite-element and finite-difference approximations. Moreover, the present paper shows that DGM schemes can be viewed as Godunov method extension to piecewise-polynomial functions. As is known, DGM involves significant computational complexity, and this brings up the question of ensuring the most effective use of all the computational capacity available. In order to speed up the calculations, operator programming method has been applied while creating the computational module. This approach makes possible compact encoding of mathematical formulas and facilitates the porting of programs to parallel architectures, such as NVidia CUDA and Intel Xeon Phi. With the software package, based on DGM, numerical simulations of supersonic flow past solid bodies has been carried out. The numerical results are in good agreement with the experimental ones.
NASA Astrophysics Data System (ADS)
Lin, Hong; Vekilov, Peter G.; Rosenberger, Franz
1996-02-01
A model for the evolution of facet morphologies in growth from solutions is presented. The numerical model links, for the first time, bulk transport of solute and impurities in a solution growth cell with microscopic interfacial kinetics processes. The macroscopic transport is dealt with as in the 2D model [H. Lin, F. Rosenberger, J.I.D. Alexander and A. Nadarajah, J. Crystal Growth 151 (1995) 153] of a crystallization cell used for lysozyme in our laboratory. The microscopic kinetics is incorporated through a meso-scale continuum model of growth step motion in response to the interfacial concentration distributions. Local growth step velocities are linearly interpolated from the values obtained at the grid points of the bulk transport simulation. Experimentally determined kinetics and transport coefficients are employed. We find that the facets remain macroscopically flat, in spite of the lower nutrient and impurity concentrations in the facet center regions. This stabilization is achieved through the formation of a microscopic depression in the facet, with nonuniform vicinal slope (step density). If the step density in the facet center exceeds a certain value, no further stabilization results on further steepening, and the facet loses its macroscopic morphological stability. This loss of morphological stability depends sensitively on the value of the steps' kinetic coefficient. For pure lysozyme-precipitant solutions, we obtain microscopic depressions with a higher slope at the facet center than at the edge. However, with an impurity that impedes step kinetics and is preferentially incorporated into the crystal, the simulations produce microscopic facet depressions with higher slope at the edge. Impurity depletion at the interface, due to low initial concentration and/or slow diffusion leads to mixed shapes, and eventually to shapes typical of growth from pure solution. Quantitative agreement with facet morphologies observed on lysozyme crystals [P.G. Vekilov and
Numerical simulations of granular dynamics II: Particle dynamics in a shaken granular material
NASA Astrophysics Data System (ADS)
Murdoch, Naomi; Michel, Patrick; Richardson, Derek C.; Nordstrom, Kerstin; Berardi, Christian R.; Green, Simon F.; Losert, Wolfgang
2012-05-01
Surfaces of planets and small bodies of our Solar System are often covered by a layer of granular material that can range from a fine regolith to a gravel-like structure of varying depths. Therefore, the dynamics of granular materials are involved in many events occurring during planetary and small-body evolution thus contributing to their geological properties. We demonstrate that the new adaptation of the parallel N-body hard-sphere code pkdgrav has the capability to model accurately the key features of the collective motion of bidisperse granular materials in a dense regime as a result of shaking. As a stringent test of the numerical code we investigate the complex collective ordering and motion of granular material by direct comparison with laboratory experiments. We demonstrate that, as experimentally observed, the scale of the collective motion increases with increasing small-particle additive concentration. We then extend our investigations to assess how self-gravity and external gravity affect collective motion. In our reduced-gravity simulations both the gravitational conditions and the frequency of the vibrations roughly match the conditions on asteroids subjected to seismic shaking, though real regolith is likely to be much more heterogeneous and less ordered than in our idealised simulations. We also show that collective motion can occur in a granular material under a wide range of inter-particle gravity conditions and in the absence of an external gravitational field. These investigations demonstrate the great interest of being able to simulate conditions that are to relevant planetary science yet unreachable by Earth-based laboratory experiments.
NASA Astrophysics Data System (ADS)
Toma, Violeta E.; Webster, Peter John
2010-03-01
A companion paper (Part I: Toma and Webster 2008), argued that the characteristics of the mean Intertropical Convergence Zone (ITCZ) arise from instabilities associated with the strong cross-equatorial pressure gradient (CEPG) that exists in the eastern Pacific Ocean as a result of the latitudinal sea-surface temperature (SST) gradient. Furthermore, it was argued that instabilities of the mean ITCZ resulted in the in situ development of easterly waves. Thus, in Part I, it was hypothesized that the mean and transient state of eastern Pacific convection was due to local processes and less so to the advection of waves from the North Atlantic Ocean. To test this hypothesis and, at the same time, consider others such as a possible role of the equatorial and subtropical orography in generating local instabilities, a series of controlled numerical experiments are designed using the WRF regional model. The domain of the model was configured to include the western Atlantic Ocean, the Isthmus of Panama and the eastern Pacific Ocean to 155°W. Lateral boundaries were set at 40°N and 40°S, thus containing the mountains of Central America, the Andes and the Sierra Madre of Mexico. In a series of experiments, analysis products were used as boundary conditions that were successively updated four times per day, set as 10-day running average fields or as running mean monthly fields. Finally, the model was run with topography essentially eliminated over the land areas. Although there are differences between the details of the resultant fields, the location of mean convection and the form of the transients remain the same. It is concluded, in support of the theoretical and diagnostic studies of Part I that orographic forcing or waves generated in the North Atlantic Ocean are not the major causes of the mean and transient nature of disturbances in the eastern Pacific.
NASA Astrophysics Data System (ADS)
Gibbes, B.; Robinson, C.; Li, L.; Lockington, D.; Li, H.
2008-12-01
Field measurements presented by [Gibbes, B., Robinson, C., Li, L., Lockington, D.A., Carey, H., 2008. Tidally driven pore water exchange within offshore intertidal sandbanks: Part I Field measurements. Estuarine, Coastal and Shelf Science 79, pp. 121-132.] revealed a tidally driven pore water flow system within an offshore intertidal sandbank in Moreton Bay, Australia. The field data suggested that this flow system might be capable of delivering nutrients, and in particular bio-available iron, across the sediment-water interface. Bio-available iron has been implicated as a key nutrient in the growth of the toxic marine cyanobacteria Lyngbya majuscula and therefore this pore water exchange process is of interest at sites where L. majuscula blooms have been observed. In this study two-dimensional numerical simulations were used in conjunction with hydraulic data from field measurements to further investigate the tidally induced pore water flow patterns. Simulation results generally showed good agreement with the field data and revealed a more complex residual pore water flow system in the sandbank than shown by the field data. The flow system, strongly influenced by the geometry of the sandbank, was characterized by two circulation cells which resulted in pore water discharge at the bank edge and also to a permanently ponded area within the sandbank interior. Simulated discharge volumes in these two zones were in the order of 0.813 m 3 and 0.143 m 3 per meter width (along shore) of sandbank per tidal cycle at the bank edge and sandbank interior respectively. Transit times of pore water circulating through these cells were found to range from ≈ 17 days to > 60 years with an average time of 780 days. The results suggest that the tidally driven flow systems might provide a mechanism for transport of bio-available iron across the sediment-water interface. This flow could constitute a previously unrecognized source of bio-available iron for L. majuscula blooms in the
Direct numerical simulations of the double scalar mixing layer. Part II: Reactive scalars
Mortensen, Mikael; de Bruyn Kops, Stephen M.; Cha, Chong M.
2007-06-15
The reacting double scalar mixing layer (RDSML) is investigated as a canonical multistream flow and a model problem for simple piloted diffusion flames. In piloted diffusion flames, the reacting fuel and oxidizer streams are initially separated by a central pilot stream at stoichiometric composition. The primary purpose of this pilot is to delay the mixing of the pure streams until a stable flame base can develop. In such multistream systems, the modeling of turbulent scalar mixing is complicated by the multiple feed streams, leading to more complex fine-scale statistics, which remain as yet an unmet modeling challenge compared to the simpler two-feed system. In Part I we described how multimodal mixture fraction probability density functions (PDFs) and conditional scalar dissipation rates can be modeled with a presumed mapping function approach. In this work we present an efficient and robust extension of the modeling to a general multistream reacting flow and compare predictions to three-dimensional direct numerical simulations (DNS) of the RDSML with a single-step reversible chemistry model and varying levels of extinction. With high extinction levels, the interaction with the pilot stream is described. Additionally, state-of-the-art combustion modeling calculations including conditional moment closure (CMC) and stationary laminar flamelet modeling (SLFM) are performed with the newly developed mixing model. Excellent agreement is found between the DNS and modeling predictions, even where the PDF is essentially a triple-delta shape near the flame base, so long as extinction levels are moderate to low. The suggested approach outlined in this paper is strictly valid only for flows that can be described by a single mixture fraction. For these flows the approach should provide engineers with fine-scale models that are of accuracy comparable to those already available for binary mixing, at only marginally higher complexity and cost. (author)
The stability of numerical methods for second order ordinary differential equations
NASA Technical Reports Server (NTRS)
Gear, C. W.
1978-01-01
An important characterization of a numerical method for first order ODE's is the region of absolute stability. If all eigenvalues of the linear problem dy/dt = Ay are inside this region, the numerical method is stable. If the second order system d/dt(dy/dt) = 2Ady/dt - By is solved as a first order system, the same result applies to the eigenvalues of the generalized eigenvalue problem (lambda-squared)I 2(lambda)A + B. No such region exists for general methods for second order equations, but in some cases a region of absolute stability can be defined for methods for the single second order equation d/dt(dy/dt) = 2ady/dt - by. The absence of a region of absolute stability can occur when different members of a system of first order equations are solved by different methods.
A numerical study of 2D detonation waves with adaptive finite volume methods on unstructured grids
NASA Astrophysics Data System (ADS)
Hu, Guanghui
2017-02-01
In this paper, a framework of adaptive finite volume solutions for the reactive Euler equations on unstructured grids is proposed. The main ingredients of the algorithm include a second order total variation diminishing Runge-Kutta method for temporal discretization, and the finite volume method with piecewise linear solution reconstruction of the conservative variables for the spatial discretization in which the least square method is employed for the reconstruction, and weighted essentially nonoscillatory strategy is used to restrain the potential numerical oscillation. To resolve the high demanding on the computational resources due to the stiffness of the system caused by the reaction term and the shock structure in the solutions, the h-adaptive method is introduced. OpenMP parallelization of the algorithm is also adopted to further improve the efficiency of the implementation. Several one and two dimensional benchmark tests on the ZND model are studied in detail, and numerical results successfully show the effectiveness of the proposed method.
A Numerical Method for Simulation of Three Dimensional Ice Accretion on Aircrafts
NASA Astrophysics Data System (ADS)
Yi, X.; Wang, K. C.; Zhu, G. L.; Gui, Y. W.
2011-09-01
A numerical method for simulation of three dimensional ice accretion on aircraft is proposed in this paper. An Eulerian method for computation of collection efficiency on icing surface is presented at first. The external flow field of gas phase is calculated with computational fluid dynamics (CFD) method, based on which the governing equations of water phase are solved, and the corresponding collection efficiency is obtained. A three-dimensional model, considering effects of runback water, is then presented, and an iterative arithmetic for solving the model is developed. The impingement characteristics of a three elements wing are computed to evaluate the numerical method for collection efficiency calculation. Ice accretion on a MS-317 swept wing is calculated, and the consequent ice shape is compared with that of an experiment and Lewice3D. All the computational results are in good agreement with data of the experiment and reference, which indicates that the proposed method is feasible.
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.
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 built-in method for the nonlinear JRC/JCS model in rock joint.
Liu, Qunyi; Xing, Wanli; Li, Ying
2014-01-01
The joint surface is widely distributed in the rock, thus leading to the nonlinear characteristics of rock mass strength and limiting the effectiveness of the linear model in reflecting characteristics. The JRC/JCS model is the nonlinear failure criterion and generally believed to describe the characteristics of joints better than other models. In order to develop the numerical program for JRC/JCS model, this paper established the relationship between the parameters of the JRC/JCS and Mohr-Coulomb models. Thereafter, the numerical implement method and implementation process of the JRC/JCS model were discussed and the reliability of the numerical method was verified by the shear tests of jointed rock mass. Finally, the effect of the JRC/JCS model parameters on the shear strength of the joint was analyzed.
VERSE-Guided Numerical RF Pulse Design: A Fast Method for Peak RF Power Control
Lee, Daeho; Grissom, William A.; Lustig, Michael; Kerr, Adam B.; Stang, Pascal P.; Pauly, John M.
2013-01-01
In parallel excitation, the computational speed of numerical radiofrequency (RF) pulse design methods is critical when subject dependencies and system nonidealities need to be incorporated on-the-fly. One important concern with optimization-based methods is high peak RF power exceeding hardware or safety limits. Hence, online controllability of the peak RF power is essential. Variable-rate selective excitation pulse reshaping is ideally suited to this problem due to its simplicity and low computational cost. In this work, we first improve the fidelity of variable-rate selective excitation implementation for discrete-time waveforms through waveform oversampling such that variable-rate selective excitation can be robustly applied to numerically designed RF pulses. Then, a variable-rate selective excitation-guided numerical RF pulse design is suggested as an online RF pulse design framework, aiming to simultaneously control peak RF power and compensate for off-resonance. PMID:22135085
Numerical and experimental validation of a particle Galerkin method for metal grinding simulation
NASA Astrophysics Data System (ADS)
Wu, C. T.; Bui, Tinh Quoc; Wu, Youcai; Luo, Tzui-Liang; Wang, Morris; Liao, Chien-Chih; Chen, Pei-Yin; Lai, Yu-Sheng
2017-08-01
In this paper, a numerical approach with an experimental validation is introduced for modelling high-speed metal grinding processes in 6061-T6 aluminum alloys. The derivation of the present numerical method starts with an establishment of a stabilized particle Galerkin approximation. A non-residual penalty term from strain smoothing is introduced as a means of stabilizing the particle Galerkin method. Additionally, second-order strain gradients are introduced to the penalized functional for the regularization of damage-induced strain localization problem. To handle the severe deformation in metal grinding simulation, an adaptive anisotropic Lagrangian kernel is employed. Finally, the formulation incorporates a bond-based failure criterion to bypass the prospective spurious damage growth issues in material failure and cutting debris simulation. A three-dimensional metal grinding problem is analyzed and compared with the experimental results to demonstrate the effectiveness and accuracy of the proposed numerical approach.
NASA Astrophysics Data System (ADS)
Gu, Boliang; Nihei, Kurt T.; Myer, Larry R.
1996-07-01
This paper describes a boundary integral equation method for simulating two-dimensional elastic wave propagation in a rock mass with nonwelded discontinuities, such as fractures, joints, and faults. The numerical formulation is based on the three-dimensional boundary integral equations that are reduced to two dimensions by numerical integration along the axis orthogonal to the plane of interest. The numerical technique requires the assembly and solution of the coefficient matrix only for the first time step, resulting in a significant reduction in computational time. Nonwelded discontinuities are each treated as an elastic contact between blocks of a fractured rock mass. Across such an elastic contact, seismic stresses are continuous and particle displacements are discontinuous by an amount which is proportional to the stress on the discontinuity and inversely to the specific stiffness of the discontinuity. Simulations demonstrate that such formulated boundary element method successfully models elastic wave propagation along and across a single fracture generated by a line source.
Takamoto, Makoto; Inoue, Tsuyoshi
2011-07-10
We present a new numerical method of special relativistic resistive magnetohydrodynamics with scalar resistivity that can treat a range of phenomena, from non-relativistic to relativistic (shock, contact discontinuity, and Alfven wave). The present scheme calculates the numerical flux of fluid by using an approximate Riemann solver and electromagnetic field by using the method of characteristics. Since this scheme uses appropriate characteristic velocities, it is capable of accurately solving problems that cannot be approximated as ideal magnetohydrodynamics and whose characteristic velocity is much lower than the velocity of light. The numerical results show that our scheme can solve the above problems as well as nearly ideal MHD problems. Our new scheme is particularly well suited to systems with initially weak magnetic field and mixed phenomena of relativistic and non-relativistic velocity, for example magnetorotational instability in an accretion disk and super Alfvenic turbulence.
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.
Eigensensitivity analysis of rotating clamped uniform beams with the asymptotic numerical method
NASA Astrophysics Data System (ADS)
Bekhoucha, F.; Rechak, S.; Cadou, J. M.
2016-12-01
In this paper, free vibrations of a rotating clamped Euler-Bernoulli beams with uniform cross section are studied using continuation method, namely asymptotic numerical method. The governing equations of motion are derived using Lagrange's method. The kinetic and strain energy expression are derived from Rayleigh-Ritz method using a set of hybrid variables and based on a linear deflection assumption. The derived equations are transformed in two eigenvalue problems, where the first is a linear gyroscopic eigenvalue problem and presents the coupled lagging and stretch motions through gyroscopic terms. While the second is standard eigenvalue problem and corresponds to the flapping motion. Those two eigenvalue problems are transformed into two functionals treated by continuation method, the Asymptotic Numerical Method. New method proposed for the solution of the linear gyroscopic system based on an augmented system, which transforms the original problem to a standard form with real symmetric matrices. By using some techniques to resolve these singular problems by the continuation method, evolution curves of the natural frequencies against dimensionless angular velocity are determined. At high angular velocity, some singular points, due to the linear elastic assumption, are computed. Numerical tests of convergence are conducted and the obtained results are compared to the exact values. Results obtained by continuation are compared to those computed with discrete eigenvalue problem.
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)
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)
Detailed Numerical Simulations on the Formation of Pillars Around H II Regions
NASA Astrophysics Data System (ADS)
Gritschneder, Matthias; Burkert, Andreas; Naab, Thorsten; Walch, Stefanie
2010-11-01
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-3 or 300 cm-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 implosion of
NASA Astrophysics Data System (ADS)
Khalili, Mohamed Hassan; Roux, Jean-Noël; Pereira, Jean-Michel; Brisard, Sébastien; Bornert, Michel
2017-03-01
The elastic moduli of a transversely isotropic model granular material, made of slightly polydisperse elastic-frictional spherical beads, in equilibrium along a one-dimensional (oedometric) compression path, as described in the companion paper [M. H. Khalili et al., Phys. Rev. E 95, 032907 (2017)], 10.1103/PhysRevE.95.032907, are investigated by numerical simulations. The relations of the five independent moduli to stresses, density, coordination number, fabric and force anisotropies are studied for different internal material states along the oedometric loading path. It is observed that elastic moduli, as in isotropic packs, are primarily determined by the coordination number, with anomalously small shear moduli in poorly coordinated systems, whatever their density. Such states also exhibit faster increasing moduli in compression, and larger off-diagonal moduli and Poisson ratios. Anisotropy affects the longitudinal moduli C11 in the axial direction and C22 in the transverse directions, and the shear modulus in the transverse plane C44, more than the shear modulus in a plane containing the axial direction C55. The results are compared to available experiments on anisotropic bead packs, revealing, despite likely differences in internal states, a very similar range of stiffness level (linked to coordination), and semiquantitative agreement as regards the influence of anisotropy. Effective medium theory (the Voigt approach) provides quite inaccurate predictions of the moduli. It also significantly underestimates ratios C11/C22 (varying between 1 and 2.2) and C55/C44 (varying from 1 to 1.6), which characterize elastic anisotropy, except in relatively weakly anisotropic states. The bulk modulus for isotropic compression and the compliance corresponding to stress increments proportional to the previous stress values are the only elastic coefficients to be correctly estimated by available predictive relations. We discuss the influences of fabric and force anisotropies
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.
Implementing a Flipped Classroom Approach in a University Numerical Methods Mathematics Course
ERIC Educational Resources Information Center
Johnston, Barbara M.
2017-01-01
This paper describes and analyses the implementation of a "flipped classroom" approach, in an undergraduate mathematics course on numerical methods. The approach replaced all the lecture contents by instructor-made videos and was implemented in the consecutive years 2014 and 2015. The sequential case study presented here begins with an…
A semi-analytical method for simulating matrix diffusion in numerical transport models
NASA Astrophysics Data System (ADS)
Falta, Ronald W.; Wang, Wenwen
2017-02-01
A semi-analytical approximation for transient matrix diffusion is developed for use in numerical contaminant transport simulators. This method is an adaptation and extension of the heat conduction method of Vinsome and Westerveld (1980) used to simulate heat losses during thermally enhanced oil recovery. The semi-analytical method is used in place of discretization of the low permeability materials, and it represents the concentration profile in the low permeability materials with a fitting function that is adjusted in each element at each time-step. The resulting matrix diffusion fluxes are added to the numerical model as linear concentration-dependent source/sink terms. Since only the high permeability zones need to be discretized, the numerical formulation is extremely efficient compared to traditional approaches that require discretization of both the high and low permeability zones. The semi-analytical method compares favorably with the analytical solution for transient one-dimensional diffusion with first order decay, with a two-layer aquifer/aquitard solution, with the solution for transport in a fracture with matrix diffusion and decay, and with a fully numerical solution for transport in a thin sand zone bounded by clay with variable decay rates.
Numerical Simulation of Drophila Flight Based on Arbitrary Langrangian-Eulerian Method
NASA Astrophysics Data System (ADS)
Erzincanli, Belkis; Sahin, Mehmet
2012-11-01
A parallel unstructured finite volume algorithm based on Arbitrary Lagrangian Eulerian (ALE) method has been developed in order to investigate the wake structure around a pair of flapping Drosophila wings. The numerical method uses a side-centered arrangement of the primitive variables that does not require any ad-hoc modifications in order to enhance pressure coupling. A radial basis function (RBF) interpolation method is also implemented in order to achieve large mesh deformations. For the parallel solution of resulting large-scale algebraic equations, a matrix factorization is introduced similar to that of the projection method for the whole coupled system and two-cycle of BoomerAMG solver is used for the scaled discrete Laplacian provided by the HYPRE library which we access through the PETSc library. The present numerical algorithm is initially validated for the flow past an oscillating circular cylinder in a channel and the flow induced by an oscillating sphere in a cubic cavity. Then the numerical algorithm is applied to the numerical simulation of flow field around a pair of flapping Drosophila wing in hover flight. The time variation of the near wake structure is shown along with the aerodynamic loads and particle traces. The authors acknowledge financial support from Turkish National Scientific and Technical Research Council (TUBITAK) through project number 111M332. The authors would like to thank Michael Dickinson and Michael Elzinga for providing the experimental data.
NASA Technical Reports Server (NTRS)
Maccormack, R. W.
1978-01-01
The calculation of flow fields past aircraft configuration at flight Reynolds numbers is considered. Progress in devising accurate and efficient numerical methods, in understanding and modeling the physics of turbulence, and in developing reliable and powerful computer hardware is discussed. Emphasis is placed on efficient solutions to the Navier-Stokes equations.
A semi-analytical method for simulating matrix diffusion in numerical transport models.
Falta, Ronald W; Wang, Wenwen
2017-02-01
A semi-analytical approximation for transient matrix diffusion is developed for use in numerical contaminant transport simulators. This method is an adaptation and extension of the heat conduction method of Vinsome and Westerveld (1980) used to simulate heat losses during thermally enhanced oil recovery. The semi-analytical method is used in place of discretization of the low permeability materials, and it represents the concentration profile in the low permeability materials with a fitting function that is adjusted in each element at each time-step. The resulting matrix diffusion fluxes are added to the numerical model as linear concentration-dependent source/sink terms. Since only the high permeability zones need to be discretized, the numerical formulation is extremely efficient compared to traditional approaches that require discretization of both the high and low permeability zones. The semi-analytical method compares favorably with the analytical solution for transient one-dimensional diffusion with first order decay, with a two-layer aquifer/aquitard solution, with the solution for transport in a fracture with matrix diffusion and decay, and with a fully numerical solution for transport in a thin sand zone bounded by clay with variable decay rates. Copyright © 2017 Elsevier B.V. All rights reserved.
A Numerical Methods Course Based on B-Learning: Integrated Learning Design and Follow Up
ERIC Educational Resources Information Center
Cepeda, Francisco Javier Delgado
2013-01-01
Information and communication technologies advance continuously, providing a real support for learning processes. Learning technologies address areas which previously have corresponded to face-to-face learning, while mobile resources are having a growing impact on education. Numerical Methods is a discipline and profession based on technology. In…
NASA Astrophysics Data System (ADS)
Stupishin, L.; Nikitin, K.; Kolesnikov, A.
2017-05-01
A methodology for shell stability research and determining buckling load, based on the mixed finite element method are proposed. Axisymmetric geometrically nonlinear shallow shells made of orthotropic material are considered. The results of numerical research of stability by changing the shape of shells, ratio of elastic modulus of the material and parameters of the support contour are presented.
A novel method of including Landau level mixing in numerical studies of the quantum Hall effect
Wooten, Rachel; Quinn, John; Macek, Joseph
2013-12-04
Landau level mixing should influence the quantum Hall effect for all except the strongest applied magnetic fields. We propose a simple method for examining the effects of Landau level mixing by incorporating multiple Landau levels into the Haldane pseudopotentials through exact numerical diagonalization. Some of the resulting pseudopotentials for the lowest and first excited Landau levels will be presented.
A novel method of including Landau level mixing in numerical studies of the quantum Hall effect
NASA Astrophysics Data System (ADS)
Wooten, Rachel; Quinn, John; Macek, Joseph
2013-12-01
Landau level mixing should influence the quantum Hall effect for all except the strongest applied magnetic fields. We propose a simple method for examining the effects of Landau level mixing by incorporating multiple Landau levels into the Haldane pseudopotentials through exact numerical diagonalization. Some of the resulting pseudopotentials for the lowest and first excited Landau levels will be presented.
A three-scale offline-online numerical method for fluid flow in porous media
NASA Astrophysics Data System (ADS)
Abdulle, Assyr; Budáč, Ondrej; Imboden, Antoine
2017-05-01
A new multiscale method combined with model order reduction is proposed for flow problems in a three-scale porous material. We derive an effective three-scale model that couples a macroscopic Darcy equation, a mesoscopic Stokes-Brinkman equation, and a microscopic Stokes equation. A corresponding three-scale numerical method is then derived using the finite element discretization with numerical quadrature, where the macroscopic and mesoscopic permeability is upscaled at quadrature points from mesoscopic and microscopic problems, respectively. The computational cost of solving numerous mesoscopic and microscopic flow problems is further reduced by applying a Petrov-Galerkin reduced basis method at the mesoscopic and microscopic scales. As there is no natural way to obtain an affine decomposition of the mesoscopic problems, which is instrumental for the efficiency of the model order reduction, we derive a mesoscopic solver that makes use of empirical interpolation techniques. A priori and a posteriori error estimates are derived for the new method that is also tested numerically to corroborate the theoretical convergence rates and illustrate its efficiency.
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.
Numerical simulation of the process of production of single crystals by the Verneuil method
NASA Astrophysics Data System (ADS)
Grzymkowski, Radoslaw; Mochnacki, Bohdan; Suchy, Josef
1985-12-01
The paper presents the mathematical model of non-stationary crystallization of Al 2O 3 by Verneuil method, while taking into account the bilateral conjugation of this process with the admixture segregation phenomenon (Cr + for example). The numerical results are also shown.
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…
Numerical simulation of pseudoelastic shape memory alloys using the large time increment method
NASA Astrophysics Data System (ADS)
Gu, Xiaojun; Zhang, Weihong; Zaki, Wael; Moumni, Ziad
2017-04-01
The paper presents a numerical implementation of the large time increment (LATIN) method for the simulation of shape memory alloys (SMAs) in the pseudoelastic range. The method was initially proposed as an alternative to the conventional incremental approach for the integration of nonlinear constitutive models. It is adapted here for the simulation of pseudoelastic SMA behavior using the Zaki-Moumni model and is shown to be especially useful in situations where the phase transformation process presents little or lack of hardening. In these situations, a slight stress variation in a load increment can result in large variations of strain and local state variables, which may lead to difficulties in numerical convergence. In contrast to the conventional incremental method, the LATIN method solve the global equilibrium and local consistency conditions sequentially for the entire loading path. The achieved solution must satisfy the conditions of static and kinematic admissibility and consistency simultaneously after several iterations. 3D numerical implementation is accomplished using an implicit algorithm and is then used for finite element simulation using the software Abaqus. Computational tests demonstrate the ability of this approach to simulate SMAs presenting flat phase transformation plateaus and subjected to complex loading cases, such as the quasi-static behavior of a stent structure. Some numerical results are contrasted to those obtained using step-by-step incremental integration.
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.
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 thermodynamic 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.
A numerical dressing method for the nonlinear superposition of solutions of the KdV equation
NASA Astrophysics Data System (ADS)
Trogdon, Thomas; Deconinck, Bernard
2014-01-01
In this paper we present the unification of two existing numerical methods for the construction of solutions of the Korteweg-de Vries (KdV) equation. The first method is used to solve the Cauchy initial-value problem on the line for rapidly decaying initial data. The second method is used to compute finite-genus solutions of the KdV equation. The combination of these numerical methods allows for the computation of exact solutions that are asymptotically (quasi-)periodic finite-gap solutions and are a nonlinear superposition of dispersive, soliton and (quasi-)periodic solutions in the finite (x, t)-plane. Such solutions are referred to as superposition solutions. We compute these solutions accurately for all values of x and t.
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.
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
A short introduction to numerical methods used in cosmological N-body simulations
NASA Astrophysics Data System (ADS)
Hellwing, Wojciech
2015-12-01
We give a short introduction to modern numerical methods commonly used in cosmological N-body simulations. First, we present some simple considerations based on linear perturbation theory which indicate the necessity for N-body simulations. Then, based on a working example of the publicly available gadget-2 code, we describe particle mesh and Barnes-Hut oct-tree methods used in numerical gravity N-body solvers. We also briefly discuss methods used in an elementary hydrodynamic implementation used for baryonic gas. Next, we give a very basic description of time integration of equations of motion commonly used in N-body codes. Finally we describe the Zeldovitch approximation as an example method for generating initial conditions for computer simulations.
NASA Astrophysics Data System (ADS)
Pedram, Masoud; Esfandiari, Akbar; Khedmati, Mohammad Reza
2017-06-01
This paper investigates the viability of damage detection using power spectral density (PSD) of structural response both numerically and experimentally. The paper establishes a sensitivity based damage detection method to use PSD. The advantages of PSD as a model updating metric are explained and its challenges are addressed. An approximate frequency response function of damaged model is used to redeem the method for the effect of incomplete measurement. The robust solution of the developed sensitivity equation is achieved through a least-squares error minimization scheme, and the challenging issues are discussed. The ability of the method in localizing and quantifying the damage and its robustness against measurement and modeling errors is investigated by a numerical example. Experimental vibration test data of a laboratory concrete beam with various level of distributed damage is used to probe the method in practical conditions. The results show that PSD of response can be used to detect damages in lower frequency ranges with acceptable accuracy.
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.
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.
Lin, W.L.; Carlson, K.D.; Chen, C.J. |
1999-05-01
In this study, a diagonal Cartesian method for thermal analysis is developed for simulation of conjugate heat transfer over complex boundaries. This method uses diagonal line segments in addition to Cartesian coordinates. The velocity fields are also modeled using the diagonal Cartesian method. The transport equations are discretized with the finite analytic (FA) method. The current work is validated by simulating a rotated lid-driven cavity flow with conjugate heat transfer, and accurate results are obtained.
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.
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.
Applications of numerical optimization methods to helicopter design problems - A survey
NASA Technical Reports Server (NTRS)
Miura, H.
1985-01-01
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.
Assessment of modern methods in numerical simulations of high speed flows
NASA Technical Reports Server (NTRS)
Pindera, M. Z.; Yang, H. Q.; Przekwas, A. J.; Tucker, K.
1992-01-01
Results of extensive studies on CFD algorithms for 2D inviscid flows in Cartesian and body fitted coordinates geometries are reviewed. These studies represent part of an ongoing investigation of combustion instabilities involving the interactions of high-speed nonlinear acoustic waves. Four numerical methods for the treatment of high speed flows are compared, namely, Roe-Sweby TVD, Yee symmetric TVD; Osher-Chakravarthy TVD; and the Colella's multi-dimensional Godunov method.
NASA Astrophysics Data System (ADS)
Hozman, J.; Tichý, T.
2017-07-01
The paper is based on the results from our recent research on path-dependent multi-asset options. Here we focus on options, payoff of which depends on the difference of the spread of two underlying assets at expiry and their average spread during the life of the option. The main idea uses a concept of the dimensional reduction to the PDE model with only two spatial variables describing this option pricing problem. Then the numerical option pricing scheme arising from the discontinuous Galerkin method is developed. Finally, a simple numerical result is presented on real market data.
NASA Astrophysics Data System (ADS)
Penenko, Alexey; Antokhin, Pavel
2016-11-01
The performance of a variational data assimilation algorithm for a transport and transformation model of atmospheric chemical composition is studied numerically in the case where the emission inventories are missing while there are additional in situ indirect concentration measurements. The algorithm is based on decomposition and splitting methods with a direct solution of the data assimilation problems at the splitting stages. This design allows avoiding iterative processes and working in real-time. In numerical experiments we study the sensitivity of data assimilation to measurement data quantity and quality.
A numerical study of rays in random media. [Monte Carlo method simulation
NASA Technical Reports Server (NTRS)
Youakim, M. Y.; Liu, C. H.; Yeh, K. C.
1973-01-01
Statistics of electromagnetic rays in a random medium are studied numerically by the Monte Carlo method. Two dimensional random surfaces with prescribed correlation functions are used to simulate the random media. Rays are then traced in these sample media. Statistics of the ray properties such as the ray positions and directions are computed. Histograms showing the distributions of the ray positions and directions at different points along the ray path as well as at given points in space are given. The numerical experiment is repeated for different cases corresponding to weakly and strongly random media with isotropic and anisotropic irregularities. Results are compared with those derived from theoretical investigations whenever possible.
Numerical study of boundary layer interaction with shocks: Method and code validation
NASA Technical Reports Server (NTRS)
Adams, Nikolaus A.
1994-01-01
A major problem in modeling of turbulent supersonic flows is the correct assessment of viscous-inviscid interaction problems. Of particular interest is the interaction of boundary layers with shocks. Present turbulence models give in most cases unsatisfactory results in the region of rapid distortion and in the separation region (if one is present) in particular with regard to mean flow profiles and turbulence quantities. The objective of the present work is the direct numerical simulation of shock boundary layer interaction. This report summarizes the first phase during which a numerical method suitable for this problem has been developed and a computer code has been written and tested.
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.
Testing the accuracy and stability of spectral methods in numerical relativity
Boyle, Michael; Lindblom, Lee; Pfeiffer, Harald P.; Scheel, Mark A.; Kidder, Lawrence E.
2007-01-15
The accuracy and stability of the Caltech-Cornell pseudospectral code is evaluated using the Kidder, Scheel, and Teukolsky (KST) representation of the Einstein evolution equations. The basic 'Mexico City tests' widely adopted by the numerical relativity community are adapted here for codes based on spectral methods. Exponential convergence of the spectral code is established, apparently limited only by numerical roundoff error or by truncation error in the time integration. A general expression for the growth of errors due to finite machine precision is derived, and it is shown that this limit is achieved here for the linear plane-wave test.
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.
Ryabinkin, Ilya G; Nagesh, Jayashree; Izmaylov, Artur F
2015-11-05
We have developed a numerical differentiation scheme that eliminates evaluation of overlap determinants in calculating the time-derivative nonadiabatic couplings (TDNACs). Evaluation of these determinants was the bottleneck in previous implementations of mixed quantum-classical methods using numerical differentiation of electronic wave functions in the Slater determinant representation. The central idea of our approach is, first, to reduce the analytic time derivatives of Slater determinants to time derivatives of molecular orbitals and then to apply a finite-difference formula. Benchmark calculations prove the efficiency of the proposed scheme showing impressive several-order-of-magnitude speedups of the TDNAC calculation step for midsize molecules.
NASA Astrophysics Data System (ADS)
Dadashzadeh, N.; Duzgun, H. S. B.; Yesiloglu-Gultekin, N.
2017-08-01
While advanced numerical techniques in slope stability analysis are successfully used in deterministic studies, they have so far found limited use in probabilistic analyses due to their high computation cost. The first-order reliability method (FORM) is one of the most efficient probabilistic techniques to perform probabilistic stability analysis by considering the associated uncertainties in the analysis parameters. However, it is not possible to directly use FORM in numerical slope stability evaluations as it requires definition of a limit state performance function. In this study, an integrated methodology for probabilistic numerical modeling of rock slope stability is proposed. The methodology is based on response surface method, where FORM is used to develop an explicit performance function from the results of numerical simulations. The implementation of the proposed methodology is performed by considering a large potential rock wedge in Sumela Monastery, Turkey. The accuracy of the developed performance function to truly represent the limit state surface is evaluated by monitoring the slope behavior. The calculated probability of failure is compared with Monte Carlo simulation (MCS) method. The proposed methodology is found to be 72% more efficient than MCS, while the accuracy is decreased with an error of 24%.
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.
Roy, R; Sevick-Muraca, E
2001-07-02
Numerical performance of two gradient-based methods, a truncated-Newton method with trust region (TN) and a nonlinear conjugate gradient (NCG), is studied and compared for a given data set and conditions specific for the contrast enhanced optical tomography problem. Our results suggest that the relative performance of the two methods depends upon the error functions, specific to the problem to be solved. The TN outperforms the NCG when maps of fluorescence lifetime are reconstructed while both methods performed well when the absorption coefficient constitutes the parameter set that is to be recovered.
Liu, Peigui; Elshall, Ahmed S.; Ye, Ming; ...
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
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 numerical simulation of shock generated ignition using the Random Choice Method
NASA Astrophysics Data System (ADS)
Clarke, J. F.; Singh, G.
Exothermically reactive gas flow in the region between a piston and a strong shock wave, (Mach 3.0), is modelled numerically using the Random Choice Method to solve the Euler equations. The numerical algorithm consists of the Random Choice scheme, formulated in a Lagrangian configuration, coupled with time-operator splitting to treat combustion chemistry. The combustion reaction is assumed to be of simple irreversible Arrhenius type. Numerical results show that ignition first occurs close to the piston face, and is followed by the formation of a compression pulse that finally contains a shock, an unsteady induction domain and a fast flame prior to transition of this system into a ZND-structured detonation.
NASA Astrophysics Data System (ADS)
Wu, Zhijun; Wong, Louis Ngai Yuen; Fan, Lifeng
2013-11-01
The viscoelastic deformation behavior of a sedimentary rock under different loading rates is numerically modeled and investigated by the numerical manifold method (NMM). By incorporating a modified 3-element viscoelastic constitutive mode in the NMM, crack initiation and propagation criteria, and crack identification and evolution techniques, the effects of the loading rates on the cracking behavior of a sedimentary rock, such as crack open displacement, crack sliding displacement, crack initiation, crack propagation and final failure mode, are successfully modeled. The numerical results reveal that under a high loading rate (>1,000 MPa/s), due to the viscoelastic property of the sedimentary rock, not only the structural behavior deviates from that of elastic model, but also different cracking processes and final failure modes are obtained.
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.
NASA Astrophysics Data System (ADS)
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.
Numerical Investigation of Penning Discharge Characteristics using 2D/3V Particle-In-Cell Method
NASA Astrophysics Data System (ADS)
Dikalyuk, A. S.; E Kuratov, S.
2017-02-01
Numerical model for the simulation of characteristics of Penning discharge is presented in the paper. The model is based on the 2D/3V axisymmetric electrostatic particle-in-cell algorithm implemented on unstructured triangular meshes. In order to simulate kinetic processes in the gas discharge plasma Monte-Carlo collision (MCC) method was incorporated into the model. Considered processes for the numerical experiments are elastic scattering of electrons on the neutral particles and ionization of neutral particles by electrons. Using this model various characteristics of Penning discharge such as anode and cathode currents, distribution of charged components in the discharge chamber have been calculated at various applied voltages and magnetic flux densities. The results of numerical experiments have been analyzed and discussed.
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.
The Standardized Candle Method for Type II Plateau Supernovae
NASA Astrophysics Data System (ADS)
Olivares E., Felipe; Hamuy, Mario; Pignata, Giuliano; Maza, José; Bersten, Melina; Phillips, Mark M.; Suntzeff, Nicholas B.; Filippenko, Alexei V.; Morrel, Nidia I.; Kirshner, Robert P.; Matheson, Thomas
2010-06-01
In this paper, we study the "standardized candle method" using a sample of 37 nearby (redshift z < 0.06) Type II plateau supernovae having BVRI photometry and optical spectroscopy. An analytic procedure is implemented to fit light curves, color curves, and velocity curves. We find that the V-I color toward the end of the plateau can be used to estimate the host-galaxy reddening with a precision of σ(AV ) = 0.2 mag. The correlation between plateau luminosity and expansion velocity previously reported in the literature is recovered. Using this relation and assuming a standard reddening law (RV = 3.1), we obtain Hubble diagrams (HDs) in the BVI bands with dispersions of ~0.4 mag. Allowing RV to vary and minimizing the spread in the HDs, we obtain a dispersion range of 0.25-0.30 mag, which implies that these objects can deliver relative distances with precisions of 12%-14%. The resulting best-fit value of RV is 1.4 ± 0.1.
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.
NASA Astrophysics Data System (ADS)
Stelzer, Zacharias; Miralles, Sophie; Cébron, David; Noir, Jérôme; Vantieghem, Stijn; Jackson, Andrew
2015-08-01
We present an investigation of the stability of liquid metal flow under the influence of an imposed magnetic field by means of a laboratory experiment as well as a linear stability analysis of the setup using the finite element method. The experimental device ZUrich Cylindrical CHannel INstability Investigation is a modified cylindrical annulus with electrically driven flow of liquid GaInSn operating at Hartmann and Reynolds numbers up to M = 2022 and Re = 2.6 ṡ 105, respectively. The magnetic field gives rise to a free shear layer at the prominent inner electrode. We identify several flow regimes characterized by the nature of the instabilities. Above a critical current I c = O ( 0 . 1 A ) , the steady flow is destabilized by a Kelvin-Helmholtz mechanism at the free shear layer. The instability consists of counterrotating vortices traveling with the mean flow. For low forcing, the vortices are restricted to the free shear layer. Their azimuthal wave number m grows with M and decreases with Re. At Re/M ≈ 25, the instability becomes container-filling and energetically significant. It enhances the radial momentum transport which manifests itself in a broadening of the free shear layer width δS. We propose that this transition may be related to an unstable Hartmann layer. At R e / M 2 = O ( 1 ) , an abrupt change is observed in the mean azimuthal velocity < u ϕ ¯ > and the friction factor F, which we interpret as the transition between an inertialess and an inertial regime.
Numerical solution of the Rosenau-KdV-RLW equation by using RBFs collocation method
NASA Astrophysics Data System (ADS)
Korkmaz, Bahar; Dereli, Yilmaz
2016-04-01
In this study, a meshfree method based on the collocation with radial basis functions (RBFs) is proposed to solve numerically an initial-boundary value problem of Rosenau-KdV-regularized long-wave (RLW) equation. Numerical values of invariants of the motion are computed to examine the fundamental conservative properties of the equation. Computational experiments for the simulation of solitary waves examine the accuracy of the scheme in terms of error norms L2 and L∞. Linear stability analysis is investigated to determine whether the present method is stable or unstable. The scheme gives unconditionally stable, and second-order convergent. The obtained results are compared with analytical solution and some other earlier works in the literature. The presented results indicate the accuracy and efficiency of the method.
A comparative study of time-marching and space-marching numerical methods. [for flowfield codes
NASA Technical Reports Server (NTRS)
Gupta, R. N.; Moss, J. N.; Simmonds, A. L.
1983-01-01
Menees (1981) has conducted an evaluation of three different flowfield codes for the Jupiter entry conditions. However, a comparison of the codes has been made difficult by the fact that the three codes use different solution procedures, different computational mesh sizes, and a different convergence criterion. There are also other differences. For an objective evaluation of the different numerical solution methods employed by the codes, it would be desirable to select a simple no-blowing perfect-gas flowfield case for which the turbulent models are well established. The present investigation is concerned with the results of such a study. It is found that the choice of the numerical method is rather problem dependent. The time-marching and the space-marching method provide both comparable results if care is taken in selecting the appropriate mesh size near the body surface.