Analytical theory of two-dimensional ring dark soliton in nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Chen, Wei; Wang, Qi; Shi, Jielong; Shen, Ming

2017-11-01

Completely stable two-dimensional ring dark soliton in nonlocal media with an arbitrary degree of nonlocality are investigated. The exact solution of the ring dark solitons is obtained with the variational method and a cylindrical nonlocal response function. The analytical results are confirmed by directly numerical simulations. We also analytically and numerically study the expansion dynamics of the gray ring dark solitons in detail.

The Accuracy of Shock Capturing in Two Spatial Dimensions

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Casper, Jay H.

1997-01-01

An assessment of the accuracy of shock capturing schemes is made for two-dimensional steady flow around a cylindrical projectile. Both a linear fourth-order method and a nonlinear third-order method are used in this study. It is shown, contrary to conventional wisdom, that captured two-dimensional shocks are asymptotically first-order, regardless of the design accuracy of the numerical method. The practical implications of this finding are discussed in the context of the efficacy of high-order numerical methods for discontinuous flows.

Numerical study of a scramjet engine flow field

NASA Technical Reports Server (NTRS)

Drummond, J. P.; Weidner, E. H.

1981-01-01

A computer program has been developed to analyze the turbulent reacting flow field in a two-dimensional scramjet engine configuration. The program numerically solves the full two-dimensional Navier-Stokes and species equations in the engine inlet and combustor, allowing consideration of flow separation and possible inlet-combustor interactions. The current work represents an intermediate step towards development of a three-dimensional program to analyze actual scramjet engine flow fields. Results from the current program are presented that predict the flow field for two inlet-combustor configurations, and comparisons of the program with experiment are given to allow assessment of the modeling that is employed.

Numerical and experimental study of Lamb wave propagation in a two-dimensional acoustic black hole

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

Yan, Shiling; Shen, Zhonghua, E-mail: shenzh@njust.edu.cn; Lomonosov, Alexey M.

2016-06-07

The propagation of laser-generated Lamb waves in a two-dimensional acoustic black-hole structure was studied numerically and experimentally. The geometrical acoustic theory has been applied to calculate the beam trajectories in the region of the acoustic black hole. The finite element method was also used to study the time evolution of propagating waves. An optical system based on the laser-Doppler vibration method was assembled. The effect of the focusing wave and the reduction in wave speed of the acoustic black hole has been validated.

Flow through three-dimensional arrangements of cylinders with alternating streamwise planar tilt

NASA Astrophysics Data System (ADS)

Sahraoui, M.; Marshall, H.; Kaviany, M.

1993-09-01

In this report, fluid flow through a three-dimensional model for the fibrous filters is examined. In this model, the three-dimensional Stokes equation with the appropriate periodic boundary conditions is solved using the finite volume method. In addition to the numerical solution, we attempt to model this flow analytically by using the two-dimensional extended analytic solution in each of the unit cells of the three-dimensional structure. Particle trajectories computed using the superimposed analytic solution of the flow field are closed to those computed using the numerical solution of the flow field. The numerical results show that the pressure drop is not affected significantly by the relative angle of rotation of the cylinders for the high porosity used in this study (epsilon = 0.8 and epsilon = 0.95). The numerical solution and the superimposed analytic solution are also compared in terms of the particle capture efficiency. The results show that the efficiency predictions using the two methods are within 10% for St = 0.01 and 5% for St = 100. As the the porosity decreases, the three-dimensional effect becomes more significant and a difference of 35% is obtained for epsilon = 0.8.

A new model for two-dimensional numerical simulation of pseudo-2D gas-solids fluidized beds

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

Li, Tingwen; Zhang, Yongmin

2013-10-11

Pseudo-two dimensional (pseudo-2D) fluidized beds, for which the thickness of the system is much smaller than the other two dimensions, is widely used to perform fundamental studies on bubble behavior, solids mixing, or clustering phenomenon in different gas-solids fluidization systems. The abundant data from such experimental systems are very useful for numerical model development and validation. However, it has been reported that two-dimensional (2D) computational fluid dynamic (CFD) simulations of pseudo-2D gas-solids fluidized beds usually predict poor quantitative agreement with the experimental data, especially for the solids velocity field. In this paper, a new model is proposed to improve themore » 2D numerical simulations of pseudo-2D gas-solids fluidized beds by properly accounting for the frictional effect of the front and back walls. Two previously reported pseudo-2D experimental systems were simulated with this model. Compared to the traditional 2D simulations, significant improvements in the numerical predictions have been observed and the predicted results are in better agreement with the available experimental data.« less

Current status of one- and two-dimensional numerical models: Successes and limitations

NASA Technical Reports Server (NTRS)

Schwartz, R. J.; Gray, J. L.; Lundstrom, M. S.

1985-01-01

The capabilities of one and two-dimensional numerical solar cell modeling programs (SCAP1D and SCAP2D) are described. The occasions when a two-dimensional model is required are discussed. The application of the models to design, analysis, and prediction are presented along with a discussion of problem areas for solar cell modeling.

Analysis of absorption and reflection mechanisms in a three-dimensional plate silencer

NASA Astrophysics Data System (ADS)

Wang, Chunqi; Huang, Lixi

2008-06-01

When a segment of a rigid duct is replaced by a plate backed by a hard-walled cavity, grazing incident sound waves induce plate vibration, hence sound reflection. Based on this mechanism, a broadband plate silencer, which works effectively from low-to-medium frequencies have been developed recently. A typical plate silencer consists of an expansion chamber with two side-branch cavities covered by light but extremely stiff plates. Such a configuration is two-dimensional in nature. In this paper, numerical study is extended to three-dimensional configurations to investigate the potential improvement in sound reflection. Finite element simulation shows that the three-dimensional configurations perform better than the corresponding two-dimensional design, especially in the relatively high frequency region. Further analysis shows that the three-dimensional design gives better plate response at higher axial modes than the simple two-dimensional design. Sound absorption mechanism is also introduced to the plate silencer by adding two dissipative chambers on the two lateral sides of a two-cavity wave reflector, hence a hybrid silencer. Numerical simulation shows that the proposed hybrid silencer is able to achieve a good moderate bandwidth with much reduced total length in comparison with pure absorption design.

Exact solutions and conservation laws of the system of two-dimensional viscous Burgers equations

NASA Astrophysics Data System (ADS)

Abdulwahhab, Muhammad Alim

2016-10-01

Fluid turbulence is one of the phenomena that has been studied extensively for many decades. Due to its huge practical importance in fluid dynamics, various models have been developed to capture both the indispensable physical quality and the mathematical structure of turbulent fluid flow. Among the prominent equations used for gaining in-depth insight of fluid turbulence is the two-dimensional Burgers equations. Its solutions have been studied by researchers through various methods, most of which are numerical. Being a simplified form of the two-dimensional Navier-Stokes equations and its wide range of applicability in various fields of science and engineering, development of computationally efficient methods for the solution of the two-dimensional Burgers equations is still an active field of research. In this study, Lie symmetry method is used to perform detailed analysis on the system of two-dimensional Burgers equations. Optimal system of one-dimensional subalgebras up to conjugacy is derived and used to obtain distinct exact solutions. These solutions not only help in understanding the physical effects of the model problem but also, can serve as benchmarks for constructing algorithms and validation of numerical solutions of the system of Burgers equations under consideration at finite Reynolds numbers. Independent and nontrivial conserved vectors are also constructed.

One-dimensional backreacting holographic superconductors with exponential nonlinear electrodynamics

NASA Astrophysics Data System (ADS)

Ghotbabadi, B. Binaei; Zangeneh, M. Kord; Sheykhi, A.

2018-05-01

In this paper, we investigate the effects of nonlinear exponential electrodynamics as well as backreaction on the properties of one-dimensional s-wave holographic superconductors. We continue our study both analytically and numerically. In analytical study, we employ the Sturm-Liouville method while in numerical approach we perform the shooting method. We obtain a relation between the critical temperature and chemical potential analytically. Our results show a good agreement between analytical and numerical methods. We observe that the increase in the strength of both nonlinearity and backreaction parameters causes the formation of condensation in the black hole background harder and critical temperature lower. These results are consistent with those obtained for two dimensional s-wave holographic superconductors.

Numerical investigation for design and critical performance evaluation of a horizontal axis hydrokinetic turbine

NASA Astrophysics Data System (ADS)

Subhra Mukherji, Suchi; Banerjee, Arindam

2010-11-01

We will discuss findings from our numerical investigation on the hydrodynamic performance of horizontal axis hydrokinetic turbines (HAHkT) under different turbine geometries and flow conditions. Hydrokinetic turbines are a class of zero-head hydropower systems which utilizes kinetic energy of flowing water to drive a generator. However, such turbines very often suffer from low efficiency which is primarily controlled by tip-speed ratio, solidity, angle of attack and number of blades. A detailed CFD study was performed using two-dimensional and three dimensional numerical models to examine the effect of each of these parameters on the performance of small HAHkTs having power capacities <= 10 kW. The two-dimensional numerical results provide an optimum angle of attack that maximizes the lift as well as lift to drag ratio yielding maximum power output. However three-dimensional numerical studies estimate optimum turbine solidity and blade numbers that produces maximum power coefficient at a given tip speed ratio. In addition, simulations were also performed to observe the axial velocity deficit at the turbine rotor downstream for different tip-speed ratios to obtain both qualitative and quantitative details about stall delay phenomena and the energy loss suffered by the turbine under ambient flow condition.

Numerical two-dimensional calculations of the formation of the solar nebula

NASA Technical Reports Server (NTRS)

Bodenheimer, Peter H.

1991-01-01

Numerical two dimensional calculations of the formation of the solar nebula are presented. The following subject areas are covered: (1) observational constraints of the properties of the initial solar nebula; (2) the physical problem; (3) review if two dimensional calculations of the formation phase; (4) recent models with hydrodynamics and radiative transport; and (5) further evolution of the system.

Numerical simulations of catastrophic disruption: Recent results

NASA Technical Reports Server (NTRS)

Benz, W.; Asphaug, E.; Ryan, E. V.

1994-01-01

Numerical simulations have been used to study high velocity two-body impacts. In this paper, a two-dimensional Largrangian finite difference hydro-code and a three-dimensional smooth particle hydro-code (SPH) are described and initial results reported. These codes can be, and have been, used to make specific predictions about particular objects in our solar system. But more significantly, they allow us to explore a broad range of collisional events. Certain parameters (size, time) can be studied only over a very restricted range within the laboratory; other parameters (initial spin, low gravity, exotic structure or composition) are difficult to study at all experimentally. The outcomes of numerical simulations lead to a more general and accurate understanding of impacts in their many forms.

The three-dimensional wake of a cylinder undergoing a combination of translational and rotational oscillation in a quiescent fluid

NASA Astrophysics Data System (ADS)

Nazarinia, M.; Lo Jacono, D.; Thompson, M. C.; Sheridan, J.

2009-06-01

Previous two-dimensional numerical studies have shown that a circular cylinder undergoing both oscillatory rotational and translational motions can generate thrust so that it will actually self-propel through a stationary fluid. Although a cylinder undergoing a single oscillation has been thoroughly studied, the combination of the two oscillations has not received much attention until now. The current research reported here extends the numerical study of Blackburn et al. [Phys. Fluids 11, L4 (1999)] both experimentally and numerically, recording detailed vorticity fields in the wake and using these to elucidate the underlying physics, examining the three-dimensional wake development experimentally, and determining the three-dimensional stability of the wake through Floquet stability analysis. Experiments conducted in the laboratory are presented for a given parameter range, confirming the early results from Blackburn et al. [Phys. Fluids 11, L4 (1999)]. In particular, we confirm the thrust generation ability of a circular cylinder undergoing combined oscillatory motions. Importantly, we also find that the wake undergoes three-dimensional transition at low Reynolds numbers (Re≃100) to an instability mode with a wavelength of about two cylinder diameters. The stability analysis indicates that the base flow is also unstable to another mode at slightly higher Reynolds numbers, broadly analogous to the three-dimensional wake transition mode for a circular cylinder, despite the distinct differences in wake/mode topology. The stability of these flows was confirmed by experimental measurements.

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

NASA Technical Reports Server (NTRS)

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

1973-01-01

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

A numerical study of incompressible juncture flows

NASA Technical Reports Server (NTRS)

Kwak, D.; Rogers, S. E.; Kaul, U. K.; Chang, J. L. C.

1986-01-01

The laminar, steady juncture flow around single or multiple posts mounted between two flat plates is simulated using the three dimensional incompressible Navier-Stokes code, INS3D. The three dimensional separation of the boundary layer and subsequent formation and development of the horseshoe vortex is computed. The computed flow compares favorably with the experimental observation. The recent numerical study to understand and quantify the juncture flow relevant to the Space Shuttle main engine power head is summarized.

The motion of a cloud of solid spherical particles falling in a cellular flow field at low Stokes number

NASA Astrophysics Data System (ADS)

Marchetti, Benjamin; Bergougnoux, Laurence; Guazzelli, Elisabeth

2017-11-01

We present a jointed experimental and numerical study examining the influence of vortical structures on the settling of a cloud of solid spherical particles under the action of gravity at low Stokes numbers. The two-dimensional model experiment uses electro-convection to generate a two-dimensional array of controlled vortices which mimics a simplified vortical flow. Particle image-velocimetry and tracking are used to examine the motion of the cloud within this vortical flow. The cloud motion is compared to the predictions of a two-way-coupling numerical simulation.

Topology of large-scale structure. IV - Topology in two dimensions

NASA Technical Reports Server (NTRS)

Melott, Adrian L.; Cohen, Alexander P.; Hamilton, Andrew J. S.; Gott, J. Richard, III; Weinberg, David H.

1989-01-01

In a recent series of papers, an algorithm was developed for quantitatively measuring the topology of the large-scale structure of the universe and this algorithm was applied to numerical models and to three-dimensional observational data sets. In this paper, it is shown that topological information can be derived from a two-dimensional cross section of a density field, and analytic expressions are given for a Gaussian random field. The application of a two-dimensional numerical algorithm for measuring topology to cross sections of three-dimensional models is demonstrated.

A numerical solution for two-dimensional Fredholm integral equations of the second kind with kernels of the logarithmic potential form

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.; Uenal, A.

1981-01-01

Two dimensional Fredholm integral equations with logarithmic potential kernels are numerically solved. The explicit consequence of these solutions to their true solutions is demonstrated. The results are based on a previous work in which numerical solutions were obtained for Fredholm integral equations of the second kind with continuous kernels.

Numerical studies of the topological Chern numbers in two dimensional electron system

NASA Astrophysics Data System (ADS)

Sheng, Donna

2004-03-01

I will report on the numerical results of the exact calculation of the topological Chern numbers in fractional and bilayer quantum Hall systems[1]. I will show that following the evolution of the Chern numbers as a function of the disorder strength and/or layer separations, various quantum phase transitions as well as the characteristic transport properties of the phases, can be determined. The hidden topological ordering in other two dimensional electron systems will also be discussed. 1. D. N. Sheng et. al., Phys. Rev. Lett. 90, 256802 (2003).

Numerical prediction of the energy efficiency of the three-dimensional fish school using the discretized Adomian decomposition method

NASA Astrophysics Data System (ADS)

Lin, Yinwei

2018-06-01

A three-dimensional modeling of fish school performed by a modified Adomian decomposition method (ADM) discretized by the finite difference method is proposed. To our knowledge, few studies of the fish school are documented due to expensive cost of numerical computing and tedious three-dimensional data analysis. Here, we propose a simple model replied on the Adomian decomposition method to estimate the efficiency of energy saving of the flow motion of the fish school. First, the analytic solutions of Navier-Stokes equations are used for numerical validation. The influences of the distance between the side-by-side two fishes are studied on the energy efficiency of the fish school. In addition, the complete error analysis for this method is presented.

Thermally induced rarefied gas flow in a three-dimensional enclosure with square cross-section

NASA Astrophysics Data System (ADS)

Zhu, Lianhua; Yang, Xiaofan; Guo, Zhaoli

2017-12-01

Rarefied gas flow in a three-dimensional enclosure induced by nonuniform temperature distribution is numerically investigated. The enclosure has a square channel-like geometry with alternatively heated closed ends and lateral walls with a linear temperature distribution. A recently proposed implicit discrete velocity method with a memory reduction technique is used to numerically simulate the problem based on the nonlinear Shakhov kinetic equation. The Knudsen number dependencies of the vortices pattern, slip velocity at the planar walls and edges, and heat transfer are investigated. The influences of the temperature ratio imposed at the ends of the enclosure and the geometric aspect ratio are also evaluated. The overall flow pattern shows similarities with those observed in two-dimensional configurations in literature. However, features due to the three-dimensionality are observed with vortices that are not identified in previous studies on similar two-dimensional enclosures at high Knudsen and small aspect ratios.

A study of frontal dynamics with application to the Australian summertime 'cool change'

NASA Technical Reports Server (NTRS)

Reeder, Michael J.; Smith, Roger K.

1987-01-01

The dynamics of frontal evolution is examined in terms of the Australian summertime cool change using a two-dimensional numerical model. The model is synthesized from observational data on surface cold fronts obtained during the Australian Cold Fronts Research Program, and the model develops a quasi-steady surface cold front during the 24 hours of integration. The characteristics of this model are compared with those of a kinematic model; it is observed that the features of the two models correspond. The two-dimensional and kinematic models are also compared with a 24-hour prediction of the cold front of February 1983 using the three-dimensional nested-grid model of the Australian Numerical Meteorology Research Center, developed by Gauntlett et al. (1984). Good correlation between these models is detected.

Coulomb double helical structure

NASA Astrophysics Data System (ADS)

Kamimura, Tetsuo; Ishihara, Osamu

2012-01-01

Structures of Coulomb clusters formed by dust particles in a plasma are studied by numerical simulation. Our study reveals the presence of various types of self-organized structures of a cluster confined in a prolate spheroidal electrostatic potential. The stable configurations depend on a prolateness parameter for the confining potential as well as on the number of dust particles in a cluster. One-dimensional string, two-dimensional zigzag structure and three-dimensional double helical structure are found as a result of the transition controlled by the prolateness parameter. The formation of stable double helical structures resulted from the transition associated with the instability of angular perturbations on double strings. Analytical perturbation study supports the findings of numerical simulations.

Advanced numerical methods for three dimensional two-phase flow calculations

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

Toumi, I.; Caruge, D.

1997-07-01

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

A fast numerical method for the valuation of American lookback put options

NASA Astrophysics Data System (ADS)

Song, Haiming; Zhang, Qi; Zhang, Ran

2015-10-01

A fast and efficient numerical method is proposed and analyzed for the valuation of American lookback options. American lookback option pricing problem is essentially a two-dimensional unbounded nonlinear parabolic problem. We reformulate it into a two-dimensional parabolic linear complementary problem (LCP) on an unbounded domain. The numeraire transformation and domain truncation technique are employed to convert the two-dimensional unbounded LCP into a one-dimensional bounded one. Furthermore, the variational inequality (VI) form corresponding to the one-dimensional bounded LCP is obtained skillfully by some discussions. The resulting bounded VI is discretized by a finite element method. Meanwhile, the stability of the semi-discrete solution and the symmetric positive definiteness of the full-discrete matrix are established for the bounded VI. The discretized VI related to options is solved by a projection and contraction method. Numerical experiments are conducted to test the performance of the proposed method.

Vortex methods for separated flows

NASA Technical Reports Server (NTRS)

Spalart, Philippe R.

1988-01-01

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

Numerical calculations of two dimensional, unsteady transonic flows with circulation

NASA Technical Reports Server (NTRS)

Beam, R. M.; Warming, R. F.

1974-01-01

The feasibility of obtaining two-dimensional, unsteady transonic aerodynamic data by numerically integrating the Euler equations is investigated. An explicit, third-order-accurate, noncentered, finite-difference scheme is used to compute unsteady flows about airfoils. Solutions for lifting and nonlifting airfoils are presented and compared with subsonic linear theory. The applicability and efficiency of the numerical indicial function method are outlined. Numerically computed subsonic and transonic oscillatory aerodynamic coefficients are presented and compared with those obtained from subsonic linear theory and transonic wind-tunnel data.

Modes of self-organization of diluted bubbly liquids in acoustic fields: One-dimensional theory.

PubMed

Gumerov, Nail A; Akhatov, Iskander S

2017-02-01

The paper is dedicated to mathematical modeling of self-organization of bubbly liquids in acoustic fields. A continuum model describing the two-way interaction of diluted polydisperse bubbly liquids and acoustic fields in weakly-nonlinear approximation is studied analytically and numerically in the one-dimensional case. It is shown that the regimes of self-organization of monodisperse bubbly liquids can be controlled by only a few dimensionless parameters. Two basic modes, clustering and propagating shock waves of void fraction (acoustically induced transparency), are identified and criteria for their realization in the space of parameters are proposed. A numerical method for solving of one-dimensional self-organization problems is developed. Computational results for mono- and polydisperse systems are discussed.

Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Demirci, Ali; Ma, Yi-Ping

2016-10-01

Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation are considered using step like initial data along a parabolic front. Employing a parabolic similarity reduction exactly reduces the study of such DSWs in two space one time (2 + 1) dimensions to finding DSW solutions of (1 + 1) dimensional equations. With this ansatz, the KP and 2DBO equations can be exactly reduced to the cylindrical Korteweg-de Vries (cKdV) and cylindrical Benjamin-Ono (cBO) equations, respectively. Whitham modulation equations which describe DSW evolution in the cKdV and cBO equations are derived and Riemann type variables are introduced. DSWs obtained from the numerical solutions of the corresponding Whitham systems and direct numerical simulations of the cKdV and cBO equations are compared with very good agreement obtained. In turn, DSWs obtained from direct numerical simulations of the KP and 2DBO equations are compared with the cKdV and cBO equations, again with good agreement. It is concluded that the (2 + 1) DSW behavior along self similar parabolic fronts can be effectively described by the DSW solutions of the reduced (1 + 1) dimensional equations.

Comparison between PVI2D and Abreu–Johnson’s Model for Petroleum Vapor Intrusion Assessment

PubMed Central

Yao, Yijun; Wang, Yue; Verginelli, Iason; Suuberg, Eric M.; Ye, Jianfeng

2018-01-01

Recently, we have developed a two-dimensional analytical petroleum vapor intrusion model, PVI2D (petroleum vapor intrusion, two-dimensional), which can help users to easily visualize soil gas concentration profiles and indoor concentrations as a function of site-specific conditions such as source strength and depth, reaction rate constant, soil characteristics, and building features. In this study, we made a full comparison of the results returned by PVI2D and those obtained using Abreu and Johnson’s three-dimensional numerical model (AJM). These comparisons, examined as a function of the source strength, source depth, and reaction rate constant, show that PVI2D can provide similar soil gas concentration profiles and source-to-indoor air attenuation factors (within one order of magnitude difference) as those by the AJM. The differences between the two models can be ascribed to some simplifying assumptions used in PVI2D and to some numerical limitations of the AJM in simulating strictly piecewise aerobic biodegradation and no-flux boundary conditions. Overall, the obtained results show that for cases involving homogenous source and soil, PVI2D can represent a valid alternative to more rigorous three-dimensional numerical models. PMID:29398981

Time-Accurate Numerical Simulations of Synthetic Jet Quiescent Air

NASA Technical Reports Server (NTRS)

Rupesh, K-A. B.; Ravi, B. R.; Mittal, R.; Raju, R.; Gallas, Q.; Cattafesta, L.

2007-01-01

The unsteady evolution of three-dimensional synthetic jet into quiescent air is studied by time-accurate numerical simulations using a second-order accurate mixed explicit-implicit fractional step scheme on Cartesian grids. Both two-dimensional and three-dimensional calculations of synthetic jet are carried out at a Reynolds number (based on average velocity during the discharge phase of the cycle V(sub j), and jet width d) of 750 and Stokes number of 17.02. The results obtained are assessed against PIV and hotwire measurements provided for the NASA LaRC workshop on CFD validation of synthetic jets.

A numerical code for a three-dimensional magnetospheric MHD equilibrium model

NASA Technical Reports Server (NTRS)

Voigt, G.-H.

1992-01-01

Two dimensional and three dimensional MHD equilibrium models were begun for Earth's magnetosphere. The original proposal was motivated by realizing that global, purely data based models of Earth's magnetosphere are inadequate for studying the underlying plasma physical principles according to which the magnetosphere evolves on the quasi-static convection time scale. Complex numerical grid generation schemes were established for a 3-D Poisson solver, and a robust Grad-Shafranov solver was coded for high beta MHD equilibria. Thus, the effects were calculated of both the magnetopause geometry and boundary conditions on the magnetotail current distribution.

Direct Numerical Simulation of a Temporally Evolving Incompressible Plane Wake: Effect of Initial Conditions on Evolution and Topology

NASA Technical Reports Server (NTRS)

Sondergaard, R.; Cantwell, B.; Mansour, N.

1997-01-01

Direct numerical simulations have been used to examine the effect of the initial disturbance field on the development of three-dimensionality and the transition to turbulence in the incompressible plane wake. The simulations were performed using a new numerical method for solving the time-dependent, three-dimensional, incompressible Navier-Stokes equations in flows with one infinite and two periodic directions. The method uses standard Fast Fourier Transforms and is applicable to cases where the vorticity field is compact in the infinite direction. Initial disturbances fields examined were combinations of two-dimensional waves and symmetric pairs of 60 deg oblique waves at the fundamental, subharmonic, and sub-subharmonic wavelengths. The results of these simulations indicate that the presence of 60 deg disturbances at the subharmonic streamwise wavelength results in the development of strong coherent three-dimensional structures. The resulting strong three-dimensional rate-of-strain triggers the growth of intense fine scale motions. Wakes initiated with 60 deg disturbances at the fundamental streamwise wavelength develop weak coherent streamwise structures, and do not develop significant fine scale motions, even at high Reynolds numbers. The wakes which develop strong three-dimensional structures exhibit growth rates on par with experimentally observed turbulent plane wakes. Wakes which develop only weak three-dimensional structures exhibit significantly lower late time growth rates. Preliminary studies of wakes initiated with an oblique fundamental and a two-dimensional subharmonic, which develop asymmetric coherent oblique structures at the subharmonic wavelength, indicate that significant fine scale motions only develop if the resulting oblique structures are above an angle of approximately 45 deg.

Chaotic attractors of relaxation oscillators

NASA Astrophysics Data System (ADS)

Guckenheimer, John; Wechselberger, Martin; Young, Lai-Sang

2006-03-01

We develop a general technique for proving the existence of chaotic attractors for three-dimensional vector fields with two time scales. Our results connect two important areas of dynamical systems: the theory of chaotic attractors for discrete two-dimensional Henon-like maps and geometric singular perturbation theory. Two-dimensional Henon-like maps are diffeomorphisms that limit on non-invertible one-dimensional maps. Wang and Young formulated hypotheses that suffice to prove the existence of chaotic attractors in these families. Three-dimensional singularly perturbed vector fields have return maps that are also two-dimensional diffeomorphisms limiting on one-dimensional maps. We describe a generic mechanism that produces folds in these return maps and demonstrate that the Wang-Young hypotheses are satisfied. Our analysis requires a careful study of the convergence of the return maps to their singular limits in the Ck topology for k >= 3. The theoretical results are illustrated with a numerical study of a variant of the forced van der Pol oscillator.

Numerical simulation of two-dimensional heat transfer in composite bodies with application to de-icing of aircraft components. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Chao, D. F. K.

1983-01-01

Transient, numerical simulations of the de-icing of composite aircraft components by electrothermal heating were performed for a two dimensional rectangular geometry. The implicit Crank-Nicolson formulation was used to insure stability of the finite-difference heat conduction equations and the phase change in the ice layer was simulated using the Enthalpy method. The Gauss-Seidel point iterative method was used to solve the system of difference equations. Numerical solutions illustrating de-icer performance for various composite aircraft structures and environmental conditions are presented. Comparisons are made with previous studies. The simulation can also be used to solve a variety of other heat conduction problems involving composite bodies.

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.

Complexity-Entropy Causality Plane as a Complexity Measure for Two-Dimensional Patterns

PubMed Central

Ribeiro, Haroldo V.; Zunino, Luciano; Lenzi, Ervin K.; Santoro, Perseu A.; Mendes, Renio S.

2012-01-01

Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less common. Here, we reduce this gap by applying the ideas of the permutation entropy combined with a relative entropic index. We build up a numerical procedure that can be easily implemented to evaluate the complexity of two or higher-dimensional patterns. We work out this method in different scenarios where numerical experiments and empirical data were taken into account. Specifically, we have applied the method to fractal landscapes generated numerically where we compare our measures with the Hurst exponent; liquid crystal textures where nematic-isotropic-nematic phase transitions were properly identified; 12 characteristic textures of liquid crystals where the different values show that the method can distinguish different phases; and Ising surfaces where our method identified the critical temperature and also proved to be stable. PMID:22916097

Flame-Generated Vorticity Production in Premixed Flame-Vortex Interactions

NASA Technical Reports Server (NTRS)

Patnaik, G.; Kailasanath, K.

2003-01-01

In this study, we use detailed time-dependent, multi-dimensional numerical simulations to investigate the relative importance of the processes leading to FGV in flame-vortex interactions in normal gravity and microgravity and to determine if the production of vorticity in flames in gravity is the same as that in zero gravity except for the contribution of the gravity term. The numerical simulations will be performed using the computational model developed at NRL, FLAME3D. FLAME3D is a parallel, multi-dimensional (either two- or three-dimensional) flame model based on FLIC2D, which has been used extensively to study the structure and stability of premixed hydrogen and methane flames.

Resonant Zener tunneling in two-dimensional periodic photonic lattices.

PubMed

Desyatnikov, Anton S; Kivshar, Yuri S; Shchesnovich, Valery S; Cavalcanti, Solange B; Hickmann, Jandir M

2007-02-15

We study Zener tunneling in two-dimensional photonic lattices and derive, for the case of hexagonal symmetry, the generalized Landau-Zener-Majorana model describing resonant interaction between high-symmetry points of the photonic spectral bands. We demonstrate that this effect can be employed for the generation of Floquet-Bloch modes and verify the model by direct numerical simulations of the tunneling effect.

Onsager vortex formation in two-component Bose–Einstein condensates in two-dimensional traps

NASA Astrophysics Data System (ADS)

Han, Junsik; Tsubota, Makoto

2018-03-01

We study numerically the dynamics of quantized vortices in two-dimensional one-component and two-component Bose–Einstein condensates (BECs) trapped by a harmonic and box potentials. In two-component miscible BECs, we confirmed the tendency of the formation of Onsager vortices in both traps. The vortices in one component separate spatially from those in the other component, which comes from their intercomponent-coupling. We also discuss the decay of the number of vortices.

Numerical simulation of the circulation of the atmosphere of Titan

NASA Technical Reports Server (NTRS)

Hourdin, F.; Levan, P.; Talagrand, O.; Courtin, Regis; Gautier, Daniel; Mckay, Christopher P.

1992-01-01

A three dimensional General Circulation Model (GCM) of Titan's atmosphere is described. Initial results obtained with an economical two dimensional (2D) axisymmetric version of the model presented a strong superrotation in the upper stratosphere. Because of this result, a more general numerical study of superrotation was started with a somewhat different version of the GCM. It appears that for a slowly rotating planet which strongly absorbs solar radiation, circulation is dominated by global equator to pole Hadley circulation and strong superrotation. The theoretical study of this superrotation is discussed. It is also shown that 2D simulations systemically lead to instabilities which make 2D models poorly adapted to numerical simulation of Titan's (or Venus) atmosphere.

Fully three-dimensional direct numerical simulation of a plunging breaker

NASA Astrophysics Data System (ADS)

Lubin, Pierre; Vincent, Stéphane; Caltagirone, Jean-Paul; Abadie, Stéphane

2003-07-01

The scope of this paper is to show the results obtained for simulating three-dimensional breaking waves by solving the Navier-Stokes equations in air and water. The interface tracking is achieved by a Lax-Wendroff TVD scheme (Total Variation Diminishing), which is able to handle interface reconnections. We first present the equations and the numerical methods used in this work. We then proceed to the study of a three-dimensional plunging breaking wave, using initial conditions corresponding to unstable periodic sinusoidal waves of large amplitudes. We compare the results obtained for two simulations, a longshore depth perturbation has been introduced in the solution of the flow equations in order to see the transition from a two-dimensional velocity field to a fully three-dimensional one after plunging. Breaking processes including overturning, splash-up and breaking induced vortex-like motion beneath the surface are presented and discussed. To cite this article: P. Lubin et al., C. R. Mecanique 331 (2003).

The dimension split element-free Galerkin method for three-dimensional potential problems

NASA Astrophysics Data System (ADS)

Meng, Z. J.; Cheng, H.; Ma, L. D.; Cheng, Y. M.

2018-06-01

This paper presents the dimension split element-free Galerkin (DSEFG) method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares (IMLS) approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.

Three-dimensional numerical study of heat transfer enhancement in separated flows

NASA Astrophysics Data System (ADS)

Kumar, Saurav; Vengadesan, S.

2017-11-01

The flow separation appears in a wide range of heat transfer applications and causes poor heat transfer performance. It motivates the study of heat transfer enhancement in laminar as well as turbulent flows over a backward facing step by means of an adiabatic fin mounted on the top wall. Recently, we have studied steady, 2-D numerical simulations in laminar flow and investigated the effect of fin length, location, and orientation. It revealed that the addition of fin causes enhancement of heat transfer and it is very effective to control the flow and thermal behavior. The fin is most effective and sensitive when it is placed exactly above the step. A slight displacement of the fin in upstream of the step causes the complete change of flow and thermal behavior. Based on the obtained 2-D results it is interesting to investigate the side wall effect in three-dimensional simulations. The comparison of two-dimensional and three-dimensional numerical simulations with the available experimental results will be presented. Special attention has to be given to capture unsteadiness in the flow and thermal field.

Computational unsteady aerodynamics for lifting surfaces

NASA Technical Reports Server (NTRS)

Edwards, John W.

1988-01-01

Two dimensional problems are solved using numerical techniques. Navier-Stokes equations are studied both in the vorticity-stream function formulation which appears to be the optimal choice for two dimensional problems, using a storage approach, and in the velocity pressure formulation which minimizes the number of unknowns in three dimensional problems. Analysis shows that compact centered conservative second order schemes for the vorticity equation are the most robust for high Reynolds number flows. Serious difficulties remain in the choice of turbulent models, to keep reasonable CPU efficiency.

[The reconstruction of two-dimensional distributions of gas concentration in the flat flame based on tunable laser absorption spectroscopy].

PubMed

Jiang, Zhi-Shen; Wang, Fei; Xing, Da-Wei; Xu, Ting; Yan, Jian-Hua; Cen, Ke-Fa

2012-11-01

The experimental method by using the tunable diode laser absorption spectroscopy combined with the model and algo- rithm was studied to reconstruct the two-dimensional distribution of gas concentration The feasibility of the reconstruction program was verified by numerical simulation A diagnostic system consisting of 24 lasers was built for the measurement of H2O in the methane/air premixed flame. The two-dimensional distribution of H2O concentration in the flame was reconstructed, showing that the reconstruction results reflect the real two-dimensional distribution of H2O concentration in the flame. This diagnostic scheme provides a promising solution for combustion control.

Experimental Investigation of the Unsteady Flow Structures of Two Interacting Pitching Wings

NASA Astrophysics Data System (ADS)

Kurt, Melike; Moored, Keith

2015-11-01

Birds, insects and fish propel themselves with unsteady motions of their wings and fins. Many of these animals are also found to fly or swim in three-dimensional flocks and schools. Numerous studies have explored the three-dimensional steady flow interactions and the two-dimensional unsteady flow interactions in collectives. Yet, the characterization of the three-dimensional unsteady interactions remains relatively unexplored. This study aims to characterize the flow structures and interactions between two sinusoidally pitching finite-span wings. The arrangement of the wings varies from a tandem to a bi-plane configuration. The vortex structures for these various arrangements are quantified by using particle image velocimetry. The vortex-wing interactions are also characterized as the synchrony between the wings is modified.

A numerical study of transition control by periodic suction-blowing

NASA Technical Reports Server (NTRS)

Biringen, Sedat

1987-01-01

The applicability of active control of transition by periodic suction-blowing is investigated via direct numerical simulations of the Navier-Stokes equations. The time-evolution of finite-amplitude disturbances in plane channel flow is compared in detail with and without control. The analysis indicates that, for relatively small three dimensional amplitudes, a two dimensional control effectively reduces disturbance growth rates even for linearly unstable Reynolds numbers. After the flow goes through secondary instability, three dimensional control seems necessary to stabilize the flow. An investigation of the temperature field suggests that passive temperature contamination is operative to reflect the flow dynamics during transition.

Computational Methods for Inviscid and Viscous Two-and-Three-Dimensional Flow Fields.

DTIC Science & Technology

1975-01-01

Difference Equations Over a Network, Watson Sei. Comput. Lab. Report, 19U9. 173- Isaacson, E. and Keller, H. B., Analaysis of Numerical Methods...element method has given a new impulse to the old mathematical theory of multivariate interpolation. We first study the one-dimensional case, which

Experimental and numerical study of control of flow separation of a symmetric airfoil with trapped vortex cavity

NASA Astrophysics Data System (ADS)

Shahid, Abdullah Bin; Mashud, Mohammad

2017-06-01

This paper summarizes the experimental campaign and numerical analysis performed aimed to analyze the potential benefit available employing a trapping vortex cell system on a high thickness symmetric aero-foil without steady suction or injection mass flow. In this work, the behavior of a two dimensional model equipped with a span wise adjusted circular cavity has been researched. Pressure distribution on the model surface and inside and the complete flow field round the model have been measured. Experimental tests have been performed varying the wind tunnel speed and also the angle of attack. For numerical analysis the two dimensional model of the airfoil and the mesh is formed through ANSYS Meshing that is run in Fluent for numerical iterate solution. In the paper the performed test campaign, the airfoil design, the adopted experimental set-up, the numerical analysis, the data post process and the results description are reported, compared a discussed.

Numerical investigation of Dean vortices in a curved pipe

NASA Astrophysics Data System (ADS)

Bernad, S. I.; Totorean, A.; Bosioc, A.; Stanciu, R.; Bernad, E. S.

2013-10-01

This study is devoted to the three-dimensional numerical simulation of developing secondary flows of Newtonian fluid through a curved circular duct. The numerical simulations produced for different Dean numbers show clearly the presence of two steady Dean vortices. Therefore, results confirm that helical flow constitutes an important flow signature in vessels, and its strength as a fluid dynamic index.

Numerical simulation and analysis of the flow in a two-staged axial fan

NASA Astrophysics Data System (ADS)

Xu, J. Q.; Dou, H. S.; Jia, H. X.; Chen, X. P.; Wei, Y. K.; Dong, M. W.

2016-05-01

In this paper, numerical simulation was performed for the internal three-dimensional turbulent flow field in the two-stage axial fan using steady three-dimensional in-compressible Navier-Stokes equations coupled with the Realizable turbulent model. The numerical simulation results of the steady analysis were combined with the flow characteristics of two- staged axial fan, the influence of the mutual effect between the blade and the vane on the flow of the two inter-stages was analyzed emphatically. This paper studied how the flow field distribution in inter-stage is influenced by the wake interaction and potential flow interaction of mutual effect in the impeller-vane inter-stage and the vane-impeller inter-stage. The results showed that: Relatively, wake interaction has an advantage over potential flow interaction in the impeller-vane inter-stage; potential flow interaction has an advantage over wake interaction in the vane-impeller inter-stage. In other words, distribution of flow field in the two interstages is determined by the rotating component.

Numerical simulation of steady supersonic flow. [spatial marching

NASA Technical Reports Server (NTRS)

Schiff, L. B.; Steger, J. L.

1981-01-01

A noniterative, implicit, space-marching, finite-difference algorithm was developed for the steady thin-layer Navier-Stokes equations in conservation-law form. The numerical algorithm is applicable to steady supersonic viscous flow over bodies of arbitrary shape. In addition, the same code can be used to compute supersonic inviscid flow or three-dimensional boundary layers. Computed results from two-dimensional and three-dimensional versions of the numerical algorithm are in good agreement with those obtained from more costly time-marching techniques.

Hydrodynamic characteristics of the two-phase flow field at gas-evolving electrodes: numerical and experimental studies

NASA Astrophysics Data System (ADS)

Liu, Cheng-Lin; Sun, Ze; Lu, Gui-Min; Yu, Jian-Guo

2018-05-01

Gas-evolving vertical electrode system is a typical electrochemical industrial reactor. Gas bubbles are released from the surfaces of the anode and affect the electrolyte flow pattern and even the cell performance. In the current work, the hydrodynamics induced by the air bubbles in a cold model was experimentally and numerically investigated. Particle image velocimetry and volumetric three-component velocimetry techniques were applied to experimentally visualize the hydrodynamics characteristics and flow fields in a two-dimensional (2D) plane and a three-dimensional (3D) space, respectively. Measurements were performed at different gas rates. Furthermore, the corresponding mathematical model was developed under identical conditions for the qualitative and quantitative analyses. The experimental measurements were compared with the numerical results based on the mathematical model. The study of the time-averaged flow field, three velocity components, instantaneous velocity and turbulent intensity indicate that the numerical model qualitatively reproduces liquid motion. The 3D model predictions capture the flow behaviour more accurately than the 2D model in this study.

Hydrodynamic characteristics of the two-phase flow field at gas-evolving electrodes: numerical and experimental studies.

PubMed

Liu, Cheng-Lin; Sun, Ze; Lu, Gui-Min; Yu, Jian-Guo

2018-05-01

Gas-evolving vertical electrode system is a typical electrochemical industrial reactor. Gas bubbles are released from the surfaces of the anode and affect the electrolyte flow pattern and even the cell performance. In the current work, the hydrodynamics induced by the air bubbles in a cold model was experimentally and numerically investigated. Particle image velocimetry and volumetric three-component velocimetry techniques were applied to experimentally visualize the hydrodynamics characteristics and flow fields in a two-dimensional (2D) plane and a three-dimensional (3D) space, respectively. Measurements were performed at different gas rates. Furthermore, the corresponding mathematical model was developed under identical conditions for the qualitative and quantitative analyses. The experimental measurements were compared with the numerical results based on the mathematical model. The study of the time-averaged flow field, three velocity components, instantaneous velocity and turbulent intensity indicate that the numerical model qualitatively reproduces liquid motion. The 3D model predictions capture the flow behaviour more accurately than the 2D model in this study.

Hydrodynamic characteristics of the two-phase flow field at gas-evolving electrodes: numerical and experimental studies

PubMed Central

Lu, Gui-Min; Yu, Jian-Guo

2018-01-01

Gas-evolving vertical electrode system is a typical electrochemical industrial reactor. Gas bubbles are released from the surfaces of the anode and affect the electrolyte flow pattern and even the cell performance. In the current work, the hydrodynamics induced by the air bubbles in a cold model was experimentally and numerically investigated. Particle image velocimetry and volumetric three-component velocimetry techniques were applied to experimentally visualize the hydrodynamics characteristics and flow fields in a two-dimensional (2D) plane and a three-dimensional (3D) space, respectively. Measurements were performed at different gas rates. Furthermore, the corresponding mathematical model was developed under identical conditions for the qualitative and quantitative analyses. The experimental measurements were compared with the numerical results based on the mathematical model. The study of the time-averaged flow field, three velocity components, instantaneous velocity and turbulent intensity indicate that the numerical model qualitatively reproduces liquid motion. The 3D model predictions capture the flow behaviour more accurately than the 2D model in this study. PMID:29892347

The possible equilibrium shapes of static pendant drops

NASA Astrophysics Data System (ADS)

Sumesh, P. T.; Govindarajan, Rama

2010-10-01

Analytical and numerical studies are carried out on the shapes of two-dimensional and axisymmetric pendant drops hanging under gravity from a solid surface. Drop shapes with both pinned and equilibrium contact angles are obtained naturally from a single boundary condition in the analytical energy optimization procedure. The numerical procedure also yields optimum energy shapes, satisfying Young's equation without the explicit imposition of a boundary condition at the plate. It is shown analytically that a static pendant two-dimensional drop can never be longer than 3.42 times the capillary length. A related finding is that a range of existing solutions for long two-dimensional drops correspond to unphysical drop shapes. Therefore, two-dimensional drops of small volume display only one static solution. In contrast, it is known that axisymmetric drops can display multiple solutions for a given volume. We demonstrate numerically that there is no limit to the height of multiple-lobed Kelvin drops, but the total volume is finite, with the volume of successive lobes forming a convergent series. The stability of such drops is in question, though. Drops of small volume can attain large heights. A bifurcation is found within the one-parameter space of Laplacian shapes, with a range of longer drops displaying a minimum in energy in the investigated space. Axisymmetric Kelvin drops exhibit an infinite number of bifurcations.

Lax-Wendroff and TVD finite volume methods for unidimensional thermomechanical numerical simulations of impacts on elastic-plastic solids

NASA Astrophysics Data System (ADS)

Heuzé, Thomas

2017-10-01

We present in this work two finite volume methods for the simulation of unidimensional impact problems, both for bars and plane waves, on elastic-plastic solid media within the small strain framework. First, an extension of Lax-Wendroff to elastic-plastic constitutive models with linear and nonlinear hardenings is presented. Second, a high order TVD method based on flux-difference splitting [1] and Superbee flux limiter [2] is coupled with an approximate elastic-plastic Riemann solver for nonlinear hardenings, and follows that of Fogarty [3] for linear ones. Thermomechanical coupling is accounted for through dissipation heating and thermal softening, and adiabatic conditions are assumed. This paper essentially focuses on one-dimensional problems since analytical solutions exist or can easily be developed. Accordingly, these two numerical methods are compared to analytical solutions and to the explicit finite element method on test cases involving discontinuous and continuous solutions. This allows to study in more details their respective performance during the loading, unloading and reloading stages. Particular emphasis is also paid to the accuracy of the computed plastic strains, some differences being found according to the numerical method used. Lax-Wendoff two-dimensional discretization of a one-dimensional problem is also appended at the end to demonstrate the extensibility of such numerical scheme to multidimensional problems.

Two-dimensional numerical simulation of boron diffusion for pyramidally textured silicon

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

Ma, Fa-Jun, E-mail: Fajun.Ma@nus.edu.sg; Duttagupta, Shubham; Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, 117576

2014-11-14

Multidimensional numerical simulation of boron diffusion is of great relevance for the improvement of industrial n-type crystalline silicon wafer solar cells. However, surface passivation of boron diffused area is typically studied in one dimension on planar lifetime samples. This approach neglects the effects of the solar cell pyramidal texture on the boron doping process and resulting doping profile. In this work, we present a theoretical study using a two-dimensional surface morphology for pyramidally textured samples. The boron diffusivity and segregation coefficient between oxide and silicon in simulation are determined by reproducing measured one-dimensional boron depth profiles prepared using different boronmore » diffusion recipes on planar samples. The established parameters are subsequently used to simulate the boron diffusion process on textured samples. The simulated junction depth is found to agree quantitatively well with electron beam induced current measurements. Finally, chemical passivation on planar and textured samples is compared in device simulation. Particularly, a two-dimensional approach is adopted for textured samples to evaluate chemical passivation. The intrinsic emitter saturation current density, which is only related to Auger and radiative recombination, is also simulated for both planar and textured samples. The differences between planar and textured samples are discussed.« less

Global Phase Diagram of a Three-Dimensional Dirty Topological Superconductor

NASA Astrophysics Data System (ADS)

Roy, Bitan; Alavirad, Yahya; Sau, Jay D.

2017-06-01

We investigate the phase diagram of a three-dimensional, time-reversal symmetric topological superconductor in the presence of charge impurities and random s -wave pairing. Combining complimentary field theoretic and numerical methods, we show that the quantum phase transition between two topologically distinct paired states (or thermal insulators), described by thermal Dirac semimetal, remains unaffected in the presence of sufficiently weak generic randomness. At stronger disorder, however, these two phases are separated by an intervening thermal metallic phase of diffusive Majorana fermions. We show that across the insulator-insulator and metal-insulator transitions, normalized thermal conductance displays single parameter scaling, allowing us to numerically extract the critical exponents across them. The pertinence of our study in strong spin-orbit coupled, three-dimensional doped narrow gap semiconductors, such as CuxBi2Se3 , is discussed.

Direct numerical simulation of human phonation

NASA Astrophysics Data System (ADS)

Bodony, Daniel; Saurabh, Shakti

2017-11-01

The generation and propagation of the human voice in three-dimensions is studied using direct numerical simulation. A full body domain is employed for the purpose of directly computing the sound in the region past the speaker's mouth. The air in the vocal tract is modeled as a compressible and viscous fluid interacting with the elastic vocal folds. The vocal fold tissue material properties are multi-layered, with varying stiffness, and a linear elastic transversely isotropic model is utilized and implemented in a quadratic finite element code. The fluid-solid domains are coupled through a boundary-fitted interface and utilize a Poisson equation-based mesh deformation method. A kinematic constraint based on a specified minimum gap between the vocal folds is applied to prevent collision during glottal closure. Both near VF flow dynamics and far-field acoustics have been studied. A comparison is drawn to current two-dimensional simulations as well as to data from the literature. Near field vocal fold dynamics and glottal flow results are studied and in good agreement with previous three-dimensional phonation studies. Far-field acoustic characteristics, when compared to their two-dimensional counterpart, are shown to be sensitive to the dimensionality. Supported by the National Science Foundation (CAREER Award Number 1150439).

Arbitrarily high-order time-stepping schemes based on the operator spectrum theory for high-dimensional nonlinear Klein-Gordon equations

NASA Astrophysics Data System (ADS)

Liu, Changying; Wu, Xinyuan

2017-07-01

In this paper we explore arbitrarily high-order Lagrange collocation-type time-stepping schemes for effectively solving high-dimensional nonlinear Klein-Gordon equations with different boundary conditions. We begin with one-dimensional periodic boundary problems and first formulate an abstract ordinary differential equation (ODE) on a suitable infinity-dimensional function space based on the operator spectrum theory. We then introduce an operator-variation-of-constants formula which is essential for the derivation of our arbitrarily high-order Lagrange collocation-type time-stepping schemes for the nonlinear abstract ODE. The nonlinear stability and convergence are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi-definite matrix under some suitable smoothness assumptions. With regard to the two dimensional Dirichlet or Neumann boundary problems, our new time-stepping schemes coupled with discrete Fast Sine / Cosine Transformation can be applied to simulate the two-dimensional nonlinear Klein-Gordon equations effectively. All essential features of the methodology are present in one-dimensional and two-dimensional cases, although the schemes to be analysed lend themselves with equal to higher-dimensional case. The numerical simulation is implemented and the numerical results clearly demonstrate the advantage and effectiveness of our new schemes in comparison with the existing numerical methods for solving nonlinear Klein-Gordon equations in the literature.

Transition between quasi-two-dimensional and three-dimensional Rayleigh-Bénard convection in a horizontal magnetic field

NASA Astrophysics Data System (ADS)

Vogt, Tobias; Ishimi, Wataru; Yanagisawa, Takatoshi; Tasaka, Yuji; Sakuraba, Ataru; Eckert, Sven

2018-01-01

Magnetohydrodynamic Rayleigh-Bénard convection was studied experimentally and numerically using a liquid metal inside a box with a square horizontal cross section and an aspect ratio of 5. Applying a sufficiently strong horizontal magnetic field converts the convective motion into a flow pattern of quasi-two-dimensional (quasi-2D) rolls arranged parallel to the magnetic field. The aim of this paper is to provide a detailed description of the flow field, which is often considered as quasi-2D. In this paper, we focus on the transition from a quasi-two-dimensional state toward a three-dimensional flow occurring with decreasing magnetic-field strength. We present systematic flow measurements that were performed by means of ultrasound Doppler velocimetry. The measured data provide insight into the dynamics of the primary convection rolls, the secondary flow induced by Ekman pumping, and they reveal the existence of small vortices that develop around the convection rolls. New flow regimes have been identified by the velocity measurements, which show a pronounced manifestation of three-dimensional flow structures as the ratio Ra /Q increases. The interaction between the primary swirling motion of the convection rolls and the secondary flow becomes increasingly strong. Significant bulging of the convection rolls causes a breakdown of the original recirculation loop driven by Ekman pumping into several smaller cells. The flow measurements are completed by direct numerical simulations. The numerical simulations have proven to be able to qualitatively reproduce the newly discovered flow regimes in the experiment.

Three- and two-dimensional simulations of counter-propagating shear experiments at high energy densities at the National Ignition Facility

DOE PAGES

Wang, Ping; Zhou, Ye; MacLaren, Stephan A.; ...

2015-11-06

Three- and two-dimensional numerical studies have been carried out to simulate recent counter-propagating shear flow experiments on the National Ignition Facility. A multi-physics three-dimensional, time-dependent radiation hydrodynamics simulation code is used. Using a Reynolds Averaging Navier-Stokes model, we show that the evolution of the mixing layer width obtained from the simulations agrees well with that measured from the experiments. A sensitivity study is conducted to illustrate a 3D geometrical effect that could confuse the measurement at late times, if the energy drives from the two ends of the shock tube are asymmetric. Implications for future experiments are discussed.

A Kronecker product splitting preconditioner for two-dimensional space-fractional diffusion equations

NASA Astrophysics Data System (ADS)

Chen, Hao; Lv, Wen; Zhang, Tongtong

2018-05-01

We study preconditioned iterative methods for the linear system arising in the numerical discretization of a two-dimensional space-fractional diffusion equation. Our approach is based on a formulation of the discrete problem that is shown to be the sum of two Kronecker products. By making use of an alternating Kronecker product splitting iteration technique we establish a class of fixed-point iteration methods. Theoretical analysis shows that the new method converges to the unique solution of the linear system. Moreover, the optimal choice of the involved iteration parameters and the corresponding asymptotic convergence rate are computed exactly when the eigenvalues of the system matrix are all real. The basic iteration is accelerated by a Krylov subspace method like GMRES. The corresponding preconditioner is in a form of a Kronecker product structure and requires at each iteration the solution of a set of discrete one-dimensional fractional diffusion equations. We use structure preserving approximations to the discrete one-dimensional fractional diffusion operators in the action of the preconditioning matrix. Numerical examples are presented to illustrate the effectiveness of this approach.

Three dimensional flow field inside compressor rotor, including blade boundary layers

NASA Technical Reports Server (NTRS)

Galmes, J. M.; Pouagere, M.; Lakshminarayana, B.

1982-01-01

The Reynolds stress equation, pressure strain correlation, and dissipative terms and diffusion are discussed in relation to turbulence modelling using the Reynolds stress model. Algebraic modeling of Reynolds stresses and calculation of the boundary layer over an axial cylinder are examined with regards to the kinetic energy model for turbulence modelling. The numerical analysis of blade and hub wall boundary layers, and an experimental study of rotor blade boundary layer in an axial flow compressor rotor are discussed. The Patankar-Spalding numerical method for two dimensional boundary layers is included.

Increased heat transfer to elliptical leading edges due to spanwise variations in the freestream momentum: Numerical and experimental results

NASA Technical Reports Server (NTRS)

Rigby, D. L.; Vanfossen, G. J.

1992-01-01

A study of the effect of spanwise variation in momentum on leading edge heat transfer is discussed. Numerical and experimental results are presented for both a circular leading edge and a 3:1 elliptical leading edge. Reynolds numbers in the range of 10,000 to 240,000 based on leading edge diameter are investigated. The surface of the body is held at a constant uniform temperature. Numerical and experimental results with and without spanwise variations are presented. Direct comparison of the two-dimensional results, that is, with no spanwise variations, to the analytical results of Frossling is very good. The numerical calculation, which uses the PARC3D code, solves the three-dimensional Navier-Stokes equations, assuming steady laminar flow on the leading edge region. Experimentally, increases in the spanwise-averaged heat transfer coefficient as high as 50 percent above the two-dimensional value were observed. Numerically, the heat transfer coefficient was seen to increase by as much as 25 percent. In general, under the same flow conditions, the circular leading edge produced a higher heat transfer rate than the elliptical leading edge. As a percentage of the respective two-dimensional values, the circular and elliptical leading edges showed similar sensitivity to span wise variations in momentum. By equating the root mean square of the amplitude of the spanwise variation in momentum to the turbulence intensity, a qualitative comparison between the present work and turbulent results was possible. It is shown that increases in leading edge heat transfer due to spanwise variations in freestream momentum are comparable to those due to freestream turbulence.

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

NASA Astrophysics Data System (ADS)

Andrade, D.; Nachbin, A.

2018-06-01

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

Plane Poiseuille flow of a rarefied gas in the presence of strong gravitation.

PubMed

Doi, Toshiyuki

2011-02-01

Plane Poiseuille flow of a rarefied gas, which flows horizontally in the presence of strong gravitation, is studied based on the Boltzmann equation. Applying the asymptotic analysis for a small variation in the flow direction [Y. Sone, Molecular Gas Dynamics (Birkhäuser, 2007)], the two-dimensional problem is reduced to a one-dimensional problem, as in the case of a Poiseuille flow in the absence of gravitation, and the solution is obtained in a semianalytical form. The reduced one-dimensional problem is solved numerically for a hard sphere molecular gas over a wide range of the gas-rarefaction degree and the gravitational strength. The presence of gravitation reduces the mass flow rate, and the effect of gravitation is significant for large Knudsen numbers. To verify the validity of the asymptotic solution, a two-dimensional problem of a flow through a long channel is directly solved numerically, and the validity of the asymptotic solution is confirmed. ©2011 American Physical Society

A Three-Dimensional Linearized Unsteady Euler Analysis for Turbomachinery Blade Rows

NASA Technical Reports Server (NTRS)

Montgomery, Matthew D.; Verdon, Joseph M.

1997-01-01

A three-dimensional, linearized, Euler analysis is being developed to provide an efficient unsteady aerodynamic analysis that can be used to predict the aeroelastic and aeroacoustic responses of axial-flow turbo-machinery blading.The field equations and boundary conditions needed to describe nonlinear and linearized inviscid unsteady flows through a blade row operating within a cylindrical annular duct are presented. A numerical model for linearized inviscid unsteady flows, which couples a near-field, implicit, wave-split, finite volume analysis to a far-field eigenanalysis, is also described. The linearized aerodynamic and numerical models have been implemented into a three-dimensional linearized unsteady flow code, called LINFLUX. This code has been applied to selected, benchmark, unsteady, subsonic flows to establish its accuracy and to demonstrate its current capabilities. The unsteady flows considered, have been chosen to allow convenient comparisons between the LINFLUX results and those of well-known, two-dimensional, unsteady flow codes. Detailed numerical results for a helical fan and a three-dimensional version of the 10th Standard Cascade indicate that important progress has been made towards the development of a reliable and useful, three-dimensional, prediction capability that can be used in aeroelastic and aeroacoustic design studies.

Numerical study of the small scale structures in Boussinesq convection

NASA Technical Reports Server (NTRS)

Weinan, E.; Shu, Chi-Wang

1992-01-01

Two-dimensional Boussinesq convection is studied numerically using two different methods: a filtered pseudospectral method and a high order accurate Essentially Nonoscillatory (ENO) scheme. The issue whether finite time singularity occurs for initially smooth flows is investigated. The numerical results suggest that the collapse of the bubble cap is unlikely to occur in resolved calculations. The strain rate corresponding to the intensification of the density gradient across the front saturates at the bubble cap. We also found that the cascade of energy to small scales is dominated by the formulation of thin and sharp fronts across which density jumps.

Two dimensional numerical prediction of deflagration-to-detonation transition in porous energetic materials.

PubMed

Narin, B; Ozyörük, Y; Ulas, A

2014-05-30

This paper describes a two-dimensional code developed for analyzing two-phase deflagration-to-detonation transition (DDT) phenomenon in granular, energetic, solid, explosive ingredients. The two-dimensional model is constructed in full two-phase, and based on a highly coupled system of partial differential equations involving basic flow conservation equations and some constitutive relations borrowed from some one-dimensional studies that appeared in open literature. The whole system is solved using an optimized high-order accurate, explicit, central-difference scheme with selective-filtering/shock capturing (SF-SC) technique, to augment central-diffencing and prevent excessive dispersion. The sources of the equations describing particle-gas interactions in terms of momentum and energy transfers make the equation system quite stiff, and hence its explicit integration difficult. To ease the difficulties, a time-split approach is used allowing higher time steps. In the paper, the physical model for the sources of the equation system is given for a typical explosive, and several numerical calculations are carried out to assess the developed code. Microscale intergranular and/or intragranular effects including pore collapse, sublimation, pyrolysis, etc. are not taken into account for ignition and growth, and a basic temperature switch is applied in calculations to control ignition in the explosive domain. Results for one-dimensional DDT phenomenon are in good agreement with experimental and computational results available in literature. A typical shaped-charge wave-shaper case study is also performed to test the two-dimensional features of the code and it is observed that results are in good agreement with those of commercial software. Copyright © 2014 Elsevier B.V. All rights reserved.

An equivalent domain integral method in the two-dimensional analysis of mixed mode crack problems

NASA Technical Reports Server (NTRS)

Raju, I. S.; Shivakumar, K. N.

1990-01-01

An equivalent domain integral (EDI) method for calculating J-integrals for two-dimensional cracked elastic bodies is presented. The details of the method and its implementation are presented for isoparametric elements. The EDI method gave accurate values of the J-integrals for two mode I and two mixed mode problems. Numerical studies showed that domains consisting of one layer of elements are sufficient to obtain accurate J-integral values. Two procedures for separating the individual modes from the domain integrals are presented.

Long-range temporal correlations in the Kardar-Parisi-Zhang growth: numerical simulations

NASA Astrophysics Data System (ADS)

Song, Tianshu; Xia, Hui

2016-11-01

To analyze long-range temporal correlations in surface growth, we study numerically the (1  +  1)-dimensional Kardar-Parisi-Zhang (KPZ) equation driven by temporally correlated noise, and obtain the scaling exponents based on two different numerical methods. Our simulations show that the numerical results are in good agreement with the dynamic renormalization group (DRG) predictions, and are also consistent with the simulation results of the ballistic deposition (BD) model.

Determination of adsorption parameters in numerical simulation for polymer flooding

NASA Astrophysics Data System (ADS)

Bao, Pengyu; Li, Aifen; Luo, Shuai; Dang, Xu

2018-02-01

A study on the determination of adsorption parameters for polymer flooding simulation was carried out. The study mainly includes polymer static adsorption and dynamic adsorption. The law of adsorption amount changing with polymer concentration and core permeability was presented, and the one-dimensional numerical model of CMG was established under the support of a large number of experimental data. The adsorption laws of adsorption experiments were applied to the one-dimensional numerical model to compare the influence of two adsorption laws on the historical matching results. The results show that the static adsorption and dynamic adsorption abide by different rules, and differ greatly in adsorption. If the static adsorption results were directly applied to the numerical model, the difficulty of the historical matching will increase. Therefore, dynamic adsorption tests in the porous medium are necessary before the process of parameter adjustment in order to achieve the ideal history matching result.

Three-dimensional transient numerical simulation for intake process in the engine intake port-valve-cylinder system.

PubMed

Luo, Ma-Ji; Chen, Guo-Hua; Ma, Yuan-Hao

2003-01-01

This paper presents a KIVA-3 code based numerical model for three-dimensional transient intake flow in the intake port-valve-cylinder system of internal combustion engine using body-fitted technique, which can be used in numerical study on internal combustion engine with vertical and inclined valves, and has higher calculation precision. A numerical simulation (on the intake process of a two-valve engine with a semi-sphere combustion chamber and a radial intake port) is provided for analysis of the velocity field and pressure field of different plane at different crank angles. The results revealed the formation of the tumble motion, the evolution of flow field parameters and the variation of tumble ratios as important information for the design of engine intake system.

Chaotic dynamics and thermodynamics of periodic systems with long-range forces

NASA Astrophysics Data System (ADS)

Kumar, Pankaj

Gravitational and electromagnetic interactions form the backbone of our theoretical understanding of the universe. While, in general, such interactions are analytically inexpressible for three-dimensional infinite systems, one-dimensional modeling allows one to treat the long-range forces exactly. Not only are one-dimensional systems of profound intrinsic interest, physicists often rely on one-dimensional models as a starting point in the analysis of their more complicated higher-dimensional counterparts. In the analysis of large systems considered in cosmology and plasma physics, periodic boundary conditions are a natural choice and have been utilized in the study of one dimensional Coulombic and gravitational systems. Such studies often employ numerical simulations to validate the theoretical predictions, and in cases where theoretical relations have not been mathematically formulated, numerical simulations serve as a powerful method in characterizing the system's physical properties. In this dissertation, analytic techniques are formulated to express the exact phase-space dynamics of spatially-periodic one-dimensional Coulombic and gravitational systems. Closed-form versions of the Hamiltonian and the electric field are derived for single-component and two-component Coulombic systems, placing the two on the same footing as the gravitational counterpart. Furthermore, it is demonstrated that a three-body variant of the spatially-periodic Coulombic or gravitational system may be reduced isomorphically to a periodic system of a single particle in a two-dimensional rhombic potential. The analytic results are utilized for developing and implementing efficient computational tools to study the dynamical and the thermodynamic properties of the systems without resorting to numerical approximations. Event-driven algorithms are devised to obtain Lyapunov spectra, radial distribution function, pressure, caloric curve, and Poincare surface of section through an N-body molecular-dynamics approach. The simulation results for the three-body systems show that the motion exhibits chaotic, quasiperiodic, and periodic behaviors in segmented regions of the phase space. The results for the large versions of the single-component and two-component Coulombic systems show no clear-cut indication of a phase transition. However, as predicted by the theoretical treatment, the simulated temperature dependencies of energy, pressure as well as Lyapunov exponent for the gravitational system indicate a phase transition and the critical temperature obtained in simulation agrees well with that from the theory.

Evaluation of a two-dimensional numerical model for air quality simulation in a street canyon

NASA Astrophysics Data System (ADS)

Okamoto, Shin `Ichi; Lin, Fu Chi; Yamada, Hiroaki; Shiozawa, Kiyoshige

For many urban areas, the most severe air pollution caused by automobile emissions appears along a road surrounded by tall buildings: the so=called street canyon. A practical two-dimensional numerical model has been developed to be applied to this kind of road structure. This model contains two submodels: a wind-field model and a diffusion model based on a Monte Carlo particle scheme. In order to evaluate the predictive performance of this model, an air quality simulation was carried out at three trunk roads in the Tokyo metropolitan area: Nishi-Shimbashi, Aoyama and Kanda-Nishikicho (using SF 6 as a tracer and NO x measurement). Since this model has two-dimensional properties and cannot be used for the parallel wind condition, the perpendicular wind condition was selected for the simulation. The correlation coefficients for the SF 6 and NO x data in Aoyama were 0.67 and 0.62, respectively. When predictive performance of this model is compared with other models, this model is comparable to the SRI model, and superior to the APPS three-dimensional numerical model.

WebCSD: the online portal to the Cambridge Structural Database

PubMed Central

Thomas, Ian R.; Bruno, Ian J.; Cole, Jason C.; Macrae, Clare F.; Pidcock, Elna; Wood, Peter A.

2010-01-01

WebCSD, a new web-based application developed by the Cambridge Crystallographic Data Centre, offers fast searching of the Cambridge Structural Database using only a standard internet browser. Search facilities include two-dimensional substructure, molecular similarity, text/numeric and reduced cell searching. Text, chemical diagrams and three-dimensional structural information can all be studied in the results browser using the efficient entry summaries and embedded three-dimensional viewer. PMID:22477776

Boundary condition computational procedures for inviscid, supersonic steady flow field calculations

NASA Technical Reports Server (NTRS)

Abbett, M. J.

1971-01-01

Results are given of a comparative study of numerical procedures for computing solid wall boundary points in supersonic inviscid flow calculatons. Twenty five different calculation procedures were tested on two sample problems: a simple expansion wave and a simple compression (two-dimensional steady flow). A simple calculation procedure was developed. The merits and shortcomings of the various procedures are discussed, along with complications for three-dimensional and time-dependent flows.

Structure of two-dimensional solitons in the context of a generalized Kadomtsev-Petviashvili equation

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

Abramyan, L.A.; Stepanyants, Yu.A.

1988-04-01

The structure of steady-state two-dimensional solutions of the soliton type with quadratic and cubic nonlinearities and power-law dispersion is analyzed numerically. It is shown that steadily coupled two-dimensional multisolitons can exist for positive dispersion in a broad class of equations, which generalize the Kadomtsev-Petviashvili equation.

Flavor and topological current correlators in parity-invariant three-dimensional QED

NASA Astrophysics Data System (ADS)

Karthik, Nikhil; Narayanan, Rajamani

2017-09-01

We use lattice regularization to study the flow of the flavor-triplet fermion current central charge CJf from its free field value in the ultraviolet limit to its conformal value in the infrared limit of the parity-invariant three-dimensional QED with two flavors of two-component fermions. The dependence of CJf on the scale is weak with a tendency to be below the free field value at intermediate distances. Our numerical data suggest that the flavor-triplet fermion current and the topological current correlators become degenerate within numerical errors in the infrared limit, thereby supporting an enhanced O(4) symmetry predicted by strong self-duality. Further, we demonstrate that fermion dynamics is necessary for the scale-invariant behavior of parity-invariant three-dimensional QED by showing that the pure gauge theory with noncompact gauge action has a nonzero bilinear condensate.

Numerical modeling of the early interaction of a planar shock with a dense particle field

NASA Astrophysics Data System (ADS)

Regele, Jonathan; Blanquart, Guillaume

2011-11-01

Dense compressible multiphase flows are of interest for multiphase turbomachinary and energetic material detonations. Still, there is little understanding of the detailed interaction mechanisms between shock waves and dense (particle volume fraction αd > 0 . 001) particle fields. A recent experimental study [Wagner et al, AIAA Aero. Sci., Orlando, 2011-188] has focused on the impingement of a planar shock wave on a dense particle curtain. In the present work, numerical solutions of the Euler equations in one and two dimensions are performed for a planar shock wave impinging on a fixed particle curtain and are compared to the experimental data for early times. Comparison of the one- and two-dimensional results demonstrate that the one-dimensional description captures the large scale flow behavior, but is inadequate to capture all the details observed in the experiments. The two-dimensional solutions are shown to reproduce the experimentally observed flow structures and provide insight into how these details originate.

Investigation of advanced counterrotation blade configuration concepts for high speed turboprop systems, task 1: Ducted propfan analysis

NASA Technical Reports Server (NTRS)

Hall, Edward J.; Delaney, Robert A.; Bettner, James L.

1990-01-01

The time-dependent three-dimensional Euler equations of gas dynamics were solved numerically to study the steady compressible transonic flow about ducted propfan propulsion systems. Aerodynamic calculations were based on a four-stage Runge-Kutta time-marching finite volume solution technique with added numerical dissipation. An implicit residual smoothing operator was used to aid convergence. Two calculation grids were employed in this study. The first grid utilized an H-type mesh network with a branch cut opening to represent the axisymmetric cowl. The second grid utilized a multiple-block mesh system with a C-type grid about the cowl. The individual blocks were numerically coupled in the Euler solver. Grid systems were generated by a combined algebraic/elliptic algortihm developed specifically for ducted propfans. Numerical calculations were initially performed for unducted propfans to verify the accuracy of the three-dimensional Euler formulation. The Euler analyses were then applied for the calculation of ducted propfan flows, and predicted results were compared with experimental data for two cases. The three-dimensional Euler analyses displayed exceptional accuracy, although certain parameters were observed to be very sensitive to geometric deflections. Both solution schemes were found to be very robust and demonstrated nearly equal efficiency and accuracy, although it was observed that the multi-block C-grid formulation provided somewhat better resolution of the cowl leading edge region.

Two-dimensional electromagnetic Child-Langmuir law of a short-pulse electron flow

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

Chen, S. H.; Tai, L. C.; Liu, Y. L.

Two-dimensional electromagnetic particle-in-cell simulations were performed to study the effect of the displacement current and the self-magnetic field on the space charge limited current density or the Child-Langmuir law of a short-pulse electron flow with a propagation distance of {zeta} and an emitting width of W from the classical regime to the relativistic regime. Numerical scaling of the two-dimensional electromagnetic Child-Langmuir law was constructed and it scales with ({zeta}/W) and ({zeta}/W){sup 2} at the classical and relativistic regimes, respectively. Our findings reveal that the displacement current can considerably enhance the space charge limited current density as compared to the well-knownmore » two-dimensional electrostatic Child-Langmuir law even at the classical regime.« less

Tight-Binding Study of Polarons in Two-Dimensional Systems: Implications for Organic Field-Effect Transistor Materials

NASA Astrophysics Data System (ADS)

Lei, Jie

2011-03-01

In order to understand the electronic and transport properties of organic field-effect transistor (FET) materials, we theoretically studied the polarons in two-dimensional systems using a tight-binding model with the Holstein type and Su--Schrieffer--Heeger type electron--lattice couplings. By numerical calculations, it was found that a carrier accepts four kinds of localization, which are named the point polaron, two-dimensional polaron, one-dimensional polaron, and the extended state. The degree of localization is sensitive to the following parameters in the model: the strength and type of electron--lattice couplings, and the signs and relative magnitudes of transfer integrals. When a parameter set for a single-crystal phase of pentacene is applied within the Holstein model, a considerably delocalized hole polaron is found, consistent with the bandlike transport mechanism.

Investigation of shock-induced combustion past blunt projectiles

NASA Technical Reports Server (NTRS)

Ahuja, J. K.; Tiwari, S. N.

1996-01-01

A numerical study is conducted to simulate shock-induced combustion in premixed hydrogen-air mixtures at various free-stream conditions and parameters. Two-dimensional axisymmetric, reacting viscous flow over blunt projectiles is computed to study shock-induced combustion at Mach 5.11 and Mach 6.46 in hydrogen-air mixture. A seven-species, seven reactions finite rate hydrogen-air chemical reaction mechanism is used combined with a finite-difference, shock-fitting method to solve the complete set of Navier-Stokes and species conservation equations. The study has allowed an improved understanding of the physics of shock-induced combustion over blunt projectiles and the numerical results can now be explained more readily with one-dimensional wave-interaction model.

Development of a linearized unsteady Euler analysis for turbomachinery blade rows

NASA Technical Reports Server (NTRS)

Verdon, Joseph M.; Montgomery, Matthew D.; Kousen, Kenneth A.

1995-01-01

A linearized unsteady aerodynamic analysis for axial-flow turbomachinery blading is described in this report. The linearization is based on the Euler equations of fluid motion and is motivated by the need for an efficient aerodynamic analysis that can be used in predicting the aeroelastic and aeroacoustic responses of blade rows. The field equations and surface conditions required for inviscid, nonlinear and linearized, unsteady aerodynamic analyses of three-dimensional flow through a single, blade row operating within a cylindrical duct, are derived. An existing numerical algorithm for determining time-accurate solutions of the nonlinear unsteady flow problem is described, and a numerical model, based upon this nonlinear flow solver, is formulated for the first-harmonic linear unsteady problem. The linearized aerodynamic and numerical models have been implemented into a first-harmonic unsteady flow code, called LINFLUX. At present this code applies only to two-dimensional flows, but an extension to three-dimensions is planned as future work. The three-dimensional aerodynamic and numerical formulations are described in this report. Numerical results for two-dimensional unsteady cascade flows, excited by prescribed blade motions and prescribed aerodynamic disturbances at inlet and exit, are also provided to illustrate the present capabilities of the LINFLUX analysis.

Renyi entropy for local quenches in 2D CFT from numerical conformal blocks

NASA Astrophysics Data System (ADS)

Kusuki, Yuya; Takayanagi, Tadashi

2018-01-01

We study the time evolution of Renyi entanglement entropy for locally excited states in two dimensional large central charge CFTs. It generically shows a logarithmical growth and we compute the coefficient of log t term. Our analysis covers the entire parameter regions with respect to the replica number n and the conformal dimension h O of the primary operator which creates the excitation. We numerically analyse relevant vacuum conformal blocks by using Zamolodchikov's recursion relation. We find that the behavior of the conformal blocks in two dimensional CFTs with a central charge c, drastically changes when the dimensions of external primary states reach the value c/32. In particular, when h O ≥ c/32 and n ≥ 2, we find a new universal formula Δ {S}_A^{(n)}˜eq nc/24(n-1) log t. Our numerical results also confirm existing analytical results using the HHLL approximation.

Two-dimensional modelling of internal arc effects in an enclosed MV cell provided with a protection porous filter

NASA Astrophysics Data System (ADS)

Rochette, D.; Clain, S.; André, P.; Bussière, W.; Gentils, F.

2007-05-01

Medium voltage (MV) cells have to respect standards (for example IEC ones (IEC TC 17C 2003 IEC 62271-200 High Voltage Switchgear and Controlgear—Part 200 1st edn)) that define security levels against internal arc faults such as an accidental electrical arc occurring in the apparatus. New protection filters based on porous materials are developed to provide better energy absorption properties and a higher protection level for people. To study the filter behaviour during a major electrical accident, a two-dimensional model is proposed. The main point is the use of a dedicated numerical scheme for a non-conservative hyperbolic problem. We present a numerical simulation of the process during the first 0.2 s when the safety valve bursts and we compare the numerical results with tests carried out in a high power test laboratory on real electrical apparatus.

Lattice Boltzmann Equation On a 2D Rectangular Grid

NASA Technical Reports Server (NTRS)

Bouzidi, MHamed; DHumieres, Dominique; Lallemand, Pierre; Luo, Li-Shi; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

We construct a multi-relaxation lattice Boltzmann model on a two-dimensional rectangular grid. The model is partly inspired by a previous work of Koelman to construct a lattice BGK model on a two-dimensional rectangular grid. The linearized dispersion equation is analyzed to obtain the constraints on the isotropy of the transport coefficients and Galilean invariance for various wave propagations in the model. The linear stability of the model is also studied. The model is numerically tested for three cases: (a) a vortex moving with a constant velocity on a mesh periodic boundary conditions; (b) Poiseuille flow with an arbitrasy inclined angle with respect to the lattice orientation: and (c) a cylinder &symmetrically placed in a channel. The numerical results of these tests are compared with either analytic solutions or the results obtained by other methods. Satisfactory results are obtained for the numerical simulations.

The development of an explicit thermochemical nonequilibrium algorithm and its application to compute three dimensional AFE flowfields

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

This study presents a three-dimensional explicit, finite-difference, shock-capturing numerical algorithm applied to viscous hypersonic flows in thermochemical nonequilibrium. The algorithm employs a two-temperature physical model. Equations governing the finite-rate chemical reactions are fully-coupled to the gas dynamic equations using a novel coupling technique. The new coupling method maintains stability in the explicit, finite-rate formulation while allowing relatively large global time steps. The code uses flux-vector accuracy. Comparisons with experimental data and other numerical computations verify the accuracy of the present method. The code is used to compute the three-dimensional flowfield over the Aeroassist Flight Experiment (AFE) vehicle at one of its trajectory points.

Energy transfer in turbulence under rotation

NASA Astrophysics Data System (ADS)

Buzzicotti, Michele; Aluie, Hussein; Biferale, Luca; Linkmann, Moritz

2018-03-01

It is known that rapidly rotating turbulent flows are characterized by the emergence of simultaneous upscale and downscale energy transfer. Indeed, both numerics and experiments show the formation of large-scale anisotropic vortices together with the development of small-scale dissipative structures. However the organization of interactions leading to this complex dynamics remains unclear. Two different mechanisms are known to be able to transfer energy upscale in a turbulent flow. The first is characterized by two-dimensional interactions among triads lying on the two-dimensional, three-component (2D3C)/slow manifold, namely on the Fourier plane perpendicular to the rotation axis. The second mechanism is three-dimensional and consists of interactions between triads with the same sign of helicity (homochiral). Here, we present a detailed numerical study of rotating flows using a suite of high-Reynolds-number direct numerical simulations (DNS) within different parameter regimes to analyze both upscale and downscale cascade ranges. We find that the upscale cascade at wave numbers close to the forcing scale is generated by increasingly dominant homochiral interactions which couple the three-dimensional bulk and the 2D3C plane. This coupling produces an accumulation of energy in the 2D3C plane, which then transfers energy to smaller wave numbers thanks to the two-dimensional mechanism. In the forward cascade range, we find that the energy transfer is dominated by heterochiral triads and is dominated primarily by interaction within the fast manifold where kz≠0 . We further analyze the energy transfer in different regions in the real-space domain. In particular, we distinguish high-strain from high-vorticity regions and we uncover that while the mean transfer is produced inside regions of strain, the rare but extreme events of energy transfer occur primarily inside the large-scale column vortices.

Backtracking Depth-Resolved Microstructures for Crystal Plasticity Identification—Part 1: Backtracking Microstructures

NASA Astrophysics Data System (ADS)

Shi, Qiwei; Latourte, Félix; Hild, François; Roux, Stéphane

2017-12-01

In situ mechanical tests performed on polycrystalline materials in a scanning electron microscope suffer from the lack of information on depth-resolved three-dimensional microstructures. The latter ones can be accessed with focused ion beam technology only postmortem, because it is destructive. The present study considers the challenge of backtracking this deformed microstructure to the reference state. This theoretical question is tackled on a numerical (synthetic) test case. A two-dimensional microstructure with one dimension along the depth is considered, and deformed using a crystal plasticity law. The proposed numerical strategy is shown to retrieve accurately the reference state.

Improved numerical methods for turbulent viscous flows aerothermal modeling program, phase 2

NASA Technical Reports Server (NTRS)

Karki, K. C.; Patankar, S. V.; Runchal, A. K.; Mongia, H. C.

1988-01-01

The details of a study to develop accurate and efficient numerical schemes to predict complex flows are described. In this program, several discretization schemes were evaluated using simple test cases. This assessment led to the selection of three schemes for an in-depth evaluation based on two-dimensional flows. The scheme with the superior overall performance was incorporated in a computer program for three-dimensional flows. To improve the computational efficiency, the selected discretization scheme was combined with a direct solution approach in which the fluid flow equations are solved simultaneously rather than sequentially.

A Numerical Study on the Screening of Blast-Induced Waves for Reducing Ground Vibration

NASA Astrophysics Data System (ADS)

Park, Dohyun; Jeon, Byungkyu; Jeon, Seokwon

2009-06-01

Blasting is often a necessary part of mining and construction operations, and is the most cost-effective way to break rock, but blasting generates both noise and ground vibration. In urban areas, noise and vibration have an environmental impact, and cause structural damage to nearby structures. Various wave-screening methods have been used for many years to reduce blast-induced ground vibration. However, these methods have not been quantitatively studied for their reduction effect of ground vibration. The present study focused on the quantitative assessment of the effectiveness in vibration reduction of line-drilling as a screening method using a numerical method. Two numerical methods were used to analyze the reduction effect toward ground vibration, namely, the “distinct element method” and the “non-linear hydrocode.” The distinct element method, by particle flow code in two dimensions (PFC 2D), was used for two-dimensional parametric analyses, and some cases of two-dimensional analyses were analyzed three-dimensionally using AUTODYN 3D, the program of the non-linear hydrocode. To analyze the screening effectiveness of line-drilling, parametric analyses were carried out under various conditions, with the spacing, diameter of drill holes, distance between the blasthole and line-drilling, and the number of rows of drill holes, including their arrangement, used as parameters. The screening effectiveness was assessed via a comparison of the vibration amplitude between cases both with and without screening. Also, the frequency distribution of ground motion of the two cases was investigated through fast Fourier transform (FFT), with the differences also examined. From our study, it was concluded that line-drilling as a screening method of blast-induced waves was considerably effective under certain design conditions. The design details for field application have also been proposed.

On the interaction of small and large eddies in two dimensional turbulent flows

NASA Technical Reports Server (NTRS)

Foias, C.; ate work.

1987-01-01

Some results concerning the interaction of small and large eddies to two dimensional turbulent flows are presented. It is shown that the amplitude of small structures decays exponentially to a small value, and from this is inferred a simplified interaction law of small and large eddies. Beside their intrinsic interest for the understanding of the physics of turbulence, these results lead to new numerical schemes to be studied in a separate work.

Numerical study of soap-film flow by nonuniform alternating electric fields

NASA Astrophysics Data System (ADS)

Nasiri, M.; Shirsavar, R.; Mollaei, S.; Ramos, A.

2017-02-01

Fluid flow of suspended liquid films induced by non-uniform alternating electric fields has been reported. The electric fields were generated by two rod-like electrodes perpendicular to the fluid surface. The observed fluid flow was explained qualitatively by considering a charge induction mechanism, where the electric field actuates on the charge induced on the film surface. In this paper we perform a numerical study of this fluid flow taking into account the charge induction mechanism. The numerical results are compared with experiments and good agreement is found. Finally, we propose the application of the device as a new kind of two dimensional fluid pump.

Numerical study of soap-film flow by nonuniform alternating electric fields.

PubMed

Nasiri, M; Shirsavar, R; Mollaei, S; Ramos, A

2017-02-01

Fluid flow of suspended liquid films induced by non-uniform alternating electric fields has been reported. The electric fields were generated by two rod-like electrodes perpendicular to the fluid surface. The observed fluid flow was explained qualitatively by considering a charge induction mechanism, where the electric field actuates on the charge induced on the film surface. In this paper we perform a numerical study of this fluid flow taking into account the charge induction mechanism. The numerical results are compared with experiments and good agreement is found. Finally, we propose the application of the device as a new kind of two dimensional fluid pump.

Rarefied gas flow through two-dimensional nozzles

NASA Technical Reports Server (NTRS)

De Witt, Kenneth J.; Jeng, Duen-Ren; Keith, Theo G., Jr.; Chung, Chan-Hong

1989-01-01

A kinetic theory analysis is made of the flow of a rarefied gas from one reservoir to another through two-dimensional nozzles with arbitrary curvature. The Boltzmann equation simplified by a model collision integral is solved by means of finite-difference approximations with the discrete ordinate method. The physical space is transformed by a general grid generation technique and the velocity space is transformed to a polar coordinate system. A numerical code is developed which can be applied to any two-dimensional passage of complicated geometry for the flow regimes from free-molecular to slip. Numerical values of flow quantities can be calculated for the entire physical space including both inside the nozzle and in the outside plume. Predictions are made for the case of parallel slots and compared with existing literature data. Also, results for the cases of convergent or divergent slots and two-dimensional nozzles with arbitrary curvature at arbitrary knudsen number are presented.

Two-dimensional wavefront reconstruction based on double-shearing and least squares fitting

NASA Astrophysics Data System (ADS)

Liang, Peiying; Ding, Jianping; Zhu, Yangqing; Dong, Qian; Huang, Yuhua; Zhu, Zhen

2017-06-01

The two-dimensional wavefront reconstruction method based on double-shearing and least squares fitting is proposed in this paper. Four one-dimensional phase estimates of the measured wavefront, which correspond to the two shears and the two orthogonal directions, could be calculated from the differential phase, which solves the problem of the missing spectrum, and then by using the least squares method the two-dimensional wavefront reconstruction could be done. The numerical simulations of the proposed algorithm are carried out to verify the feasibility of this method. The influence of noise generated from different shear amount and different intensity on the accuracy of the reconstruction is studied and compared with the results from the algorithm based on single-shearing and least squares fitting. Finally, a two-grating lateral shearing interference experiment is carried out to verify the wavefront reconstruction algorithm based on doubleshearing and least squares fitting.

Numerical study of three-dimensional separation and flow control at a wing/body junction

NASA Technical Reports Server (NTRS)

Ash, Robert L.; Lakshmanan, Balakrishnan

1989-01-01

The problem of three-dimensional separation and flow control at a wing/body junction has been investigated numerically using a three-dimensional Navier-Stokes code. The numerical code employs an algebraic grid generation technique for generating the grid for unmodified junction and an elliptic grid generation technique for filleted fin junction. The results for laminar flow past a blunt fin/flat plate junction demonstrate that after grid refinement, the computations agree with experiment and reveal a strong dependency of the number of vortices at the junction on Mach number and Reynolds number. The numerical results for pressure distribution, particle paths and limiting streamlines for turbulent flow past a swept fin show a decrease in the peak pressure and in the extent of the separated flow region compared to the laminar case. The results for a filleted juncture indicate that the streamline patterns lose much of their vortical character with proper filleting. Fillets with a radius of three and one-half times the fin leading edge diameter or two times the incoming boundary layer thickness, significantly weaken the usual necklace interaction vortex for the Mach number and Reynolds number considered in the present study.

Numerical simulation of the control of the three-dimensional transition process in boundary layers

NASA Technical Reports Server (NTRS)

Kral, L. D.; Fasel, H. F.

1990-01-01

Surface heating techniques to control the three-dimensional laminar-turbulent transition process are numerically investigated for a water boundary layer. The Navier-Stokes and energy equations are solved using a fully implicit finite difference/spectral method. The spatially evolving boundary layer is simulated. Results of both passive and active methods of control are shown for small amplitude two-dimensional and three-dimensional disturbance waves. Control is also applied to the early stages of the secondary instability process using passive or active control techniques.

Chimera states in two-dimensional networks of locally coupled oscillators

NASA Astrophysics Data System (ADS)

Kundu, Srilena; Majhi, Soumen; Bera, Bidesh K.; Ghosh, Dibakar; Lakshmanan, M.

2018-02-01

Chimera state is defined as a mixed type of collective state in which synchronized and desynchronized subpopulations of a network of coupled oscillators coexist and the appearance of such anomalous behavior has strong connection to diverse neuronal developments. Most of the previous studies on chimera states are not extensively done in two-dimensional ensembles of coupled oscillators by taking neuronal systems with nonlinear coupling function into account while such ensembles of oscillators are more realistic from a neurobiological point of view. In this paper, we report the emergence and existence of chimera states by considering locally coupled two-dimensional networks of identical oscillators where each node is interacting through nonlinear coupling function. This is in contrast with the existence of chimera states in two-dimensional nonlocally coupled oscillators with rectangular kernel in the coupling function. We find that the presence of nonlinearity in the coupling function plays a key role to produce chimera states in two-dimensional locally coupled oscillators. We analytically verify explicitly in the case of a network of coupled Stuart-Landau oscillators in two dimensions that the obtained results using Ott-Antonsen approach and our analytical finding very well matches with the numerical results. Next, we consider another type of important nonlinear coupling function which exists in neuronal systems, namely chemical synaptic function, through which the nearest-neighbor (locally coupled) neurons interact with each other. It is shown that such synaptic interacting function promotes the emergence of chimera states in two-dimensional lattices of locally coupled neuronal oscillators. In numerical simulations, we consider two paradigmatic neuronal oscillators, namely Hindmarsh-Rose neuron model and Rulkov map for each node which exhibit bursting dynamics. By associating various spatiotemporal behaviors and snapshots at particular times, we study the chimera states in detail over a large range of coupling parameter. The existence of chimera states is confirmed by instantaneous angular frequency, order parameter and strength of incoherence.

Chimera states in two-dimensional networks of locally coupled oscillators.

PubMed

Kundu, Srilena; Majhi, Soumen; Bera, Bidesh K; Ghosh, Dibakar; Lakshmanan, M

2018-02-01

Chimera state is defined as a mixed type of collective state in which synchronized and desynchronized subpopulations of a network of coupled oscillators coexist and the appearance of such anomalous behavior has strong connection to diverse neuronal developments. Most of the previous studies on chimera states are not extensively done in two-dimensional ensembles of coupled oscillators by taking neuronal systems with nonlinear coupling function into account while such ensembles of oscillators are more realistic from a neurobiological point of view. In this paper, we report the emergence and existence of chimera states by considering locally coupled two-dimensional networks of identical oscillators where each node is interacting through nonlinear coupling function. This is in contrast with the existence of chimera states in two-dimensional nonlocally coupled oscillators with rectangular kernel in the coupling function. We find that the presence of nonlinearity in the coupling function plays a key role to produce chimera states in two-dimensional locally coupled oscillators. We analytically verify explicitly in the case of a network of coupled Stuart-Landau oscillators in two dimensions that the obtained results using Ott-Antonsen approach and our analytical finding very well matches with the numerical results. Next, we consider another type of important nonlinear coupling function which exists in neuronal systems, namely chemical synaptic function, through which the nearest-neighbor (locally coupled) neurons interact with each other. It is shown that such synaptic interacting function promotes the emergence of chimera states in two-dimensional lattices of locally coupled neuronal oscillators. In numerical simulations, we consider two paradigmatic neuronal oscillators, namely Hindmarsh-Rose neuron model and Rulkov map for each node which exhibit bursting dynamics. By associating various spatiotemporal behaviors and snapshots at particular times, we study the chimera states in detail over a large range of coupling parameter. The existence of chimera states is confirmed by instantaneous angular frequency, order parameter and strength of incoherence.

Two-dimensional homogeneous isotropic fluid turbulence with polymer additives

NASA Astrophysics Data System (ADS)

Gupta, Anupam; Perlekar, Prasad; Pandit, Rahul

2015-03-01

We carry out an extensive and high-resolution direct numerical simulation of homogeneous, isotropic turbulence in two-dimensional fluid films with air-drag-induced friction and with polymer additives. Our study reveals that the polymers (a) reduce the total fluid energy, enstrophy, and palinstrophy; (b) modify the fluid energy spectrum in both inverse- and forward-cascade régimes; (c) reduce small-scale intermittency; (d) suppress regions of high vorticity and strain rate; and (e) stretch in strain-dominated regions. We compare our results with earlier experimental studies and propose new experiments.

Two-dimensional solitary waves and periodic waves on coupled nonlinear electrical transmission lines

NASA Astrophysics Data System (ADS)

Wang, Heng; Zheng, Shuhua

2017-06-01

By using the dynamical system approach, the exact travelling wave solutions for a system of coupled nonlinear electrical transmission lines are studied. Based on this method, the bifurcations of phase portraits of a dynamical system are given. The two-dimensional solitary wave solutions and periodic wave solutions on coupled nonlinear transmission lines are obtained. With the aid of Maple, the numerical simulations are conducted for solitary wave solutions and periodic wave solutions to the model equation. The results presented in this paper improve upon previous studies.

Three-dimensional effects on pure tone fan noise due to inflow distortion. [rotor blade noise prediction

NASA Technical Reports Server (NTRS)

Kobayashi, H.

1978-01-01

Two dimensional, quasi three dimensional and three dimensional theories for the prediction of pure tone fan noise due to the interaction of inflow distortion with a subsonic annular blade row were studied with the aid of an unsteady three dimensional lifting surface theory. The effects of compact and noncompact source distributions on pure tone fan noise in an annular cascade were investigated. Numerical results show that the strip theory and quasi three-dimensional theory are reasonably adequate for fan noise prediction. The quasi three-dimensional method is more accurate for acoustic power and model structure prediction with an acoustic power estimation error of about plus or minus 2db.

Three-dimensional compact explicit-finite difference time domain scheme with density variation

NASA Astrophysics Data System (ADS)

Tsuchiya, Takao; Maruta, Naoki

2018-07-01

In this paper, the density variation is implemented in the three-dimensional compact-explicit finite-difference time-domain (CE-FDTD) method. The formulation is first developed based on the continuity equation and the equation of motion, which include the density. Some numerical demonstrations are performed for the three-dimensional sound wave propagation in a two density layered medium. The numerical results are compared with the theoretical results to verify the proposed formulation.

Nonlinear initial-boundary value solutions by the finite element method. [for Navier-Stokes equations of two dimensional flow

NASA Technical Reports Server (NTRS)

Baker, A. J.

1974-01-01

The finite-element method is used to establish a numerical solution algorithm for the Navier-Stokes equations for two-dimensional flows of a viscous compressible fluid. Numerical experiments confirm the advection property for the finite-element equivalent of the nonlinear convection term for both unidirectional and recirculating flowfields. For linear functionals, the algorithm demonstrates good accuracy using coarse discretizations and h squared convergence with discretization refinement.

A solution for two-dimensional Fredholm integral equations of the second kind with periodic, semiperiodic, or nonperiodic kernels. [integral representation of the stationary Navier-Stokes problem

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.; Uenal, A.

1981-01-01

A numerical scheme for solving two dimensional Fredholm integral equations of the second kind is developed. The proof of the convergence of the numerical scheme is shown for three cases: the case of periodic kernels, the case of semiperiodic kernels, and the case of nonperiodic kernels. Applications to the incompressible, stationary Navier-Stokes problem are of primary interest.

Rocket injector anomalies study. Volume 1: Description of the mathematical model and solution procedure

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Singhal, A. K.; Tam, L. T.

1984-01-01

The capability of simulating three dimensional two phase reactive flows with combustion in the liquid fuelled rocket engines is demonstrated. This was accomplished by modifying an existing three dimensional computer program (REFLAN3D) with Eulerian Lagrangian approach to simulate two phase spray flow, evaporation and combustion. The modified code is referred as REFLAN3D-SPRAY. The mathematical formulation of the fluid flow, heat transfer, combustion and two phase flow interaction of the numerical solution procedure, boundary conditions and their treatment are described.

An interaction algorithm for prediction of mean and fluctuating velocities in two-dimensional aerodynamic wake flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Orzechowski, J. A.

1980-01-01

A theoretical analysis is presented yielding sets of partial differential equations for determination of turbulent aerodynamic flowfields in the vicinity of an airfoil trailing edge. A four phase interaction algorithm is derived to complete the analysis. Following input, the first computational phase is an elementary viscous corrected two dimensional potential flow solution yielding an estimate of the inviscid-flow induced pressure distribution. Phase C involves solution of the turbulent two dimensional boundary layer equations over the trailing edge, with transition to a two dimensional parabolic Navier-Stokes equation system describing the near-wake merging of the upper and lower surface boundary layers. An iteration provides refinement of the potential flow induced pressure coupling to the viscous flow solutions. The final phase is a complete two dimensional Navier-Stokes analysis of the wake flow in the vicinity of a blunt-bases airfoil. A finite element numerical algorithm is presented which is applicable to solution of all partial differential equation sets of inviscid-viscous aerodynamic interaction algorithm. Numerical results are discussed.

Dimensionally regularized Tsallis' statistical mechanics and two-body Newton's gravitation

NASA Astrophysics Data System (ADS)

Zamora, J. D.; Rocca, M. C.; Plastino, A.; Ferri, G. L.

2018-05-01

Typical Tsallis' statistical mechanics' quantifiers like the partition function and the mean energy exhibit poles. We are speaking of the partition function Z and the mean energy 〈 U 〉 . The poles appear for distinctive values of Tsallis' characteristic real parameter q, at a numerable set of rational numbers of the q-line. These poles are dealt with dimensional regularization resources. The physical effects of these poles on the specific heats are studied here for the two-body classical gravitation potential.

Computing the optimal path in stochastic dynamical systems

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

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

2016-08-15

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

Numerical simulation for heat transfer performance in unsteady flow of Williamson fluid driven by a wedge-geometry

NASA Astrophysics Data System (ADS)

Hamid, Aamir; Hashim; Khan, Masood

2018-06-01

The main concern of this communication is to investigate the two-layer flow of a non-Newtonian rheological fluid past a wedge-shaped geometry. One remarkable aspect of this article is the mathematical formulation for two-dimensional flow of Williamson fluid by incorporating the effect of infinite shear rate viscosity. The impacts of heat transfer mechanism on time-dependent flow field are further studied. At first, we employ the suitable non-dimensional variables to transmute the time-dependent governing flow equations into a system of non-linear ordinary differential equations. The converted conservation equations are numerically integrated subject to physically suitable boundary conditions with the aid of Runge-Kutta Fehlberg integration procedure. The effects of involved pertinent parameters, such as, moving wedge parameter, wedge angle parameter, local Weissenberg number, unsteadiness parameter and Prandtl number on the non-dimensional velocity and temperature distributions have been evaluated. In addition, the numerical values of the local skin friction coefficient and the local Nusselt number are compared and presented through tables. The outcomes of this study indicate that the rate of heat transfer increases with the growth of both wedge angle parameter and unsteadiness parameter. Moreover, a substantial rise in the fluid velocity is observed with enhancement in the viscosity ratio parameter while an opposite trend is true for the non-dimensional temperature field. A comparison is presented between the current study and already published works and results found to be in outstanding agreement. Finally, the main findings of this article are highlighted in the last section.

Transient Two-Dimensional Analysis of Side Load in Liquid Rocket Engine Nozzles

NASA Technical Reports Server (NTRS)

Wang, Ten-See

2004-01-01

Two-dimensional planar and axisymmetric numerical investigations on the nozzle start-up side load physics were performed. The objective of this study is to develop a computational methodology to identify nozzle side load physics using simplified two-dimensional geometries, in order to come up with a computational strategy to eventually predict the three-dimensional side loads. The computational methodology is based on a multidimensional, finite-volume, viscous, chemically reacting, unstructured-grid, and pressure-based computational fluid dynamics formulation, and a transient inlet condition based on an engine system modeling. The side load physics captured in the low aspect-ratio, two-dimensional planar nozzle include the Coanda effect, afterburning wave, and the associated lip free-shock oscillation. Results of parametric studies indicate that equivalence ratio, combustion and ramp rate affect the side load physics. The side load physics inferred in the high aspect-ratio, axisymmetric nozzle study include the afterburning wave; transition from free-shock to restricted-shock separation, reverting back to free-shock separation, and transforming to restricted-shock separation again; and lip restricted-shock oscillation. The Mach disk loci and wall pressure history studies reconfirm that combustion and the associated thermodynamic properties affect the formation and duration of the asymmetric flow.

The program FANS-3D (finite analytic numerical simulation 3-dimensional) and its applications

NASA Technical Reports Server (NTRS)

Bravo, Ramiro H.; Chen, Ching-Jen

1992-01-01

In this study, the program named FANS-3D (Finite Analytic Numerical Simulation-3 Dimensional) is presented. FANS-3D was designed to solve problems of incompressible fluid flow and combined modes of heat transfer. It solves problems with conduction and convection modes of heat transfer in laminar flow, with provisions for radiation and turbulent flows. It can solve singular or conjugate modes of heat transfer. It also solves problems in natural convection, using the Boussinesq approximation. FANS-3D was designed to solve heat transfer problems inside one, two and three dimensional geometries that can be represented by orthogonal planes in a Cartesian coordinate system. It can solve internal and external flows using appropriate boundary conditions such as symmetric, periodic and user specified.

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

NASA Astrophysics Data System (ADS)

Castiglioni, Giacomo

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

Direct numerical simulation of axisymmetric turbulence

NASA Astrophysics Data System (ADS)

Qu, Bo; Bos, Wouter J. T.; Naso, Aurore

2017-09-01

The dynamics of decaying, strictly axisymmetric, incompressible turbulence is investigated using direct numerical simulations. It is found that the angular momentum is a robust invariant of the system. It is further shown that long-lived coherent structures are generated by the flow. These structures can be associated with stationary solutions of the Euler equations. The structures obey relations in agreement with predictions from selective decay principles, compatible with the decay laws of the system. Two different types of decay scenarios are highlighted. The first case results in a quasi-two-dimensional flow with a dynamical behavior in the poloidal plane similar to freely decaying two-dimensional turbulence. In a second regime, the long-time dynamics is dominated by a single three-dimensional mode.

The third-order structure function in two dimensions: The Rashomon effect

NASA Astrophysics Data System (ADS)

Cerbus, Rory T.; Chakraborty, Pinaki

2017-11-01

We study the third-order longitudinal structure function, S3(r), in two-dimensional turbulence. In three dimensions, there is considerable theoretical, experimental, and numerical consensus regarding the validity of Kolmogorov's arch-famous " /4 5 th law" for S3(r). By contrast, in two dimensions, two disparate cascades, changed dissipation anomalies, a large-scale drag, and other factors conspire to create several versions of the S3(r) "law." This single quantity can vary considerably when viewed from different perspectives, reminiscent of the "Rashomon effect" in anthropology. After reviewing the history and usage of S3(r) in two-dimensional turbulence, we show that S3(r) generically embodies a mixture of energy and enstrophy fluxes. Building on this result, we derive S3(r) laws for freely decaying and forced two-dimensional turbulent flows, where we also account for the effects of a large-scale drag, an inextricable feature of quasi two-dimensional turbulence in experimental and atmospheric flows. We draw attention to the caution needed in interpreting S3(r) in two-dimensional turbulence.

A meshless method using radial basis functions for numerical solution of the two-dimensional KdV-Burgers equation

NASA Astrophysics Data System (ADS)

Zabihi, F.; Saffarian, M.

2016-07-01

The aim of this article is to obtain the numerical solution of the two-dimensional KdV-Burgers equation. We construct the solution by using a different approach, that is based on using collocation points. The solution is based on using the thin plate splines radial basis function, which builds an approximated solution with discretizing the time and the space to small steps. We use a predictor-corrector scheme to avoid solving the nonlinear system. The results of numerical experiments are compared with analytical solutions to confirm the accuracy and efficiency of the presented scheme.

Numerical modeling method on the movement of water flow and suspended solids in two-dimensional sedimentation tanks in the wastewater treatment plant.

PubMed

Zeng, Guang-Ming; Jiang, Yi-Min; Qin, Xiao-Sheng; Huang, Guo-He; Li, Jian-Bing

2003-01-01

Taking the distributing calculation of velocity and concentration as an example, the paper established a series of governing equations by the vorticity-stream function method, and dispersed the equations by the finite differencing method. After figuring out the distribution field of velocity, the paper also calculated the concentration distribution in sedimentation tank by using the two-dimensional concentration transport equation. The validity and feasibility of the numerical method was verified through comparing with experimental data. Furthermore, the paper carried out a tentative exploration into the application of numerical simulation of sedimentation tanks.

Numerically exploring the 1D-2D dimensional crossover on spin dynamics in the doped Hubbard model

DOE PAGES

Kung, Y. F.; Bazin, C.; Wohlfeld, K.; ...

2017-11-02

Using determinant quantum Monte Carlo (DQMC) simulations, we systematically study the doping dependence of the crossover from one to two dimensions and its impact on the magnetic properties of the Hubbard model. A square lattice of chains is used, in which the dimensionality can be tuned by varying the interchain coupling t ⊥. The dynamical spin structure factor and static quantities, such as the static spin susceptibility and nearest-neighbor spin correlation function, are characterized in the one- and two-dimensional limits as a benchmark. When the dimensionality is tuned between these limits, the magnetic properties, while evolving smoothly from one tomore » two dimensions, drastically change regardless of the doping level. This suggests that the spin excitations in the two-dimensional Hubbard model, even in the heavily doped case, cannot be explained using the spinon picture known from one dimension. In conclusion, the DQMC calculations are complemented by cluster perturbation theory studies to form a more complete picture of how the crossover occurs as a function of doping and how doped holes impact magnetic order.« less

An Evaluation of Four Methods of Numerical Analysis for Two-Dimensional Airfoil Flows. Revision.

DTIC Science & Technology

1985-07-06

distribution as determined by the Eppler and Chang potential codes for the four airfoil geometries is shown in Figures 3-6. Here, 2 n-- Cp (P-Po)/.5pUo where...SPD- 1037-01. 2) Eppler , R., and D.M. Somers. A Computer Program for the Design and Analysis of Low Speed Airfoils . NASA Technical Memorandum 80210. 3...OF NUMERICAL n ANALYSIS FORI TWO-DIMENSIONAL AIRFOIL FLOWS Roger Burke APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED DAVID TAYLOR NAVAL SHIP R

Analytic and numeric Green's functions for a two-dimensional electron gas in an orthogonal magnetic field

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

Cresti, Alessandro; Grosso, Giuseppe; Parravicini, Giuseppe Pastori

2006-05-15

We have derived closed analytic expressions for the Green's function of an electron in a two-dimensional electron gas threaded by a uniform perpendicular magnetic field, also in the presence of a uniform electric field and of a parabolic spatial confinement. A workable and powerful numerical procedure for the calculation of the Green's functions for a large infinitely extended quantum wire is considered exploiting a lattice model for the wire, the tight-binding representation for the corresponding matrix Green's function, and the Peierls phase factor in the Hamiltonian hopping matrix element to account for the magnetic field. The numerical evaluation of themore » Green's function has been performed by means of the decimation-renormalization method, and quite satisfactorily compared with the analytic results worked out in this paper. As an example of the versatility of the numerical and analytic tools here presented, the peculiar semilocal character of the magnetic Green's function is studied in detail because of its basic importance in determining magneto-transport properties in mesoscopic systems.« less

Influence of the Numerical Scheme on the Solution Quality of the SWE for Tsunami Numerical Codes: The Tohoku-Oki, 2011Example.

NASA Astrophysics Data System (ADS)

Reis, C.; Clain, S.; Figueiredo, J.; Baptista, M. A.; Miranda, J. M. A.

2015-12-01

Numerical tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly depends on the numerical tool quality and the design of efficient numerical schemes still receives important attention to provide robust and accurate solutions. In this study we propose a comparative study between the efficiency of two volume finite numerical codes with second-order discretization implemented with different method to solve the non-conservative shallow water equations, the MUSCL (Monotonic Upstream-Centered Scheme for Conservation Laws) and the MOOD methods (Multi-dimensional Optimal Order Detection) which optimize the accuracy of the approximation in function of the solution local smoothness. The MUSCL is based on a priori criteria where the limiting procedure is performed before updated the solution to the next time-step leading to non-necessary accuracy reduction. On the contrary, the new MOOD technique uses a posteriori detectors to prevent the solution from oscillating in the vicinity of the discontinuities. Indeed, a candidate solution is computed and corrections are performed only for the cells where non-physical oscillations are detected. Using a simple one-dimensional analytical benchmark, 'Single wave on a sloping beach', we show that the classical 1D shallow-water system can be accurately solved with the finite volume method equipped with the MOOD technique and provide better approximation with sharper shock and less numerical diffusion. For the code validation, we also use the Tohoku-Oki 2011 tsunami and reproduce two DART records, demonstrating that the quality of the solution may deeply interfere with the scenario one can assess. This work is funded by the Portugal-France research agreement, through the research project GEONUM FCT-ANR/MAT-NAN/0122/2012.Numerical tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly depends on the numerical tool quality and the design of efficient numerical schemes still receives important attention to provide robust and accurate solutions. In this study we propose a comparative study between the efficiency of two volume finite numerical codes with second-order discretization implemented with different method to solve the non-conservative shallow water equations, the MUSCL (Monotonic Upstream-Centered Scheme for Conservation Laws) and the MOOD methods (Multi-dimensional Optimal Order Detection) which optimize the accuracy of the approximation in function of the solution local smoothness. The MUSCL is based on a priori criteria where the limiting procedure is performed before updated the solution to the next time-step leading to non-necessary accuracy reduction. On the contrary, the new MOOD technique uses a posteriori detectors to prevent the solution from oscillating in the vicinity of the discontinuities. Indeed, a candidate solution is computed and corrections are performed only for the cells where non-physical oscillations are detected. Using a simple one-dimensional analytical benchmark, 'Single wave on a sloping beach', we show that the classical 1D shallow-water system can be accurately solved with the finite volume method equipped with the MOOD technique and provide better approximation with sharper shock and less numerical diffusion. For the code validation, we also use the Tohoku-Oki 2011 tsunami and reproduce two DART records, demonstrating that the quality of the solution may deeply interfere with the scenario one can assess. This work is funded by the Portugal-France research agreement, through the research project GEONUM FCT-ANR/MAT-NAN/0122/2012.

Further studies on stability analysis of nonlinear Roesser-type two-dimensional systems

NASA Astrophysics Data System (ADS)

Dai, Xiao-Lin

2014-04-01

This paper is concerned with further relaxations of the stability analysis of nonlinear Roesser-type two-dimensional (2D) systems in the Takagi-Sugeno fuzzy form. To achieve the goal, a novel slack matrix variable technique, which is homogenous polynomially parameter-dependent on the normalized fuzzy weighting functions with arbitrary degree, is developed and the algebraic properties of the normalized fuzzy weighting functions are collected into a set of augmented matrices. Consequently, more information about the normalized fuzzy weighting functions is involved and the relaxation quality of the stability analysis is significantly improved. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed result.

Numerical Study of a Three Dimensional Interaction between two bow Shock Waves and the Aerodynamic Heating on a Wedge Shaped Nose Cone

NASA Astrophysics Data System (ADS)

Wu, N.; Wang, J. H.; Shen, L.

2017-03-01

This paper presents a numerical investigation on the three-dimensional interaction between two bow shock waves in two environments, i.e. ground high-enthalpy wind tunnel test and real space flight, using Fluent 15.0. The first bow shock wave, also called induced shock wave, which is generated by the leading edge of a hypersonic vehicle. The other bow shock wave can be deemed objective shock wave, which is generated by the cowl clip of hypersonic inlet, and in this paper the inlet is represented by a wedge shaped nose cone. The interaction performances including flow field structures, aerodynamic pressure and heating are analyzed and compared between the ground test and the real space flight. Through the analysis and comparison, we can find the following important phenomena: 1) Three-dimensional complicated flow structures appear in both cases, but only in the real space flight condition, a local two-dimensional type IV interaction appears; 2) The heat flux and pressure in the interaction region are much larger than those in the no-interaction region in both cases, but the peak values of the heat flux and pressure in real space flight are smaller than those in ground test. 3) The interaction region on the objective surface are different in the two cases, and there is a peak value displacement of 3 mm along the stagnation line.

Numerical study of shock-induced combustion in methane-air mixtures

NASA Technical Reports Server (NTRS)

Yungster, Shaye; Rabinowitz, Martin J.

1993-01-01

The shock-induced combustion of methane-air mixtures in hypersonic flows is investigated using a new reaction mechanism consisting of 19 reacting species and 52 elementary reactions. This reduced model is derived from a full kinetic mechanism via the Detailed Reduction technique. Zero-dimensional computations of several shock-tube experiments are presented first. The reaction mechanism is then combined with a fully implicit Navier-Stokes computational fluid dynamics (CFD) code to conduct numerical simulations of two-dimensional and axisymmetric shock-induced combustion experiments of stoichiometric methane-air mixtures at a Mach number of M = 6.61. Applications to the ram accelerator concept are also presented.

Problems in nonlinear acoustics: Scattering of sound by sound, parametric receiving arrays, nonlinear effects in asymmetric sound beams and pulsed finite amplitude sound beams

NASA Astrophysics Data System (ADS)

Hamilton, Mark F.

1989-08-01

Four projects are discussed in this annual summary report, all of which involve basic research in nonlinear acoustics: Scattering of Sound by Sound, a theoretical study of two nonconlinear Gaussian beams which interact to produce sum and difference frequency sound; Parametric Receiving Arrays, a theoretical study of parametric reception in a reverberant environment; Nonlinear Effects in Asymmetric Sound Beams, a numerical study of two dimensional finite amplitude sound fields; and Pulsed Finite Amplitude Sound Beams, a numerical time domain solution of the KZK equation.

Numerical study of radiometric forces via the direct solution of the Boltzmann kinetic equation

NASA Astrophysics Data System (ADS)

Anikin, Yu. A.

2011-07-01

The two-dimensional rarefied gas motion in a Crookes radiometer and the resulting radiometric forces are studied by numerically solving the Boltzmann kinetic equation. The collision integral is directly evaluated using a projection method, and second-order accurate TVD schemes are used to solve the advection equation. The radiometric forces are found as functions of the Knudsen number and the temperatures, and their spatial distribution is analyzed.

Dispersion analysis and measurement of circular cylindrical wedge-like acoustic waveguides.

PubMed

Yu, Tai-Ho

2015-09-01

This study investigated the propagation of flexural waves along the outer edge of a circular cylindrical wedge, the phase velocities, and the corresponding mode displacements. Thus far, only approximate solutions have been derived because the corresponding boundary-value problems are complex. In this study, dispersion curves were determined using the bi-dimensional finite element method and derived through the separation of variables and the Hamilton principle. Modal displacement calculations clarified that the maximal deformations appeared at the outer edge of the wedge tip. Numerical examples indicated how distinct thin-film materials deposited on the outer surface of the circular cylindrical wedge influenced the dispersion curves. Additionally, dispersion curves were measured using a laser-induced guided wave, a knife-edge measurement scheme, and a two-dimensional fast Fourier transform method. Both the numerical and experimental results correlated closely, thus validating the numerical solution. Copyright © 2015 Elsevier B.V. All rights reserved.

Two-dimensional atmospheric transport and chemistry model - Numerical experiments with a new advection algorithm

NASA Technical Reports Server (NTRS)

Shia, Run-Lie; Ha, Yuk Lung; Wen, Jun-Shan; Yung, Yuk L.

1990-01-01

Extensive testing of the advective scheme proposed by Prather (1986) has been carried out in support of the California Institute of Technology-Jet Propulsion Laboratory two-dimensional model of the middle atmosphere. The original scheme is generalized to include higher-order moments. In addition, it is shown how well the scheme works in the presence of chemistry as well as eddy diffusion. Six types of numerical experiments including simple clock motion and pure advection in two dimensions have been investigated in detail. By comparison with analytic solutions, it is shown that the new algorithm can faithfully preserve concentration profiles, has essentially no numerical diffusion, and is superior to a typical fourth-order finite difference scheme.

Comparison of Implicit Collocation Methods for the Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules; Jezequel, Fabienne; Zukor, Dorothy (Technical Monitor)

2001-01-01

We combine a high-order compact finite difference scheme to approximate spatial derivatives arid collocation techniques for the time component to numerically solve the two dimensional heat equation. We use two approaches to implement the collocation methods. The first one is based on an explicit computation of the coefficients of polynomials and the second one relies on differential quadrature. We compare them by studying their merits and analyzing their numerical performance. All our computations, based on parallel algorithms, are carried out on the CRAY SV1.

Quantification of topological changes of vorticity contours in two-dimensional Navier-Stokes flow.

PubMed

Ohkitani, Koji; Al Sulti, Fayeza

2010-06-01

A characterization of reconnection of vorticity contours is made by direct numerical simulations of the two-dimensional Navier-Stokes flow at a relatively low Reynolds number. We identify all the critical points of the vorticity field and classify them by solving an eigenvalue problem of its Hessian matrix on the basis of critical-point theory. The numbers of hyperbolic (saddles) and elliptic (minima and maxima) points are confirmed to satisfy Euler's index theorem numerically. Time evolution of these indices is studied for a simple initial condition. Generally speaking, we have found that the indices are found to decrease in number with time. This result is discussed in connection with related works on streamline topology, in particular, the relationship between stagnation points and the dissipation. Associated elementary procedures in physical space, the merging of vortices, are studied in detail for a number of snapshots. A similar analysis is also done using the stream function.

2-dimensional implicit hydrodynamics on adaptive grids

NASA Astrophysics Data System (ADS)

Stökl, A.; Dorfi, E. A.

2007-12-01

We present a numerical scheme for two-dimensional hydrodynamics computations using a 2D adaptive grid together with an implicit discretization. The combination of these techniques has offered favorable numerical properties applicable to a variety of one-dimensional astrophysical problems which motivated us to generalize this approach for two-dimensional applications. Due to the different topological nature of 2D grids compared to 1D problems, grid adaptivity has to avoid severe grid distortions which necessitates additional smoothing parameters to be included into the formulation of a 2D adaptive grid. The concept of adaptivity is described in detail and several test computations demonstrate the effectivity of smoothing. The coupled solution of this grid equation together with the equations of hydrodynamics is illustrated by computation of a 2D shock tube problem.

Anharmonic, dimensionality and size effects in phonon transport

NASA Astrophysics Data System (ADS)

Thomas, Iorwerth O.; Srivastava, G. P.

2017-12-01

We have developed and employed a numerically efficient semi- ab initio theory, based on density-functional and relaxation-time schemes, to examine anharmonic, dimensionality and size effects in phonon transport in three- and two-dimensional solids of different crystal symmetries. Our method uses third- and fourth-order terms in crystal Hamiltonian expressed in terms of a temperature-dependent Grüneisen’s constant. All input to numerical calculations are generated from phonon calculations based on the density-functional perturbation theory. It is found that four-phonon processes make important and measurable contribution to lattice thermal resistivity above the Debye temperature. From our numerical results for bulk Si, bulk Ge, bulk MoS2 and monolayer MoS2 we find that the sample length dependence of phonon conductivity is significantly stronger in low-dimensional solids.

On the modeling of the bottom particles segregation with non-linear diffusion equations: application to the marine sand ripples

NASA Astrophysics Data System (ADS)

Tiguercha, Djlalli; Bennis, Anne-claire; Ezersky, Alexander

2015-04-01

The elliptical motion in surface waves causes an oscillating motion of the sand grains leading to the formation of ripple patterns on the bottom. Investigation how the grains with different properties are distributed inside the ripples is a difficult task because of the segration of particle. The work of Fernandez et al. (2003) was extended from one-dimensional to two-dimensional case. A new numerical model, based on these non-linear diffusion equations, was developed to simulate the grain distribution inside the marine sand ripples. The one and two-dimensional models are validated on several test cases where segregation appears. Starting from an homogeneous mixture of grains, the two-dimensional simulations demonstrate different segregation patterns: a) formation of zones with high concentration of light and heavy particles, b) formation of «cat's eye» patterns, c) appearance of inverse Brazil nut effect. Comparisons of numerical results with the new set of field data and wave flume experiments show that the two-dimensional non-linear diffusion equations allow us to reproduce qualitatively experimental results on particles segregation.

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods

DOE PAGES

James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe; ...

2018-02-26

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme-tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one andmore » two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro-modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. Lastly, we describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.« less

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods

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

James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme-tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one andmore » two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro-modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. Lastly, we describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.« less

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods

NASA Astrophysics Data System (ADS)

James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe; Robinson, Neil J.; Tsvelik, Alexei M.

2018-04-01

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb–Liniger model, 1  +  1D quantum chromodynamics, as well as Landau–Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.

New developments in the theoretical treatment of low dimensional strongly correlated systems.

PubMed

James, Andrew J A; Konik, Robert M; Lecheminant, Philippe; Robinson, Neil; Tsvelik, Alexei M

2017-10-09

We review two important non-perturbative approaches for extracting the physics of low- dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of confor- mal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme- tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro- modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics. © 2017 IOP Publishing Ltd.

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods.

PubMed

James, Andrew J A; Konik, Robert M; Lecheminant, Philippe; Robinson, Neil J; Tsvelik, Alexei M

2018-02-26

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1  +  1D quantum chromodynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.

NUMERICAL SIMULATIONS OF KELVIN–HELMHOLTZ INSTABILITY: A TWO-DIMENSIONAL PARAMETRIC STUDY

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

Tian, Chunlin; Chen, Yao, E-mail: chunlin.tian@sdu.edu.cn

2016-06-10

Using two-dimensional simulations, we numerically explore the dependences of Kelvin–Helmholtz (KH) instability upon various physical parameters, including viscosity, the width of the sheared layer, flow speed, and magnetic field strength. In most cases, a multi-vortex phase exists between the initial growth phase and the final single-vortex phase. The parametric study shows that the evolutionary properties, such as phase duration and vortex dynamics, are generally sensitive to these parameters, except in certain regimes. An interesting result is that for supersonic flows, the phase durations and saturation of velocity growth approach constant values asymptotically as the sonic Mach number increases. We confirmmore » that the linear coupling between magnetic field and KH modes is negligible if the magnetic field is weak enough. The morphological behavior suggests that the multi-vortex coalescence might be driven by the underlying wave–wave interaction. Based on these results, we present a preliminary discussion of several events observed in the solar corona. The numerical models need to be further improved to perform a practical diagnostic of the coronal plasma properties.« less

Spontaneous supersymmetry breaking in two dimensional lattice super QCD

DOE PAGES

Catterall, Simon; Veernala, Aarti

2015-10-02

We report on a non-perturbative study of two dimensional N=(2,2) super QCD. Our lattice formulation retains a single exact supersymmetry at non-zero lattice spacing, and contains N f fermions in the fundamental representation of a U(N c) gauge group. The lattice action we employ contains an additional Fayet-Iliopoulos term which is also invariant under the exact lattice supersymmetry. This work constitutes the first numerical study of this theory which serves as a toy model for understanding some of the issues that are expected to arise in four dimensional super QCD. As a result, we present evidence that the exact supersymmetrymore » breaks spontaneously when N f < N c in agreement with theoretical expectations.« less

Physiology driven adaptivity for the numerical solution of the bidomain equations.

PubMed

Whiteley, Jonathan P

2007-09-01

Previous work [Whiteley, J. P. IEEE Trans. Biomed. Eng. 53:2139-2147, 2006] derived a stable, semi-implicit numerical scheme for solving the bidomain equations. This scheme allows the timestep used when solving the bidomain equations numerically to be chosen by accuracy considerations rather than stability considerations. In this study we modify this scheme to allow an adaptive numerical solution in both time and space. The spatial mesh size is determined by the gradient of the transmembrane and extracellular potentials while the timestep is determined by the values of: (i) the fast sodium current; and (ii) the calcium release from junctional sarcoplasmic reticulum to myoplasm current. For two-dimensional simulations presented here, combining the numerical algorithm in the paper cited above with the adaptive algorithm presented here leads to an increase in computational efficiency by a factor of around 250 over previous work, together with significantly less computational memory being required. The speedup for three-dimensional simulations is likely to be more impressive.

Numerical simulations of compressible mixing layers

NASA Technical Reports Server (NTRS)

Normand, Xavier

1990-01-01

Direct numerical simulations of two-dimensional temporally growing compressible mixing layers are presented. The Kelvin-Helmholtz instability is initially excited by a white-noise perturbation superimposed onto a hyperbolic tangent meanflow profile. The linear regime is studied at low resolution in the case of two flows of equal temperatures, for convective Mach numbers from 0.1 to 1 and for different values of the Reynolds number. At higher resolution, the complete evolution of a two-eddy mixing layer between two flows of different temperatures is simulated at moderate Reynolds number. Similarities and differences between flows of equal convective Mach numbers are discussed.

Vorticity vector-potential method based on time-dependent curvilinear coordinates for two-dimensional rotating flows in closed configurations

NASA Astrophysics Data System (ADS)

Fu, Yuan; Zhang, Da-peng; Xie, Xi-lin

2018-04-01

In this study, a vorticity vector-potential method for two-dimensional viscous incompressible rotating driven flows is developed in the time-dependent curvilinear coordinates. The method is applicable in both inertial and non-inertial frames of reference with the advantage of a fixed and regular calculation domain. The numerical method is applied to triangle and curved triangle configurations in constant and varying rotational angular velocity cases respectively. The evolutions of flow field are studied. The geostrophic effect, unsteady effect and curvature effect on the evolutions are discussed.

Fluid flow and fuel-air mixing in a motored two-dimensional Wankel rotary engine

NASA Technical Reports Server (NTRS)

Shih, T. I.-P.; Nguyen, H. L.; Stegeman, J.

1986-01-01

The implicit-factored method of Beam and Warming was employed to obtain numerical solutions to the conservation equations of mass, species, momentum, and energy to study the unsteady, multidimensional flow and mixing of fuel and air inside the combustion chambers of a two-dimensional Wankel rotary engine under motored conditions. The effects of the following engine design and operating parameters on fluid flow and fuel-air mixing during the intake and compression cycles were studied: engine speed, angle of gaseous fuel injection during compression cycle, and speed of the fuel leaving fuel injector.

Fluid flow and fuel-air mixing in a motored two-dimensional Wankel rotary engine

NASA Astrophysics Data System (ADS)

Shih, T. I.-P.; Nguyen, H. L.; Stegeman, J.

1986-06-01

The implicit-factored method of Beam and Warming was employed to obtain numerical solutions to the conservation equations of mass, species, momentum, and energy to study the unsteady, multidimensional flow and mixing of fuel and air inside the combustion chambers of a two-dimensional Wankel rotary engine under motored conditions. The effects of the following engine design and operating parameters on fluid flow and fuel-air mixing during the intake and compression cycles were studied: engine speed, angle of gaseous fuel injection during compression cycle, and speed of the fuel leaving fuel injector.

Vorticity vector-potential method based on time-dependent curvilinear coordinates for two-dimensional rotating flows in closed configurations

NASA Astrophysics Data System (ADS)

Fu, Yuan; Zhang, Da-peng; Xie, Xi-lin

2018-03-01

In this study, a vorticity vector-potential method for two-dimensional viscous incompressible rotating driven flows is developed in the time-dependent curvilinear coordinates. The method is applicable in both inertial and non-inertial frames of reference with the advantage of a fixed and regular calculation domain. The numerical method is applied to triangle and curved triangle configurations in constant and varying rotational angular velocity cases respectively. The evolutions of flow field are studied. The geostrophic effect, unsteady effect and curvature effect on the evolutions are discussed.

Multiscale solutions of radiative heat transfer by the discrete unified gas kinetic scheme

NASA Astrophysics Data System (ADS)

Luo, Xiao-Ping; Wang, Cun-Hai; Zhang, Yong; Yi, Hong-Liang; Tan, He-Ping

2018-06-01

The radiative transfer equation (RTE) has two asymptotic regimes characterized by the optical thickness, namely, optically thin and optically thick regimes. In the optically thin regime, a ballistic or kinetic transport is dominant. In the optically thick regime, energy transport is totally dominated by multiple collisions between photons; that is, the photons propagate by means of diffusion. To obtain convergent solutions to the RTE, conventional numerical schemes have a strong dependence on the number of spatial grids, which leads to a serious computational inefficiency in the regime where the diffusion is predominant. In this work, a discrete unified gas kinetic scheme (DUGKS) is developed to predict radiative heat transfer in participating media. Numerical performances of the DUGKS are compared in detail with conventional methods through three cases including one-dimensional transient radiative heat transfer, two-dimensional steady radiative heat transfer, and three-dimensional multiscale radiative heat transfer. Due to the asymptotic preserving property, the present method with relatively coarse grids gives accurate and reliable numerical solutions for large, small, and in-between values of optical thickness, and, especially in the optically thick regime, the DUGKS demonstrates a pronounced computational efficiency advantage over the conventional numerical models. In addition, the DUGKS has a promising potential in the study of multiscale radiative heat transfer inside the participating medium with a transition from optically thin to optically thick regimes.

Meso-beta scale numerical simulation studies of terrain-induced jet streak mass and momentum perturbations

NASA Technical Reports Server (NTRS)

Lin, Yuh-Lang; Kaplan, Michael L.

1994-01-01

An in-depth analysis of observed gravity waves and their relationship to precipitation bands over the Montana mesonetwork during the 11-12 July 1981 CCOPE case study indicated two episodes of coherent waves. While geostrophic adjustment, shearing instability, and terrain were all implicated separately or in combination as possible wave generation mechanisms, the lack of upper-air data within the wave genesis region made it difficult to define the genesis processes from observations alone. The first part of this paper, 3D Numerical Modeling Studies of Terrain-Induced Mass/Momentum Perturbations, employs a mesoscale numerical model to help diagnose the intricate early wave generation mechanisms during the first observed gravity wave episode. The meso-beta scale numerical model is used to study various simulations of the role of multiple geostrophic adjustment processes in focusing a region for gravity wave genesis. The second part of this paper, Linear Theory and Theoretical Modeling, investigates the response of non-resting rotating homogeneous and continuously stratified Boussinesq models of the terrestrial atmosphere to temporally impulsive and uniformly propagating three-dimensional localized zonal momentum sources representative of midlatitude jet streaks. The methods of linear perturbation theory applied to the potential vorticity (PV) and wave field equations are used to study the geostrophic adjustment dynamics. The total zonal and meridional wind perturbations are separated into geostrophic and ageostrophic components in order to define and follow the evolution of both the primary and secondary mesocirculations accompanying midlatitude jetogenesis forced by geostrophic adjustment processes. This problem is addressed to help fill the gap in understanding the dynamics and structure of mesoscale inertia-gravity waves forced by geostrophic adjustment processes in simple two-dimensional quiescent current systems and those produced by mesoscale numerical models simulating the orographic and diabatic perturbation of three-dimensional quasi-geostrophically balanced synoptic scale jet streaks associated with complex baroclinic severe storm producing environments.

A two-dimensional kinematic dynamo model of the ionospheric magnetic field at Venus

NASA Technical Reports Server (NTRS)

Cravens, T. E.; Wu, D.; Shinagawa, H.

1990-01-01

The results of a high-resolution, two-dimensional, time dependent, kinematic dynamo model of the ionospheric magnetic field of Venus are presented. Various one-dimensional models are considered and the two-dimensional model is then detailed. In this model, the two-dimensional magnetic induction equation, the magnetic diffusion-convection equation, is numerically solved using specified plasma velocities. Origins of the vertical velocity profile and of the horizontal velocities are discussed. It is argued that the basic features of the vertical magnetic field profile remain unaltered by horizontal flow effects and also that horizontal plasma flow can strongly affect the magnetic field for altitudes above 300 km.

The void spectrum in two-dimensional numerical simulations of gravitational clustering

NASA Technical Reports Server (NTRS)

Kauffmann, Guinevere; Melott, Adrian L.

1992-01-01

An algorithm for deriving a spectrum of void sizes from two-dimensional high-resolution numerical simulations of gravitational clustering is tested, and it is verified that it produces the correct results where those results can be anticipated. The method is used to study the growth of voids as clustering proceeds. It is found that the most stable indicator of the characteristic void 'size' in the simulations is the mean fractional area covered by voids of diameter d, in a density field smoothed at its correlation length. Very accurate scaling behavior is found in power-law numerical models as they evolve. Eventually, this scaling breaks down as the nonlinearity reaches larger scales. It is shown that this breakdown is a manifestation of the undesirable effect of boundary conditions on simulations, even with the very large dynamic range possible here. A simple criterion is suggested for deciding when simulations with modest large-scale power may systematically underestimate the frequency of larger voids.

Numerical simulations of SHPB experiments for the dynamic compressive strength and failure of ceramics

NASA Astrophysics Data System (ADS)

Anderson, Charles E., Jr.; O'Donoghue, Padraic E.; Lankford, James; Walker, James D.

1992-06-01

Complementary to a study of the compressive strength of ceramic as a function of strain rate and confinement, numerical simulations of the split-Hopkinson pressure bar (SHPB) experiments have been performed using the two-dimensional wave propagation computer program HEMP. The numerical effort had two main thrusts. Firstly, the interpretation of the experimental data relies on several assumptions. The numerical simulations were used to investigate the validity of these assumptions. The second part of the effort focused on computing the idealized constitutive response of a ceramic within the SHPB experiment. These numerical results were then compared against experimental data. Idealized models examined included a perfectly elastic material, an elastic-perfectly plastic material, and an elastic material with failure. Post-failure material was modeled as having either no strength, or a strength proportional to the mean stress. The effects of confinement were also studied. Conclusions concerning the dynamic behavior of a ceramic up to and after failure are drawn from the numerical study.

Heat transfer of phase-change materials in two-dimensional cylindrical coordinates

NASA Technical Reports Server (NTRS)

Labdon, M. B.; Guceri, S. I.

1981-01-01

Two-dimensional phase-change problem is numerically solved in cylindrical coordinates (r and z) by utilizing two Taylor series expansions for the temperature distributions in the neighborhood of the interface location. These two expansions form two polynomials in r and z directions. For the regions sufficiently away from the interface the temperature field equations are numerically solved in the usual way and the results are coupled with the polynomials. The main advantages of this efficient approach include ability to accept arbitrarily time dependent boundary conditions of all types and arbitrarily specified initial temperature distributions. A modified approach using a single Taylor series expansion in two variables is also suggested.

Diffusion with resetting inside a circle

NASA Astrophysics Data System (ADS)

Chatterjee, Abhinava; Christou, Christos; Schadschneider, Andreas

2018-06-01

We study the Brownian motion of a particle in a bounded circular two-dimensional domain in search for a stationary target on the boundary of the domain. The process switches between two modes: one where it performs a two-dimensional diffusion inside the circle and one where it diffuses along the one-dimensional boundary. During the process, the Brownian particle resets to its initial position with a constant rate r . The Fokker-Planck formalism allows us to calculate the mean time to absorption (MTA) as well as the optimal resetting rate for which the MTA is minimized. From the derived analytical results the parameter regions where resetting reduces the search time can be specified. We also provide a numerical method for the verification of our results.

Logarithmic Superdiffusion in Two Dimensional Driven Lattice Gases

NASA Astrophysics Data System (ADS)

Krug, J.; Neiss, R. A.; Schadschneider, A.; Schmidt, J.

2018-03-01

The spreading of density fluctuations in two-dimensional driven diffusive systems is marginally anomalous. Mode coupling theory predicts that the diffusivity in the direction of the drive diverges with time as (ln t)^{2/3} with a prefactor depending on the macroscopic current-density relation and the diffusion tensor of the fluctuating hydrodynamic field equation. Here we present the first numerical verification of this behavior for a particular version of the two-dimensional asymmetric exclusion process. Particles jump strictly asymmetrically along one of the lattice directions and symmetrically along the other, and an anisotropy parameter p governs the ratio between the two rates. Using a novel massively parallel coupling algorithm that strongly reduces the fluctuations in the numerical estimate of the two-point correlation function, we are able to accurately determine the exponent of the logarithmic correction. In addition, the variation of the prefactor with p provides a stringent test of mode coupling theory.

Theoretical analysis and simulations of strong terahertz radiation from the interaction of ultrashort laser pulses with gases

NASA Astrophysics Data System (ADS)

Chen, Min; Pukhov, Alexander; Peng, Xiao-Yu; Willi, Oswald

2008-10-01

Terahertz (THz) radiation from the interaction of ultrashort laser pulses with gases is studied both by theoretical analysis and particle-in-cell (PIC) simulations. A one-dimensional THz generation model based on the transient ionization electric current mechanism is given, which explains the results of one-dimensional PIC simulations. At the same time the relation between the final THz field and the initial transient ionization current is shown. One- and two-dimensional simulations show that for the THz generation the contribution of the electric current due to ionization is much larger than the one driven by the usual ponderomotive force. Ionization current generated by different laser pulses and gases is also studied numerically. Based on the numerical results we explain the scaling laws for THz emission observed in the recent experiments performed by Xie [Phys. Rev. Lett. 96, 075005 (2006)]. We also study the effective parameter region for the carrier envelop phase measurement by the use of THz generation.

Theoretical analysis and simulations of strong terahertz radiation from the interaction of ultrashort laser pulses with gases.

PubMed

Chen, Min; Pukhov, Alexander; Peng, Xiao-Yu; Willi, Oswald

2008-10-01

Terahertz (THz) radiation from the interaction of ultrashort laser pulses with gases is studied both by theoretical analysis and particle-in-cell (PIC) simulations. A one-dimensional THz generation model based on the transient ionization electric current mechanism is given, which explains the results of one-dimensional PIC simulations. At the same time the relation between the final THz field and the initial transient ionization current is shown. One- and two-dimensional simulations show that for the THz generation the contribution of the electric current due to ionization is much larger than the one driven by the usual ponderomotive force. Ionization current generated by different laser pulses and gases is also studied numerically. Based on the numerical results we explain the scaling laws for THz emission observed in the recent experiments performed by Xie et al. [Phys. Rev. Lett. 96, 075005 (2006)]. We also study the effective parameter region for the carrier envelop phase measurement by the use of THz generation.

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

USGS Publications Warehouse

Casulli, Vincenzo; Cheng, Ralph T.

1992-01-01

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

Development of an integrated BEM for hot fluid-structure interaction

NASA Technical Reports Server (NTRS)

Banerjee, P. K.; Dargush, G. F.

1989-01-01

The Boundary Element Method (BEM) is chosen as a basic analysis tool principally because the definition of quantities like fluxes, temperature, displacements, and velocities is very precise on a boundary base discretization scheme. One fundamental difficulty is, of course, that the entire analysis requires a very considerable amount of analytical work which is not present in other numerical methods. During the last 18 months all of this analytical work was completed and a two-dimensional, general purpose code was written. Some of the early results are described. It is anticipated that within the next two to three months almost all two-dimensional idealizations will be examined. It should be noted that the analytical work for the three-dimensional case has also been done and numerical implementation will begin next year.

The Fifth Symposium on Numerical and Physical Aspects of Aerodynamic Flows

NASA Technical Reports Server (NTRS)

1992-01-01

This volume contains the papers presented at the Fifth Symposium on Numerical and Physical Aspects of Aerodynamic Flows, held at the California State University, Long Beach, from 13 to 15 January 1992. The symposium, like its immediate predecessors, considers the calculation of flows of relevance to aircraft, ships, and missiles with emphasis on the solution of two-dimensional unsteady and three-dimensional equations.

Effects of friction on forced two-dimensional Navier-Stokes turbulence.

PubMed

Blackbourn, Luke A K; Tran, Chuong V

2011-10-01

Large-scale dissipation mechanisms have been routinely employed in numerical simulations of two-dimensional turbulence to absorb energy at large scales, presumably mimicking the quasisteady picture of Kraichnan in an unbounded fluid. Here, "side effects" of such a mechanism--mechanical friction--on the small-scale dynamics of forced two-dimensional Navier-Stokes turbulence are elaborated by both theoretical and numerical analysis. Given a positive friction coefficient α, viscous dissipation of enstrophy has been known to vanish in the inviscid limit ν→0. This effectively renders the scale-neutral friction the only mechanism responsible for enstrophy dissipation in that limit. The resulting dynamical picture is that the classical enstrophy inertial range becomes a dissipation range in which the dissipation of enstrophy by friction mainly occurs. For each α>0, there exists a critical viscosity ν(c), which depends on physical parameters, separating the regimes of predominant viscous and frictional dissipation of enstrophy. It is found that ν(c)=[η'(1/3)/(Ck(f)(2))]exp[-η'(1/3)/(Cα)], where η' is half the enstrophy injection rate, k(f) is the forcing wave number, and C is a nondimensional constant (the Kraichnan-Batchelor constant). The present results have important theoretical and practical implications. Apparently, mechanical friction is a poor choice in numerical attempts to address fundamental issues concerning the direct enstrophy transfer in two-dimensional Navier-Stokes turbulence. Furthermore, as relatively strong friction naturally occurs on the surfaces and at lateral boundaries of experimental fluids as well as at the interfaces of shallow layers in geophysical fluid models, the frictional effects discussed in this study are crucial in understanding the dynamics of these systems.

Dynamic stability analysis for capillary channel flow: One-dimensional and three-dimensional computations and the equivalent steady state technique

NASA Astrophysics Data System (ADS)

Grah, Aleksander; Dreyer, Michael E.

2010-01-01

Spacecraft technology provides a series of applications for capillary channel flow. It can serve as a reliable means for positioning and transport of liquids under low gravity conditions. Basically, capillary channels provide liquid paths with one or more free surfaces. A problem may be flow instabilities leading to a collapse of the liquid surfaces. A result is undesired gas ingestion and a two phase flow which can in consequence cause several technical problems. The presented capillary channel consists of parallel plates with two free liquid surfaces. The flow rate is established by a pump at the channel outlet, creating a lower pressure within the channel. Owing to the pressure difference between the liquid phase and the ambient gas phase the free surfaces bend inwards and remain stable as long as they are able to resist the steady and unsteady pressure effects. For the numerical prediction of the flow stability two very different models are used. The one-dimensional unsteady model is mainly based on the Bernoulli equation, the continuity equation, and the Gauss-Laplace equation. For three-dimensional evaluations an open source computational fluid dynamics (CFD) tool is applied. For verifications the numerical results are compared with quasisteady and unsteady data of a sounding rocket experiment. Contrary to previous experiments this one results in a significantly longer observation sequence. Furthermore, the critical point of the steady flow instability could be approached by a quasisteady technique. As in previous experiments the comparison to the numerical model evaluation shows a very good agreement for the movement of the liquid surfaces and for the predicted flow instability. The theoretical prediction of the flow instability is related to the speed index, based on characteristic velocities of the capillary channel flow. Stable flow regimes are defined by stability criteria for steady and unsteady flow. The one-dimensional computation of the speed index is based on the technique of the equivalent steady system, which is published for the first time in the present paper. This approach assumes that for every unsteady state an equivalent steady state with a special boundary condition can be formulated. The equivalent steady state technique enables a reformulation of the equation system and an efficient and reliable speed index computation. Furthermore, the existence of the numerical singularity at the critical point of the steady flow instability, postulated in previous publication, is demonstrated in detail. The numerical singularity is related to the stability criterion for steady flow and represents the numerical consequence of the liquid surface collapse. The evaluation and generation of the pressure diagram is demonstrated in detail with a series of numerical dynamic flow studies. The stability diagram, based on one-dimensional computation, gives a detailed overview of the stable and instable flow regimes. This prediction is in good agreement with the experimentally observed critical flow conditions and results of three-dimensional CFD computations.

A numerical study of candidate transverse fuel injector configurations in the Langley scramjet engine

NASA Technical Reports Server (NTRS)

Drummond, J. P.

1980-01-01

A computer program has been developed that numerically solves the two-dimensional Navier-Stokes and species equations near one or more transverse hydrogen fuel injectors in a scramjet engine. The program currently computes the turbulent mixing and reaction of hydrogen fuel and air, and allows the study of separated regions of the flow immediately preceding and following the injectors. The complex shock-expansion structure produced by the injectors in this region of the engine can also be represented. Results are presented that describe the flow field near two opposing transverse fuel injectors and two opposing staged (multiple) injectors, and comparisons between the two configurations are made to assess their mixing and flameholding qualities.

A variational principle for compressible fluid mechanics: Discussion of the multi-dimensional theory

NASA Technical Reports Server (NTRS)

Prozan, R. J.

1982-01-01

The variational principle for compressible fluid mechanics previously introduced is extended to two dimensional flow. The analysis is stable, exactly conservative, adaptable to coarse or fine grids, and very fast. Solutions for two dimensional problems are included. The excellent behavior and results lend further credence to the variational concept and its applicability to the numerical analysis of complex flow fields.

Unsteady three-dimensional marginal separation caused by surface-mounted obstacles and/or local suction

NASA Astrophysics Data System (ADS)

Braun, Stefan; Kluwick, Alfred

2004-09-01

Earlier investigations of steady two-dimensional marginally separated laminar boundary layers have shown that the non-dimensional wall shear (or equivalently the negative non-dimensional perturbation displacement thickness) is governed by a nonlinear integro-differential equation. This equation contains a single controlling parameter Gamma characterizing, for example, the angle of attack of a slender airfoil and has the important property that (real) solutions exist up to a critical value Gamma_c of Gamma only. Here we investigate three-dimensional unsteady perturbations of an incompressible steady two-dimensional marginally separated laminar boundary layer with special emphasis on the flow behaviour near Gamma_c. Specifically, it is shown that the integro differential equation which governs these disturbances if Gamma_c {-} Gamma {=} O(1) reduces to a nonlinear partial differential equation known as the Fisher equation as Gamma approaches the critical value Gamma_c. This in turn leads to a significant simplification of the problem allowing, among other things, a systematic study of devices used in boundary-layer control and an analytical investigation of the conditions leading to the formation of finite-time singularities which have been observed in earlier numerical studies of unsteady two-dimensional and three-dimensional flows in the vicinity of a line of symmetry. Also, it is found that it is possible to construct exact solutions which describe waves of constant form travelling in the spanwise direction. These waves may contain singularities which can be interpreted as vortex sheets. The existence of these solutions strongly suggests that solutions of the Fisher equation which lead to finite-time blow-up may be extended beyond the blow-up time, thereby generating moving singularities which can be interpreted as vortical structures qualitatively similar to those emerging in direct numerical simulations of near critical (i.e. transitional) laminar separation bubbles. This is supported by asymptotic analysis.

Verification on spray simulation of a pintle injector for liquid rocket engine

NASA Astrophysics Data System (ADS)

Son, Min; Yu, Kijeong; Radhakrishnan, Kanmaniraja; Shin, Bongchul; Koo, Jaye

2016-02-01

The pintle injector used for a liquid rocket engine is a newly re-attracted injection system famous for its wide throttle ability with high efficiency. The pintle injector has many variations with complex inner structures due to its moving parts. In order to study the rotating flow near the injector tip, which was observed from the cold flow experiment using water and air, a numerical simulation was adopted and a verification of the numerical model was later conducted. For the verification process, three types of experimental data including velocity distributions of gas flows, spray angles and liquid distribution were all compared using simulated results. The numerical simulation was performed using a commercial simulation program with the Eulerian multiphase model and axisymmetric two dimensional grids. The maximum and minimum velocities of gas were within the acceptable range of agreement, however, the spray angles experienced up to 25% error when the momentum ratios were increased. The spray density distributions were quantitatively measured and had good agreement. As a result of this study, it was concluded that the simulation method was properly constructed to study specific flow characteristics of the pintle injector despite having the limitations of two dimensional and coarse grids.

Two-dimensional numerical simulation of flow around three-stranded rope

NASA Astrophysics Data System (ADS)

Wang, Xinxin; Wan, Rong; Huang, Liuyi; Zhao, Fenfang; Sun, Peng

2016-08-01

Three-stranded rope is widely used in fishing gear and mooring system. Results of numerical simulation are presented for flow around a three-stranded rope in uniform flow. The simulation was carried out to study the hydrodynamic characteristics of pressure and velocity fields of steady incompressible laminar and turbulent wakes behind a three-stranded rope. A three-cylinder configuration and single circular cylinder configuration are used to model the three-stranded rope in the two-dimensional simulation. The governing equations, Navier-Stokes equations, are solved by using two-dimensional finite volume method. The turbulence flow is simulated using Standard κ-ɛ model and Shear-Stress Transport κ-ω (SST) model. The drag of the three-cylinder model and single cylinder model is calculated for different Reynolds numbers by using control volume analysis method. The pressure coefficient is also calculated for the turbulent model and laminar model based on the control surface method. From the comparison of the drag coefficient and the pressure of the single cylinder and three-cylinder models, it is found that the drag coefficients of the three-cylinder model are generally 1.3-1.5 times those of the single circular cylinder for different Reynolds numbers. Comparing the numerical results with water tank test data, the results of the three-cylinder model are closer to the experiment results than the single cylinder model results.

Random packing of regular polygons and star polygons on a flat two-dimensional surface.

PubMed

Cieśla, Michał; Barbasz, Jakub

2014-08-01

Random packing of unoriented regular polygons and star polygons on a two-dimensional flat continuous surface is studied numerically using random sequential adsorption algorithm. Obtained results are analyzed to determine the saturated random packing ratio as well as its density autocorrelation function. Additionally, the kinetics of packing growth and available surface function are measured. In general, stars give lower packing ratios than polygons, but when the number of vertexes is large enough, both shapes approach disks and, therefore, properties of their packing reproduce already known results for disks.

Computer modeling of inversion layer MOS solar cells and arrays

NASA Technical Reports Server (NTRS)

Ho, Fat Duen

1991-01-01

A two dimensional numerical model of the inversion layer metal insulator semiconductor (IL/MIS) solar cell is proposed by using the finite element method. The two-dimensional current flow in the device is taken into account in this model. The electrostatic potential distribution, the electron concentration distribution, and the hole concentration distribution for different terminal voltages are simulated. The results of simple calculation are presented. The existing problems for this model are addressed. Future work is proposed. The MIS structures are studied and some of the results are reported.

Comparison of Speed-Up Over Hills Derived from Wind-Tunnel Experiments, Wind-Loading Standards, and Numerical Modelling

NASA Astrophysics Data System (ADS)

Safaei Pirooz, Amir A.; Flay, Richard G. J.

2018-03-01

We evaluate the accuracy of the speed-up provided in several wind-loading standards by comparison with wind-tunnel measurements and numerical predictions, which are carried out at a nominal scale of 1:500 and full-scale, respectively. Airflow over two- and three-dimensional bell-shaped hills is numerically modelled using the Reynolds-averaged Navier-Stokes method with a pressure-driven atmospheric boundary layer and three different turbulence models. Investigated in detail are the effects of grid size on the speed-up and flow separation, as well as the resulting uncertainties in the numerical simulations. Good agreement is obtained between the numerical prediction of speed-up, as well as the wake region size and location, with that according to large-eddy simulations and the wind-tunnel results. The numerical results demonstrate the ability to predict the airflow over a hill with good accuracy with considerably less computational time than for large-eddy simulation. Numerical simulations for a three-dimensional hill show that the speed-up and the wake region decrease significantly when compared with the flow over two-dimensional hills due to the secondary flow around three-dimensional hills. Different hill slopes and shapes are simulated numerically to investigate the effect of hill profile on the speed-up. In comparison with more peaked hill crests, flat-topped hills have a lower speed-up at the crest up to heights of about half the hill height, for which none of the standards gives entirely satisfactory values of speed-up. Overall, the latest versions of the National Building Code of Canada and the Australian and New Zealand Standard give the best predictions of wind speed over isolated hills.

Numerical simulation of three-dimensional transonic turbulent projectile aerodynamics by TVD schemes

NASA Technical Reports Server (NTRS)

Shiau, Nae-Haur; Hsu, Chen-Chi; Chyu, Wei-Jao

1989-01-01

The two-dimensional symmetric TVD scheme proposed by Yee has been extended to and investigated for three-dimensional thin-layer Navier-Stokes simulation of complex aerodynamic problems. An existing three-dimensional Navier-stokes code based on the beam and warming algorithm is modified to provide an option of using the TVD algorithm and the flow problem considered is a transonic turbulent flow past a projectile with sting at ten-degree angle of attack. Numerical experiments conducted for three flow cases, free-stream Mach numbers of 0.91, 0.96 and 1.20 show that the symmetric TVD algorithm can provide surface pressure distribution in excellent agreement with measured data; moreover, the rate of convergence to attain a steady state solution is about two times faster than the original beam and warming algorithm.

Numerical modeling of simultaneous tracer release and piscicide treatment for invasive species control in the Chicago Sanitary and Ship Canal, Chicago, Illinois

USGS Publications Warehouse

Zhu, Zhenduo; Motta, Davide; Jackson, P. Ryan; Garcia, Marcelo H.

2017-01-01

In December 2009, during a piscicide treatment targeting the invasive Asian carp in the Chicago Sanitary and Ship Canal, Rhodamine WT dye was released to track and document the transport and dispersion of the piscicide. In this study, two modeling approaches are presented to reproduce the advection and dispersion of the dye tracer (and piscicide), a one-dimensional analytical solution and a three-dimensional numerical model. The two approaches were compared with field measurements of concentration and their applicability is discussed. Acoustic Doppler current profiler measurements were used to estimate the longitudinal dispersion coefficients at ten cross sections, which were taken as reference for calibrating the longitudinal dispersion coefficient in the one-dimensional analytical solution. While the analytical solution is fast, relatively simple, and can fairly accurately predict the core of the observed concentration time series at points downstream, it does not capture the tail of the breakthrough curves. These tails are well reproduced by the three-dimensional model, because it accounts for the effects of dead zones and a power plant which withdraws nearly 80 % of the water from the canal for cooling purposes before returning it back to the canal.

High-resolution two-dimensional and three-dimensional modeling of wire grid polarizers and micropolarizer arrays

NASA Astrophysics Data System (ADS)

Vorobiev, Dmitry; Ninkov, Zoran

2017-11-01

Recent advances in photolithography allowed the fabrication of high-quality wire grid polarizers for the visible and near-infrared regimes. In turn, micropolarizer arrays (MPAs) based on wire grid polarizers have been developed and used to construct compact, versatile imaging polarimeters. However, the contrast and throughput of these polarimeters are significantly worse than one might expect based on the performance of large area wire grid polarizers or MPAs, alone. We investigate the parameters that affect the performance of wire grid polarizers and MPAs, using high-resolution two-dimensional and three-dimensional (3-D) finite-difference time-domain simulations. We pay special attention to numerical errors and other challenges that arise in models of these and other subwavelength optical devices. Our tests show that simulations of these structures in the visible and near-IR begin to converge numerically when the mesh size is smaller than ˜4 nm. The performance of wire grid polarizers is very sensitive to the shape, spacing, and conductivity of the metal wires. Using 3-D simulations of micropolarizer "superpixels," we directly study the cross talk due to diffraction at the edges of each micropolarizer, which decreases the contrast of MPAs to ˜200∶1.

Limitations to the use of two-dimensional thermal modeling of a nuclear waste repository

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

Davis, B.W.

1979-01-04

Thermal modeling of a nuclear waste repository is basic to most waste management predictive models. It is important that the modeling techniques accurately determine the time-dependent temperature distribution of the waste emplacement media. Recent modeling studies show that the time-dependent temperature distribution can be accurately modeled in the far-field using a 2-dimensional (2-D) planar numerical model; however, the near-field cannot be modeled accurately enough by either 2-D axisymmetric or 2-D planar numerical models for repositories in salt. The accuracy limits of 2-D modeling were defined by comparing results from 3-dimensional (3-D) TRUMP modeling with results from both 2-D axisymmetric andmore » 2-D planar. Both TRUMP and ADINAT were employed as modeling tools. Two-dimensional results from the finite element code, ADINAT were compared with 2-D results from the finite difference code, TRUMP; they showed almost perfect correspondence in the far-field. This result adds substantially to confidence in future use of ADINAT and its companion stress code ADINA for thermal stress analysis. ADINAT was found to be somewhat sensitive to time step and mesh aspect ratio. 13 figures, 4 tables.« less

The Effect of Three-Dimensional Freestream Disturbances on the Supersonic Flow Past a Wedge

NASA Technical Reports Server (NTRS)

Duck, Peter W.; Lasseigne, D. Glenn; Hussaini, M. Y.

1997-01-01

The interaction between a shock wave (attached to a wedge) and small amplitude, three-dimensional disturbances of a uniform, supersonic, freestream flow are investigated. The paper extends the two-dimensional study of Duck et al, through the use of vector potentials, which render the problem tractable by the same techniques as in the two-dimensional case, in particular by expansion of the solution by means of a Fourier-Bessel series, in appropriately chosen coordinates. Results are presented for specific classes of freestream disturbances, and the study shows conclusively that the shock is stable to all classes of disturbances (i.e. time periodic perturbations to the shock do not grow downstream), provided the flow downstream of the shock is supersonic (loosely corresponding to the weak shock solution). This is shown from our numerical results and also by asymptotic analysis of the Fourier-Bessel series, valid far downstream of the shock.

A mixed finite difference/Galerkin method for three-dimensional Rayleigh-Benard convection

NASA Technical Reports Server (NTRS)

Buell, Jeffrey C.

1988-01-01

A fast and accurate numerical method, for nonlinear conservation equation systems whose solutions are periodic in two of the three spatial dimensions, is presently implemented for the case of Rayleigh-Benard convection between two rigid parallel plates in the parameter region where steady, three-dimensional convection is known to be stable. High-order streamfunctions secure the reduction of the system of five partial differential equations to a system of only three. Numerical experiments are presented which verify both the expected convergence rates and the absolute accuracy of the method.

Universal Profile of the Vortex Condensate in Two-Dimensional Turbulence

NASA Astrophysics Data System (ADS)

Laurie, Jason; Boffetta, Guido; Falkovich, Gregory; Kolokolov, Igor; Lebedev, Vladimir

2014-12-01

An inverse turbulent cascade in a restricted two-dimensional periodic domain creates a condensate—a pair of coherent system-size vortices. We perform extensive numerical simulations of this system and carry out theoretical analysis based on momentum and energy exchanges between the turbulence and the vortices. We show that the vortices have a universal internal structure independent of the type of small-scale dissipation, small-scale forcing, and boundary conditions. The theory predicts not only the vortex inner region profile, but also the amplitude, which both perfectly agree with the numerical data.

Time-dependent difference theory for noise propagation in a two-dimensional duct. [of a turbofan engine

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1979-01-01

A time dependent numerical formulation was derived for sound propagation in a two dimensional straight soft-walled duct in the absence of mean flow. The time dependent governing acoustic-difference equations and boundary conditions were developed along with the maximum stable time increment. Example calculations were presented for sound attenuation in hard and soft wall ducts. The time dependent analysis were found to be superior to the conventional steady numerical analysis because of much shorter solution times and the elimination of matrix storage requirements.

Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules

1999-01-01

In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.

A Navier-Stokes solution of the three-dimensional viscous compressible flow in a centrifugal compressor impeller

NASA Technical Reports Server (NTRS)

Harp, J. L., Jr.

1977-01-01

A two-dimensional time-dependent computer code was utilized to calculate the three-dimensional steady flow within the impeller blading. The numerical method is an explicit time marching scheme in two spatial dimensions. Initially, an inviscid solution is generated on the hub blade-to-blade surface by the method of Katsanis and McNally (1973). Starting with the known inviscid solution, the viscous effects are calculated through iteration. The approach makes it possible to take into account principal impeller fluid-mechanical effects. It is pointed out that the second iterate provides a complete solution to the three-dimensional, compressible, Navier-Stokes equations for flow in a centrifugal impeller. The problems investigated are related to the study of a radial impeller and a backswept impeller.

A discontinuous Galerkin method for poroelastic wave propagation: The two-dimensional case

NASA Astrophysics Data System (ADS)

Dudley Ward, N. F.; Lähivaara, T.; Eveson, S.

2017-12-01

In this paper, we consider a high-order discontinuous Galerkin (DG) method for modelling wave propagation in coupled poroelastic-elastic media. The upwind numerical flux is derived as an exact solution for the Riemann problem including the poroelastic-elastic interface. Attenuation mechanisms in both Biot's low- and high-frequency regimes are considered. The current implementation supports non-uniform basis orders which can be used to control the numerical accuracy element by element. In the numerical examples, we study the convergence properties of the proposed DG scheme and provide experiments where the numerical accuracy of the scheme under consideration is compared to analytic and other numerical solutions.

New numerical method for radiation heat transfer in nonhomogeneous participating media

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

Howell, J.R.; Tan, Zhiqiang

A new numerical method, which solves the exact integral equations of distance-angular integration form for radiation transfer, is introduced in this paper. By constructing and prestoring the numerical integral formulas for the distance integral for appropriate kernel functions, this method eliminates the time consuming evaluations of the kernels of the space integrals in the formal computations. In addition, when the number of elements in the system is large, the resulting coefficient matrix is quite sparse. Thus, either considerable time or much storage can be saved. A weakness of the method is discussed, and some remedies are suggested. As illustrations, somemore » one-dimensional and two-dimensional problems in both homogeneous and inhomogeneous emitting, absorbing, and linear anisotropic scattering media are studied. Some results are compared with available data. 13 refs.« less

Numerical investigation of the effects of compressibility on the flutter of a cantilevered plate in an inviscid, subsonic, open flow

NASA Astrophysics Data System (ADS)

Colera, Manuel; Pérez-Saborid, Miguel

2018-06-01

We have carried out a numerical study of the influence of the upstream Mach number on the flutter of a two-dimensional, cantilevered, flexible plate subject to a subsonic, inviscid, open flow. We have assumed a linear elastic model for the plate and that the fluid flow is governed by the linearized potential theory. The fluid equations are solved with a novel frequency-domain, finite differences method to obtain the generalized aerodynamic forces as a function of the plate displacements. Then, these generalized forces are coupled to the equation of motion of the plate and an eigenvalue analysis is performed to find the flutter point. The obtained results are in good agreement with those of related theoretical and experimental studies found in the literature. To the best of our knowledge, the analysis performed here is the first self-consistent, parametric study of the influence of the compressibility on the flutter point of a two-dimensional cantilevered plate in subsonic flow.

Numerical studies of interacting vortices

NASA Technical Reports Server (NTRS)

Liu, G. C.; Hsu, C. H.

1985-01-01

To get a basic understanding of the physics of flowfields modeled by vortex filaments with finite vortical cores, systematic numerical studies of the interactions of two dimensional vortices and pairs of coaxial axisymmetric circular vortex rings were made. Finite difference solutions of the unsteady incompressible Navier-Stokes equations were carried out using vorticity and stream function as primary variables. Special emphasis was placed on the formulation of appropriate boundary conditions necessary for the calculations in a finite computational domain. Numerical results illustrate the interaction of vortex filaments, demonstrate when and how they merge with each other, and establish the region of validity for an asymptotic analysis.

Symmetry-breaking instability of quadratic soliton bound states

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

Delque, Michaeel; Departement d'Optique P.M. Duffieux, Institut FEMTO-ST, Universite de Franche-Comte, CNRS UMR 6174, F-25030 Besancon; Fanjoux, Gil

We study both numerically and experimentally two-dimensional soliton bound states in quadratic media and demonstrate their symmetry-breaking instability. The experiment is performed in a potassium titanyl phosphate crystal in a type-II configuration. The bound state is generated by the copropagation of the antisymmetric fundamental beam locked in phase with the symmetrical second harmonic one. Experimental results are in good agreement with numerical simulations of the nonlinear wave equations.

Boundary acquisition for setup of numerical simulation

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

Diegert, C.

1997-12-31

The author presents a work flow diagram that includes a path that begins with taking experimental measurements, and ends with obtaining insight from results produced by numerical simulation. Two examples illustrate this path: (1) Three-dimensional imaging measurement at micron scale, using X-ray tomography, provides information on the boundaries of irregularly-shaped alumina oxide particles held in an epoxy matrix. A subsequent numerical simulation predicts the electrical field concentrations that would occur in the observed particle configurations. (2) Three-dimensional imaging measurement at meter scale, again using X-ray tomography, provides information on the boundaries fossilized bone fragments in a Parasaurolophus crest recently discoveredmore » in New Mexico. A subsequent numerical simulation predicts acoustic response of the elaborate internal structure of nasal passageways defined by the fossil record. The author must both add value, and must change the format of the three-dimensional imaging measurements before the define the geometric boundary initial conditions for the automatic mesh generation, and subsequent numerical simulation. The author applies a variety of filters and statistical classification algorithms to estimate the extents of the structures relevant to the subsequent numerical simulation, and capture these extents as faceted geometries. The author will describe the particular combination of manual and automatic methods used in the above two examples.« less

Two-dimensional modulated ion-acoustic excitations in electronegative plasmas

NASA Astrophysics Data System (ADS)

Panguetna, Chérif S.; Tabi, Conrad B.; Kofané, Timoléon C.

2017-09-01

Two-dimensional modulated ion-acoustic waves are investigated in an electronegative plasma. Through the reductive perturbation expansion, the governing hydrodynamic equations are reduced to a Davey-Stewartson system with two-space variables. The latter is used to study the modulational instability of ion-acoustic waves along with the effect of plasma parameters, namely, the negative ion concentration ratio (α) and the electron-to-negative ion temperature ratio (σn). A parametric analysis of modulational instability is carried out, where regions of plasma parameters responsible for the emergence of modulated ion-acoustic waves are discussed, with emphasis on the behavior of the instability growth rate. Numerically, using perturbed plane waves as initial conditions, parameters from the instability regions give rise to series of dromion solitons under the activation of modulational instability. The sensitivity of the numerical solutions to plasma parameters is discussed. Some exact solutions in the form one- and two-dromion solutions are derived and their response to the effect of varying α and σn is discussed as well.

The TORSED method for construction of TORT boundary sources from external DORT flux files

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

Rhoades, W.A.

1993-08-01

The TORSED method provides a means of coupling cylindrical two-dimensional DORT fluxes or fluences to a three-dimensional TORT calculation in Cartesian geometry through construction of external boundary sources for TORT. This can be important for several reasons. The two-dimensional environment may be too large for TORT simulation. The two-dimensional environment may be truly cylindrical in nature, and thus, better treated in that geometry. It may be desired to use a single environment calculation to study numerous local perturbations. In Section I the TORSED code is described in detail and the diverse demonstration problems that accompany the code distribution are discussed.more » In Section II, an updated discussion of the VISA code is given. VISA is required to preprocess the DORT files for use in TORSED. In Section III, the references are listed.« less

Mixed-mode fracture mechanics parameters of elliptical interface cracks in anisotropic bimaterials

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

Xue, Y.; Qu, J.

1999-07-01

Two-dimensional interface cracks in anisotropic bimaterials have been studied extensively in the literature. However, solutions to three-dimensional interface cracks in anisotropic bimaterials are not available, except for circular (penny-shaped) cracks. In this paper, an elliptical crack on the interface between two anisotropic elastic half-spaces is considered. A formal solution is obtained by using the Stroh method in two dimensional elasticity in conjunction with the Fourier transform method. To illustrate the solution procedure, an elliptical delamination in a cross-ply composite is solved. Numerical results of the stress intensity factors and energy release rate along the crack front are obtained terms ofmore » the interfacial matrix M. It is found that the fields near the crack front are often in mixed mode, due to material anisotropy and the three dimensional nature of the crack front.« less

Three-dimensional marginal separation

NASA Technical Reports Server (NTRS)

Duck, Peter W.

1988-01-01

The three dimensional marginal separation of a boundary layer along a line of symmetry is considered. The key equation governing the displacement function is derived, and found to be a nonlinear integral equation in two space variables. This is solved iteratively using a pseudo-spectral approach, based partly in double Fourier space, and partly in physical space. Qualitatively, the results are similar to previously reported two dimensional results (which are also computed to test the accuracy of the numerical scheme); however quantitatively the three dimensional results are much different.

Metal-superconductor transition in low-dimensional superconducting clusters embedded in two-dimensional electron systems

NASA Astrophysics Data System (ADS)

Bucheli, D.; Caprara, S.; Castellani, C.; Grilli, M.

2013-02-01

Motivated by recent experimental data on thin film superconductors and oxide interfaces, we propose a random-resistor network apt to describe the occurrence of a metal-superconductor transition in a two-dimensional electron system with disorder on the mesoscopic scale. We consider low-dimensional (e.g. filamentary) structures of a superconducting cluster embedded in the two-dimensional network and we explore the separate effects and the interplay of the superconducting structure and of the statistical distribution of local critical temperatures. The thermal evolution of the resistivity is determined by a numerical calculation of the random-resistor network and, for comparison, a mean-field approach called effective medium theory (EMT). Our calculations reveal the relevance of the distribution of critical temperatures for clusters with low connectivity. In addition, we show that the presence of spatial correlations requires a modification of standard EMT to give qualitative agreement with the numerical results. Applying the present approach to an LaTiO3/SrTiO3 oxide interface, we find that the measured resistivity curves are compatible with a network of spatially dense but loosely connected superconducting islands.

The Numerical Analysis of a Turbulent Compressible Jet. Degree awarded by Ohio State Univ., 2000

NASA Technical Reports Server (NTRS)

DeBonis, James R.

2001-01-01

A numerical method to simulate high Reynolds number jet flows was formulated and applied to gain a better understanding of the flow physics. Large-eddy simulation was chosen as the most promising approach to model the turbulent structures due to its compromise between accuracy and computational expense. The filtered Navier-Stokes equations were developed including a total energy form of the energy equation. Subgrid scale models for the momentum and energy equations were adapted from compressible forms of Smagorinsky's original model. The effect of using disparate temporal and spatial accuracy in a numerical scheme was discovered through one-dimensional model problems and a new uniformly fourth-order accurate numerical method was developed. Results from two- and three-dimensional validation exercises show that the code accurately reproduces both viscous and inviscid flows. Numerous axisymmetric jet simulations were performed to investigate the effect of grid resolution, numerical scheme, exit boundary conditions and subgrid scale modeling on the solution and the results were used to guide the three-dimensional calculations. Three-dimensional calculations of a Mach 1.4 jet showed that this LES simulation accurately captures the physics of the turbulent flow. The agreement with experimental data was relatively good and is much better than results in the current literature. Turbulent intensities indicate that the turbulent structures at this level of modeling are not isotropic and this information could lend itself to the development of improved subgrid scale models for LES and turbulence models for RANS simulations. A two point correlation technique was used to quantify the turbulent structures. Two point space correlations were used to obtain a measure of the integral length scale, which proved to be approximately 1/2 D(sub j). Two point space-time correlations were used to obtain the convection velocity for the turbulent structures. This velocity ranged from 0.57 to 0.71 U(sub j).

Oscillations and stability of numerical solutions of the heat conduction equation

NASA Technical Reports Server (NTRS)

Kozdoba, L. A.; Levi, E. V.

1976-01-01

The mathematical model and results of numerical solutions are given for the one dimensional problem when the linear equations are written in a rectangular coordinate system. All the computations are easily realizable for two and three dimensional problems when the equations are written in any coordinate system. Explicit and implicit schemes are shown in tabular form for stability and oscillations criteria; the initial temperature distribution is considered uniform.

A numerical study of blood flow using mixture theory

PubMed Central

Wu, Wei-Tao; Aubry, Nadine; Massoudi, Mehrdad; Kim, Jeongho; Antaki, James F.

2014-01-01

In this paper, we consider the two dimensional flow of blood in a rectangular microfluidic channel. We use Mixture Theory to treat this problem as a two-component system: One component is the red blood cells (RBCs) modeled as a generalized Reiner–Rivlin type fluid, which considers the effects of volume fraction (hematocrit) and influence of shear rate upon viscosity. The other component, plasma, is assumed to behave as a linear viscous fluid. A CFD solver based on OpenFOAM® was developed and employed to simulate a specific problem, namely blood flow in a two dimensional micro-channel, is studied. Finally to better understand this two-component flow system and the effects of the different parameters, the equations are made dimensionless and a parametric study is performed. PMID:24791016

A numerical study of blood flow using mixture theory.

PubMed

Wu, Wei-Tao; Aubry, Nadine; Massoudi, Mehrdad; Kim, Jeongho; Antaki, James F

2014-03-01

In this paper, we consider the two dimensional flow of blood in a rectangular microfluidic channel. We use Mixture Theory to treat this problem as a two-component system: One component is the red blood cells (RBCs) modeled as a generalized Reiner-Rivlin type fluid, which considers the effects of volume fraction (hematocrit) and influence of shear rate upon viscosity. The other component, plasma, is assumed to behave as a linear viscous fluid. A CFD solver based on OpenFOAM ® was developed and employed to simulate a specific problem, namely blood flow in a two dimensional micro-channel, is studied. Finally to better understand this two-component flow system and the effects of the different parameters, the equations are made dimensionless and a parametric study is performed.

A numerical study of three-dimensional diurnal variations within the thermosphere.

NASA Technical Reports Server (NTRS)

Volland, H.; Mayr, H. G.

1973-01-01

A thermosphere model with a realistic temperature profile is assumed. Heat conduction waves are introduced in addition to gravity waves. The temporal and spatial distribution of ion-neutral collisions is taken into account. However, the influence of viscosity waves is neglected. Viscosity-wave effects are simulated by an effective height-dependent collision number. Numerical calculations are conducted of the generation and propagation of two of the most important symmetric tidal waves at thermospheric heights. The influence of the solar EUV-heat upon the generation of the two tidal modes is investigated.

A tool for simulating collision probabilities of animals with marine renewable energy devices.

PubMed

Schmitt, Pál; Culloch, Ross; Lieber, Lilian; Molander, Sverker; Hammar, Linus; Kregting, Louise

2017-01-01

The mathematical problem of establishing a collision probability distribution is often not trivial. The shape and motion of the animal as well as of the the device must be evaluated in a four-dimensional space (3D motion over time). Earlier work on wind and tidal turbines was limited to a simplified two-dimensional representation, which cannot be applied to many new structures. We present a numerical algorithm to obtain such probability distributions using transient, three-dimensional numerical simulations. The method is demonstrated using a sub-surface tidal kite as an example. Necessary pre- and post-processing of the data created by the model is explained, numerical details and potential issues and limitations in the application of resulting probability distributions are highlighted.

An incompressible two-dimensional multiphase particle-in-cell model for dense particle flows

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

Snider, D.M.; O`Rourke, P.J.; Andrews, M.J.

1997-06-01

A two-dimensional, incompressible, multiphase particle-in-cell (MP-PIC) method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to a Eulerian grid and then mapping back computed stress tensors to particle positions. This approach utilizes the best of Eulerian/Eulerian continuum models and Eulerian/Lagrangian discrete models. The solution scheme allows for distributions of types, sizes, and density of particles,more » with no numerical diffusion from the Lagrangian particle calculations. The computational method is implicit with respect to pressure, velocity, and volume fraction in the continuum solution thus avoiding courant limits on computational time advancement. MP-PIC simulations are compared with one-dimensional problems that have analytical solutions and with two-dimensional problems for which there are experimental data.« less

Simple Numerical Modelling for Gasdynamic Design of Wave Rotors

NASA Astrophysics Data System (ADS)

Okamoto, Koji; Nagashima, Toshio

The precise estimation of pressure waves generated in the passages is a crucial factor in wave rotor design. However, it is difficult to estimate the pressure wave analytically, e.g. by the method of characteristics, because the mechanism of pressure-wave generation and propagation in the passages is extremely complicated as compared to that in a shock tube. In this study, a simple numerical modelling scheme was developed to facilitate the design procedure. This scheme considers the three dominant factors in the loss mechanism —gradual passage opening, wall friction and leakage— for simulating the pressure waves precisely. The numerical scheme itself is based on the one-dimensional Euler equations with appropriate source terms to reduce the calculation time. The modelling of these factors was verified by comparing the results with those of a two-dimensional numerical simulation, which were previously validated by the experimental data in our previous study. Regarding wave rotor miniaturization, the leakage flow effect, which involves the interaction between adjacent cells, was investigated extensively. A port configuration principle was also examined and analyzed in detail to verify the applicability of the present numerical modelling scheme to the wave rotor design.

Analysis of a two-dimensional type 6 shock-interference pattern using a perfect-gas code and a real-gas code

NASA Technical Reports Server (NTRS)

Bertin, J. J.; Graumann, B. W.

1973-01-01

Numerical codes were developed to calculate the two dimensional flow field which results when supersonic flow encounters double wedge configurations whose angles are such that a type 4 pattern occurs. The flow field model included the shock interaction phenomena for a delta wing orbiter. Two numerical codes were developed, one which used the perfect gas relations and a second which incorporated a Mollier table to define equilibrium air properties. The two codes were used to generate theoretical surface pressure and heat transfer distributions for velocities from 3,821 feet per second to an entry condition of 25,000 feet per second.

On the V-Line Radon Transform and Its Imaging Applications

PubMed Central

Morvidone, M.; Nguyen, M. K.; Truong, T. T.; Zaidi, H.

2010-01-01

Radon transforms defined on smooth curves are well known and extensively studied in the literature. In this paper, we consider a Radon transform defined on a discontinuous curve formed by a pair of half-lines forming the vertical letter V. If the classical two-dimensional Radon transform has served as a work horse for tomographic transmission and/or emission imaging, we show that this V-line Radon transform is the backbone of scattered radiation imaging in two dimensions. We establish its analytic inverse formula as well as a corresponding filtered back projection reconstruction procedure. These theoretical results allow the reconstruction of two-dimensional images from Compton scattered radiation collected on a one-dimensional collimated camera. We illustrate the working principles of this imaging modality by presenting numerical simulation results. PMID:20706545

Three dimensional simulation of nucleate boiling heat and mass transfer in cooling passages of internal combustion engines

NASA Astrophysics Data System (ADS)

Mehdipour, R.; Baniamerian, Z.; Delauré, Y.

2016-05-01

An accurate knowledge of heat transfer and temperature distribution in vehicle engines is essential to have a good management of heat transfer performance in combustion engines. This may be achieved by numerical simulation of flow through the engine cooling passages; but the task becomes particularly challenging when boiling occurs. Neglecting two phase flow processes in the simulation would however result in significant inaccuracy in the predictions. In this study a three dimensional numerical model is proposed using Fluent 6.3 to simulate heat transfer of fluid flowing through channels of conventional size. Results of the present theoretical and numerical model are then compared with some empirical results. For high fluid flow velocities, departure between experimental and numerical results is about 9 %, while for lower velocity conditions, the model inaccuracy increases to 18 %. One of the outstanding capabilities of the present model, beside its ability to simulate two phase fluid flow and heat transfer in three dimensions, is the prediction of the location of bubble formation and condensation which can be a key issue in the evaluation of the engine performance and thermal stresses.

Numerical relativity for D dimensional axially symmetric space-times: Formalism and code tests

NASA Astrophysics Data System (ADS)

Zilhão, Miguel; Witek, Helvi; Sperhake, Ulrich; Cardoso, Vitor; Gualtieri, Leonardo; Herdeiro, Carlos; Nerozzi, Andrea

2010-04-01

The numerical evolution of Einstein’s field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modeling black hole production in TeV gravity scenarios, to analysis of the stability of exact solutions, and to tests of cosmic censorship. In order to investigate these questions, we extend numerical relativity to more general space-times than those investigated hitherto, by developing a framework to study the numerical evolution of D dimensional vacuum space-times with an SO(D-2) isometry group for D≥5, or SO(D-3) for D≥6. Performing a dimensional reduction on a (D-4) sphere, the D dimensional vacuum Einstein equations are rewritten as a 3+1 dimensional system with source terms, and presented in the Baumgarte, Shapiro, Shibata, and Nakamura formulation. This allows the use of existing 3+1 dimensional numerical codes with small adaptations. Brill-Lindquist initial data are constructed in D dimensions and a procedure to match them to our 3+1 dimensional evolution equations is given. We have implemented our framework by adapting the Lean code and perform a variety of simulations of nonspinning black hole space-times. Specifically, we present a modified moving puncture gauge, which facilitates long-term stable simulations in D=5. We further demonstrate the internal consistency of the code by studying convergence and comparing numerical versus analytic results in the case of geodesic slicing for D=5, 6.

Numerical model of two-dimensional heterogeneous combustion in porous media under natural convection or forced filtration

NASA Astrophysics Data System (ADS)

Lutsenko, Nickolay A.

2018-03-01

A novel mathematical model and original numerical method for investigating the two-dimensional waves of heterogeneous combustion in porous media are proposed and described in detail. The mathematical model is constructed within the framework of the model of interacting interpenetrating continua and includes equations of state, continuity, momentum conservation and energy for solid and gas phases. Combustion, considered in the paper, is due to the exothermic reaction between fuel in the porous solid medium and oxidiser contained in the gas flowing through the porous object. The original numerical method is based on a combination of explicit and implicit finite-difference schemes. A distinctive feature of the proposed model is that the gas velocity at the open boundaries (inlet and outlet) of the porous object is unknown and has to be found from the solution of the problem, i.e. the flow rate of the gas regulates itself. This approach allows processes to be modelled not only under forced filtration, but also under free convection, when there is no forced gas input in porous objects, which is typical for many natural or anthropogenic disasters (burning of peatlands, coal dumps, landfills, grain elevators). Some two-dimensional time-dependent problems of heterogeneous combustion in porous objects have been solved using the proposed numerical method. It is shown that two-dimensional waves of heterogeneous combustion in porous media can propagate in two modes with different characteristics, as in the case of one-dimensional combustion, but the combustion front can move in a complex manner, and gas dynamics within the porous objects can be complicated. When natural convection takes place, self-sustaining combustion waves can go through the all parts of the object regardless of where an ignition zone was located, so the all combustible material in each part of the object is burned out, in contrast to forced filtration.

Numerical Investigation of Transitional and Turbulent Axisymmetric Wakes at Supersonic Speeds

DTIC Science & Technology

1998-01-21

numerical simu- lations, absolute and global instabilities were found for a two-dimensional bluff body with a blunt base by [ Hannemann & Oertel (1989...geometry", Center for Turbu- lence Research Manuscript 143. [ Hannemann & Oertel (1989)] Hannemann , K. & Oertel, H., Jr., 1989, "Numerical Simulation

Zeldovich pancakes in observational data are cold

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

Brinckmann, Thejs; Lindholmer, Mikkel; Hansen, Steen

The present day universe consists of galaxies, galaxy clusters, one-dimensional filaments and two-dimensional sheets or pancakes, all of which combine to form the cosmic web. The so called ''Zeldovich pancakes' are very difficult to observe, because their overdensity is only slightly greater than the average density of the universe. Falco et al. [1] presented a method to identify Zeldovich pancakes in observational data, and these were used as a tool for estimating the mass of galaxy clusters. Here we expand and refine that observational detection method. We study two pancakes on scales of 10 Mpc, identified from spectroscopically observed galaxiesmore » near the Coma cluster, and compare with twenty numerical pancakes.We find that the observed structures have velocity dispersions of about 100 km/sec, which is relatively low compared to typical groups and filaments. These velocity dispersions are consistent with those found for the numerical pancakes. We also confirm that the identified structures are in fact two-dimensional structures. Finally, we estimate the stellar to total mass of the observational pancakes to be 2 · 10{sup −4}, within one order of magnitude, which is smaller than that of clusters of galaxies.« less

Numerical analysis of flow in ultra micro centrifugal compressor -influence of meridional configuration

NASA Astrophysics Data System (ADS)

Kaneko, Masanao; Tsujita, Hoshio; Hirano, Toshiyuki

2013-04-01

A single stage ultra micro centrifugal compressor constituting ultra micro gas turbine is required to operate at high rotational speed in order to achieve the pressure ratio which establishes the gas turbine cycle. As a consequence, the aerodynamic losses can be increased by the interaction of a shock wave with the boundary layer on the blade surface. Moreover, the centrifugal force which exceeds the allowable stress of the impeller material can act on the root of blades. On the other hand, the restrictions of processing technology for the downsizing of impeller not only relatively enlarge the size of tip clearance but also make it difficult to shape the impeller with the three-dimensional blade. Therefore, it is important to establish the design technology for the impeller with the two-dimensional blade which possesses the sufficient aerodynamic performance and enough strength to bear the centrifugal force caused by the high rotational speed. In this study, the flow in two types of impeller with the two-dimensional blade which have different meridional configuration was analyzed numerically. The computed results clarified the influence of the meridional configuration on the loss generations in the impeller passage.

Duct flow nonuniformities: Effect of struts in SSME HGM II(+)

NASA Technical Reports Server (NTRS)

Burke, Roger

1988-01-01

A numerical study, using the INS3D flow solver, of laminar and turbulent flow around a two dimensional strut, and three dimensional flow around a strut in an annulus is presented. A multi-block procedure was used to calculate two dimensional laminar flow around two struts in parallel, with each strut represented by one computational block. Single block calculations were performed for turbulent flow around a two dimensional strut, using a Baldwin-Lomax turbulence model to parameterize the turbulent shear stresses. A modified Baldwin-Lomax model was applied to the case of a three dimensional strut in an annulus. The results displayed the essential features of wing-body flows, including the presence of a horseshoe vortex system at the junction of the strut and the lower annulus surface. A similar system was observed at the upper annulus surface. The test geometries discussed were useful in developing the capability to perform multiblock calculations, and to simulate turbulent flow around obstructions located between curved walls. Both of these skills will be necessary to model the three dimensional flow in the strut assembly of the SSME. Work is now in progress on performing a three dimensional two block turbulent calculation of the flow in the turnaround duct (TAD) and strut/fuel bowl juncture region.

Chinks in Solar Dynamo Theory: Turbulent Diffusion, Dynamo Waves and Magnetic Helicity

NASA Technical Reports Server (NTRS)

DeLuca, E. E.; Wagner, William J. (Technical Monitor)

2001-01-01

We have investigated the generation of magnetic fields in the Sun using two-dimensional and three-dimensional numerical simulations. The results of our investigations have been presented at scientific meetings and published.

Numerical simulation of the three-dimensional river antidunes

NASA Astrophysics Data System (ADS)

Iwasaki, T.; Inoue, T.; Onda, S.; Yabe, H.

2017-12-01

This study presents numerical simulations of the formation and development of the three-dimensional river antidunes. We use a Boussinesq type depth-integrated hydrodynamic model to account for the non-hydrostatic pressure effects on the flow field, dissipative feature of the free surface and the bed shear stress distribution. In addition, a non-equilibrium bedload transport model is incorporated into the model to consider the lag effect of the bedload transport on the bedform dynamics. The model is applied to idealized laboratory-scale conditions, i.e., steady water and sediment supplies, uniform sediment and a straight channel with constant slope and channel width, to understand the model performance and applicability. The results show that the model is able to reproduce an upstream-migrating antidunes and associated free surface dynamics. The model also captures the formation of the two dimensional and the three-dimensional antidunes. The antidunes reproduced by the model are somewhat unstable, i.e., the repeated cycle of dissipation and regeneration of antidunes is observed. In addition, as the calculation progresses, the modelled three-dimensional antidunes generally tend to lose their three-dimensionality, i.e., the reduction of the spanwise wavenumber. In the early stage of the calculation, the antidune mode is dominant, whereas, the free bars also develop when the formative condition of bars is satisfied. The numerical results show the coexisting of free bars and antidunes, which are a common evident in flume experiments and field observations.

Two-dimensional numerical model for the high electron mobility transistor

NASA Astrophysics Data System (ADS)

Loret, Dany

1987-11-01

A two-dimensional numerical drift-diffusion model for the High Electron Mobility Transistor (HEMT) is presented. Special attention is paid to the modeling of the current flow over the heterojunction. A finite difference scheme is used to solve the equations, and a variable mesh spacing was implemented to cope with the strong variations of functions near the heterojunction. Simulation results are compared to experimental data for a 0.7 μm gate length device. Small-signal transconductances and cut-off frequency obtained from the 2-D model agree well with the experimental values from S-parameter measurements. It is shown that the numerical models give good insight into device behaviour, including important parasitic effects such as electron injection into the bulk GaAs.

Simulation of plasma double-layer structures

NASA Technical Reports Server (NTRS)

Borovsky, J. E.; Joyce, G.

1982-01-01

Electrostatic plasma double layers are numerically simulated by means of a magnetized 2 1/2 dimensional particle in cell method. The investigation of planar double layers indicates that these one dimensional potential structures are susceptible to periodic disruption by instabilities in the low potential plasmas. Only a slight increase in the double layer thickness with an increase in its obliqueness to the magnetic field is observed. Weak magnetization results in the double layer electric field alignment of accelerated particles and strong magnetization results in their magnetic field alignment. The numerical simulations of spatially periodic two dimensional double layers also exhibit cyclical instability. A morphological invariance in two dimensional double layers with respect to the degree of magnetization implies that the potential structures scale with Debye lengths rather than with gyroradii. Electron beam excited electrostatic electron cyclotron waves and (ion beam driven) solitary waves are present in the plasmas adjacent to the double layers.

Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part I: The one-dimensional case

NASA Astrophysics Data System (ADS)

Vilar, François; Shu, Chi-Wang; Maire, Pierre-Henri

2016-05-01

One of the main issues in the field of numerical schemes is to ally robustness with accuracy. Considering gas dynamics, numerical approximations may generate negative density or pressure, which may lead to nonlinear instability and crash of the code. This phenomenon is even more critical using a Lagrangian formalism, the grid moving and being deformed during the calculation. Furthermore, most of the problems studied in this framework contain very intense rarefaction and shock waves. In this paper, the admissibility of numerical solutions obtained by high-order finite-volume-scheme-based methods, such as the discontinuous Galerkin (DG) method, the essentially non-oscillatory (ENO) and the weighted ENO (WENO) finite volume schemes, is addressed in the one-dimensional Lagrangian gas dynamics framework. After briefly recalling how to derive Lagrangian forms of the 1D gas dynamics system of equations, a discussion on positivity-preserving approximate Riemann solvers, ensuring first-order finite volume schemes to be positive, is then given. This study is conducted for both ideal gas and non-ideal gas equations of state (EOS), such as the Jones-Wilkins-Lee (JWL) EOS or the Mie-Grüneisen (MG) EOS, and relies on two different techniques: either a particular definition of the local approximation of the acoustic impedances arising from the approximate Riemann solver, or an additional time step constraint relative to the cell volume variation. Then, making use of the work presented in [89,90,22], this positivity study is extended to high-orders of accuracy, where new time step constraints are obtained, and proper limitation is required. Through this new procedure, scheme robustness is highly improved and hence new problems can be tackled. Numerical results are provided to demonstrate the effectiveness of these methods. This paper is the first part of a series of two. The whole analysis presented here is extended to the two-dimensional case in [85], and proves to fit a wide range of numerical schemes in the literature, such as those presented in [19,64,15,82,84].

Two-Dimensional Motions of Rockets

ERIC Educational Resources Information Center

Kang, Yoonhwan; Bae, Saebyok

2007-01-01

We analyse the two-dimensional motions of the rockets for various types of rocket thrusts, the air friction and the gravitation by using a suitable representation of the rocket equation and the numerical calculation. The slope shapes of the rocket trajectories are discussed for the three types of rocket engines. Unlike the projectile motions, the…

Nonlinear cascades in two-dimensional turbulent magnetoconvection.

PubMed

Skandera, Dan; Müller, Wolf-Christian

2009-06-05

The dynamics of spectral transport in two-dimensional turbulent convection of electrically conducting fluids is studied by means of direct numerical simulations in the frame of the magnetohydrodynamic Boussinesq approximation. The system performs quasioscillations between two different regimes of small-scale turbulence: one dominated by nonlinear magnetohydrodynamic interactions; the other governed by buoyancy forces. The self-excited change of turbulent states is reported here for the first time. The process is controlled by the ideal invariant cross helicity, H;{C}=integral_{S}dSv.b. The observations are explained by the interplay of convective driving with the nonlinear spectral transfer of total magnetohydrodynamic energy and cross helicity.

Cancellation exponent and multifractal structure in two-dimensional magnetohydrodynamics: direct numerical simulations and Lagrangian averaged modeling.

PubMed

Graham, Jonathan Pietarila; Mininni, Pablo D; Pouquet, Annick

2005-10-01

We present direct numerical simulations and Lagrangian averaged (also known as alpha model) simulations of forced and free decaying magnetohydrodynamic turbulence in two dimensions. The statistics of sign cancellations of the current at small scales is studied using both the cancellation exponent and the fractal dimension of the structures. The alpha model is found to have the same scaling behavior between positive and negative contributions as the direct numerical simulations. The alpha model is also able to reproduce the time evolution of these quantities in free decaying turbulence. At large Reynolds numbers, an independence of the cancellation exponent with the Reynolds numbers is observed.

Multiple scattering in the high-frequency limit with second-order shadowing function from 2D anisotropic rough dielectric surfaces: I. Theoretical study

NASA Astrophysics Data System (ADS)

Bourlier, C.; Berginc, G.

2004-07-01

In this paper the first- and second-order Kirchhoff approximation is applied to study the backscattering enhancement phenomenon, which appears when the surface rms slope is greater than 0.5. The formulation is reduced to the geometric optics approximation in which the second-order illumination function is taken into account. This study is developed for a two-dimensional (2D) anisotropic stationary rough dielectric surface and for any surface slope and height distributions assumed to be statistically even. Using the Weyl representation of the Green function (which introduces an absolute value over the surface elevation in the phase term), the incoherent scattering coefficient under the stationary phase assumption is expressed as the sum of three terms. The incoherent scattering coefficient then requires the numerical computation of a ten- dimensional integral. To reduce the number of numerical integrations, the geometric optics approximation is applied, which assumes that the correlation between two adjacent points is very strong. The model is then proportional to two surface slope probabilities, for which the slopes would specularly reflect the beams in the double scattering process. In addition, the slope distributions are related with each other by a propagating function, which accounts for the second-order illumination function. The companion paper is devoted to the simulation of this model and comparisons with an 'exact' numerical method.

Numerical Schemes and Computational Studies for Dynamically Orthogonal Equations (Multidisciplinary Simulation, Estimation, and Assimilation Systems: Reports in Ocean Science and Engineering)

DTIC Science & Technology

2011-08-01

heat transfers [49, 52]. However, the DO method has not yet been applied to Boussinesq flows, and the numerical challenges of the DO decomposition for...used a PCE scheme to study mixing in a two-dimensional (2D) microchannel and improved the efficiency of their solution scheme by decoupling the...to several Navier-Stokes flows and their stochastic dynamics has been studied, including mean-mode and mode-mode energy transfers for 2D flows and

Comprehensive Numerical Analysis of Finite Difference Time Domain Methods for Improving Optical Waveguide Sensor Accuracy

PubMed Central

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.

Insights from depth-averaged numerical simulation of flow at bridge abutments in compound channels.

DOT National Transportation Integrated Search

2011-07-01

Two-dimensional, depth-averaged flow models are used to study the distribution of flow around spill-through abutments situated on floodplains in compound channels and rectangular channels (flow on very wide floodplains may be treated as rectangular c...

Determination of the Fracture Parameters in a Stiffened Composite Panel

NASA Technical Reports Server (NTRS)

Lin, Chung-Yi

2000-01-01

A modified J-integral, namely the equivalent domain integral, is derived for a three-dimensional anisotropic cracked solid to evaluate the stress intensity factor along the crack front using the finite element method. Based on the equivalent domain integral method with auxiliary fields, an interaction integral is also derived to extract the second fracture parameter, the T-stress, from the finite element results. The auxiliary fields are the two-dimensional plane strain solutions of monoclinic materials with the plane of symmetry at x(sub 3) = 0 under point loads applied at the crack tip. These solutions are expressed in a compact form based on the Stroh formalism. Both integrals can be implemented into a single numerical procedure to determine the distributions of stress intensity factor and T-stress components, T11, T13, and thus T33, along a three-dimensional crack front. The effects of plate thickness and crack length on the variation of the stress intensity factor and T-stresses through the thickness are investigated in detail for through-thickness center-cracked plates (isotropic and orthotropic) and orthotropic stiffened panels under pure mode-I loading conditions. For all the cases studied, T11 remains negative. For plates with the same dimensions, a larger size of crack yields larger magnitude of the normalized stress intensity factor and normalized T-stresses. The results in orthotropic stiffened panels exhibit an opposite trend in general. As expected, for the thicker panels, the fracture parameters evaluated through the thickness, except the region near the free surfaces, approach two-dimensional plane strain solutions. In summary, the numerical methods presented in this research demonstrate their high computational effectiveness and good numerical accuracy in extracting these fracture parameters from the finite element results in three-dimensional cracked solids.

Solitary solutions including spatially localized chaos and their interactions in two-dimensional Kolmogorov flow.

PubMed

Hiruta, Yoshiki; Toh, Sadayoshi

2015-12-01

Two-dimensional Kolmogorov flow in wide periodic boxes is numerically investigated. It is shown that the total flow rate in the direction perpendicular to the force controls the characteristics of the flow, especially the existence of spatially localized solitary solutions such as traveling waves, periodic solutions, and chaotic solutions, which can behave as elementary components of the flow. We propose a procedure to construct approximate solutions consisting of solitary solutions. It is confirmed by direct numerical simulations that these solutions are stable and represent interactions between elementary components such as collisions, coexistence, and collapse of chaos.

Collisionless Boltzmann equation approach for the study of stellar discs within barred galaxies

NASA Astrophysics Data System (ADS)

Bienaymé, Olivier

2018-04-01

We have studied the kinematics of stellar disc populations within the solar neighbourhood in order to find the imprints of the Galactic bar. We carried out the analysis by developing a numerical resolution of the 2D2V (two-dimensional in the physical space, 2D, and two-dimensional in the velocity motion, 2V) collisionless Boltzmann equation and modelling the stellar motions within the plane of the Galaxy within the solar neighbourhood. We recover similar results to those obtained by other authors using N-body simulations, but we are also able to numerically identify faint structures thanks to the cancelling of the Poisson noise. We find that the ratio of the bar pattern speed to the local circular frequency is in the range ΩB/Ω = 1.77 to 1.91. If the Galactic bar angle orientation is within the range from 24 to 45 degrees, the bar pattern speed is between 46 and 49 km s-1 kpc-1.

Simulation of two-dimensional turbulent flows in a rotating annulus

NASA Astrophysics Data System (ADS)

Storey, Brian D.

2004-05-01

Rotating water tank experiments have been used to study fundamental processes of atmospheric and geophysical turbulence in a controlled laboratory setting. When these tanks are undergoing strong rotation the forced turbulent flow becomes highly two dimensional along the axis of rotation. An efficient numerical method has been developed for simulating the forced quasi-geostrophic equations in an annular geometry to model current laboratory experiments. The algorithm employs a spectral method with Fourier series and Chebyshev polynomials as basis functions. The algorithm has been implemented on a parallel architecture to allow modelling of a wide range of spatial scales over long integration times. This paper describes the derivation of the model equations, numerical method, testing and performance of the algorithm. Results provide reasonable agreement with the experimental data, indicating that such computations can be used as a predictive tool to design future experiments.

Temperature distributions and thermal stresses in a graded zirconia/metal gas path seal system for aircraft gas turbine engines

NASA Technical Reports Server (NTRS)

Taylor, C. M.; Bill, R. C.

1978-01-01

A ceramic/metallic aircraft gas turbine outer gas path seal designed for improved engine performance was studied. Transient temperature and stress profiles in a test seal geometry were determined by numerical analysis. During a simulated engine deceleration cycle from sea-level takeoff to idle conditions, the maximum seal temperature occurred below the seal surface, therefore the top layer of the seal was probably subjected to tensile stresses exceeding the modulus of rupture. In the stress analysis both two- and three-dimensional finite element computer programs were used. Predicted trends of the simpler and more easily usable two-dimensional element programs were borne out by the three-dimensional finite element program results.

Multistability in bidirectional associative memory neural networks

NASA Astrophysics Data System (ADS)

Huang, Gan; Cao, Jinde

2008-04-01

In this Letter, the multistability issue is studied for Bidirectional Associative Memory (BAM) neural networks. Based on the existence and stability analysis of the neural networks with or without delay, it is found that the 2 n-dimensional networks can have 3 equilibria and 2 equilibria of them are locally exponentially stable, where each layer of the BAM network has n neurons. Furthermore, the results has been extended to (n+m)-dimensional BAM neural networks, where there are n and m neurons on the two layers respectively. Finally, two numerical examples are presented to illustrate the validity of our results.

Two-dimensional simulations of stimulated Brillouin scattering in laser produced plasmas

NASA Astrophysics Data System (ADS)

Amin, M. R.; Capjack, C. E.; Frycz, P.; Rozmus, W.; Tikhonchuk, V. T.

1993-07-01

A system of electromagnetic and ion acoustic wave equations coupled via the ponderomotive force are solved numerically in a two-dimensional planar geometry. The competition between forward, side, and backward Brillouin scattering of the finite size laser beam is studied for the first time without the standard paraxial optics approximation. Simulations reveal a strong dependence of the scattered light characteristics on the geometry of the interaction region, the shape of the pump beam, and the ion acoustic wave damping. The main effects include side and forward scattering enhancement and a stimulation of collimated backward scattered radiation.

Casimir interaction of rodlike particles in a two-dimensional critical system.

PubMed

Eisenriegler, E; Burkhardt, T W

2016-09-01

We consider the fluctuation-induced interaction of two thin, rodlike particles, or "needles," immersed in a two-dimensional critical fluid of Ising symmetry right at the critical point. Conformally mapping the plane containing the needles onto a simpler geometry in which the stress tensor is known, we analyze the force and torque between needles of arbitrary length, separation, and orientation. For infinite and semi-infinite needles we utilize the mapping of the plane bounded by the needles onto the half plane, and for two needles of finite length we use the mapping onto an annulus. For semi-infinite and infinite needles the force is expressed in terms of elementary functions, and we also obtain analytical results for the force and torque between needles of finite length with separation much greater than their length. Evaluating formulas in our approach numerically for several needle geometries and surface universality classes, we study the full crossover from small to large values of the separation to length ratio. In these two limits the numerical results agree with results for infinitely long needles and with predictions of the small-particle operator expansion, respectively.

Three-Dimensional Numerical Simulation to Mud Turbine for LWD

NASA Astrophysics Data System (ADS)

Yao, Xiaojiang; Dong, Jingxin; Shang, Jie; Zhang, Guanqi

Hydraulic performance analysis was discussed for a type of turbine on generator used for LWD. The simulation models were built by CFD analysis software FINE/Turbo, and full three-dimensional numerical simulation was carried out for impeller group. The hydraulic parameter such as power, speed and pressure drop, were calculated in two kinds of medium water and mud. Experiment was built in water environment. The error of numerical simulation was less than 6%, verified by experiment. Based on this rationalization proposals would be given to choice appropriate impellers, and the rationalization of methods would be explored.

Analytical approximation and numerical simulations for periodic travelling water waves

NASA Astrophysics Data System (ADS)

Kalimeris, Konstantinos

2017-12-01

We present recent analytical and numerical results for two-dimensional periodic travelling water waves with constant vorticity. The analytical approach is based on novel asymptotic expansions. We obtain numerical results in two different ways: the first is based on the solution of a constrained optimization problem, and the second is realized as a numerical continuation algorithm. Both methods are applied on some examples of non-constant vorticity. This article is part of the theme issue 'Nonlinear water waves'.

A Two-Dimensional Numerical Investigation of Transport of Malaria-Infected Red Blood Cells in Stenotic Microchannels

PubMed Central

Tao, Yong; Rongin, Uwitije; Xing, Zhongwen

2016-01-01

The malaria-infected red blood cells experience a significant decrease in cell deformability and increase in cell membrane adhesion. Blood hemodynamics in microvessels is significantly affected by the alteration of the mechanical property as well as the aggregation of parasitized red blood cells. In this study, we aim to numerically study the connection between cell-level mechanobiological properties of human red blood cells and related malaria disease state by investigating the transport of multiple red blood cell aggregates passing through microchannels with symmetric stenosis. Effects of stenosis magnitude, aggregation strength, and cell deformability on cell rheology and flow characteristics were studied by a two-dimensional model using the fictitious domain-immersed boundary method. The results indicated that the motion and dissociation of red blood cell aggregates were influenced by these factors and the flow resistance increases with the increase of aggregating strength and cell stiffness. Further, the roughness of the velocity profile was enhanced by cell aggregation, which considerably affected the blood flow characteristics. The study may assist us in understanding cellular-level mechanisms in disease development. PMID:28105411

Low-dimensional chaos in turbulence

NASA Technical Reports Server (NTRS)

Vastano, John A.

1989-01-01

Direct numerical simulations are being performed on two different fluid flows in an attempt to discover the mechanism underlying the transition to turbulence in each. The first system is Taylor-Couette flow; the second, two-dimensional flow over an airfoil. Both flows exhibit a gradual transition to high-dimensional turbulence through low-dimensional chaos. The hope is that the instabilities leading to chaos will be easier to relate to physical processes in this case, and that the understanding of these mechanisms can then be applied to a wider array of turbulent systems.

Applications of an exponential finite difference technique

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

Handschuh, R.F.; Keith, T.G. Jr.

1988-07-01

An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.

A comparison of etched-geometry and overgrown silicon permeable base transistors by two-dimensional numerical simulations

NASA Astrophysics Data System (ADS)

Vojak, B. A.; Alley, G. D.

1983-08-01

Two-dimensional numerical simulations are used to compare etched geometry and overgrown Si permeable base transistors (PTBs), considering both the etched collector and etched emitter biasing conditions made possible by the asymmetry of the etched structure. In PTB devices, the two-dimensional nature of the depletion region near the Schottky contact base grating results in a smaller electron barrier and, therefore, a larger collector current in the etched than in the overgrown structure. The parasitic feedback effects which result at high base-to-emitter bias levels lead to a deviation from the square-law behavior found in the collector characteristics of the overgrown PBT. These structures also have lower device capacitances and smaller transconductances at high base-to-emitter voltages. As a result, overgrown and etched structures have comparable predicted maximum values of the small signal unity short-circuit current gain frequency and maximum oscillation frequency.

Nature of self-diffusion in two-dimensional fluids

NASA Astrophysics Data System (ADS)

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; Talkner, Peter; Kidera, Akinori; Lee, Eok Kyun

2017-12-01

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. We numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(t\\sqrt{{ln}t}), however with a rescaled time.

Forces in inhomogeneous open active-particle systems.

PubMed

Razin, Nitzan; Voituriez, Raphael; Elgeti, Jens; Gov, Nir S

2017-11-01

We study the force that noninteracting pointlike active particles apply to a symmetric inert object in the presence of a gradient of activity and particle sources and sinks. We consider two simple patterns of sources and sinks that are common in biological systems. We analytically solve a one-dimensional model designed to emulate higher-dimensional systems, and study a two-dimensional model by numerical simulations. We specify when the particle flux due to the creation and annihilation of particles can act to smooth the density profile that is induced by a gradient in the velocity of the active particles, and find the net resultant force due to both the gradient in activity and the particle flux. These results are compared qualitatively to observations of nuclear motion inside the oocyte, that is driven by a gradient in activity of actin-coated vesicles.

Scaling relations for watersheds

NASA Astrophysics Data System (ADS)

Fehr, E.; Kadau, D.; Araújo, N. A. M.; Andrade, J. S., Jr.; Herrmann, H. J.

2011-09-01

We study the morphology of watersheds in two and three dimensional systems subjected to different degrees of spatial correlations. The response of these objects to small, local perturbations is also investigated with extensive numerical simulations. We find the fractal dimension of the watersheds to generally decrease with the Hurst exponent, which quantifies the degree of spatial correlations. Moreover, in two dimensions, our results match the range of fractal dimensions 1.10≤df≤1.15 observed for natural landscapes. We report that the watershed is strongly affected by local perturbations. For perturbed two and three dimensional systems, we observe a power-law scaling behavior for the distribution of areas (volumes) enclosed by the original and the displaced watershed and for the distribution of distances between outlets. Finite-size effects are analyzed and the resulting scaling exponents are shown to depend significantly on the Hurst exponent. The intrinsic relation between watershed and invasion percolation, as well as relations between exponents conjectured in previous studies with two dimensional systems, are now confirmed by our results in three dimensions.

Advantages of multigrid methods for certifying the accuracy of PDE modeling

NASA Technical Reports Server (NTRS)

Forester, C. K.

1981-01-01

Numerical techniques for assessing and certifying the accuracy of the modeling of partial differential equations (PDE) to the user's specifications are analyzed. Examples of the certification process with conventional techniques are summarized for the three dimensional steady state full potential and the two dimensional steady Navier-Stokes equations using fixed grid methods (FG). The advantages of the Full Approximation Storage (FAS) scheme of the multigrid technique of A. Brandt compared with the conventional certification process of modeling PDE are illustrated in one dimension with the transformed potential equation. Inferences are drawn for how MG will improve the certification process of the numerical modeling of two and three dimensional PDE systems. Elements of the error assessment process that are common to FG and MG are analyzed.

Flow transition with 2-D roughness elements in a 3-D channel

NASA Technical Reports Server (NTRS)

Liu, Zhining; Liu, Chaoquin; Mccormick, Stephen F.

1993-01-01

We develop a new numerical approach to study the spatially evolving instability of the streamwise dominant flow in the presence of roughness elements. The difficulty in handling the flow over the boundary surface with general geometry is removed by using a new conservative form of the governing equations and an analytical mapping. The numerical scheme uses second-order backward Euler in time, fourth-order central differences in all three spatial directions, and boundary-fitted staggered grids. A three-dimensional channel with multiple two-dimensional-type roughness elements is employed as the test case. Fourier analysis is used to decompose different Fourier modes of the disturbance. The results show that surface roughness leads to transition at lower Reynolds number than for smooth channels.

Direct numerical simulations of three-dimensional electrokinetic flows

NASA Astrophysics Data System (ADS)

Chiam, Keng-Hwee

2006-11-01

We discuss direct numerical simulations of three-dimensional electrokinetic flows in microfluidic devices. In particular, we focus on the study of the electrokinetic instability that develops when two solutions with different electrical conductivities are coupled to an external electric field. We characterize this ``mixing'' instability as a function of the parameters of the model, namely the Reynolds number of the flow, the electric Peclet number of the electrolyte solution, and the ratio of the electroosmotic to the electroviscous time scales. Finally, we describe how this model breaks down when the length scale of the device approaches the nanoscale, where the width of the electric Debye layer is comparable to the width of the channel, and discuss solutions to overcome this.

Two-Dimensional Grids About Airfoils and Other Shapes

NASA Technical Reports Server (NTRS)

Sorenson, R.

1982-01-01

GRAPE computer program generates two-dimensional finite-difference grids about airfoils and other shapes by use of Poisson differential equation. GRAPE can be used with any boundary shape, even one specified by tabulated points and including limited number of sharp corners. Numerically stable and computationally fast, GRAPE provides aerodynamic analyst with efficient and consistant means of grid generation.

Surface representations of two- and three-dimensional fluid flow topology

NASA Technical Reports Server (NTRS)

Helman, James L.; Hesselink, Lambertus

1990-01-01

We discuss our work using critical point analysis to generate representations of the vector field topology of numerical flow data sets. Critical points are located and characterized in a two-dimensional domain, which may be either a two-dimensional flow field or the tangential velocity field near a three-dimensional body. Tangent curves are then integrated out along the principal directions of certain classes of critical points. The points and curves are linked to form a skeleton representing the two-dimensional vector field topology. When generated from the tangential velocity field near a body in a three-dimensional flow, the skeleton includes the critical points and curves which provide a basis for analyzing the three-dimensional structure of the flow separation. The points along the separation curves in the skeleton are used to start tangent curve integrations to generate surfaces representing the topology of the associated flow separations.

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Adamian, A.

1988-01-01

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

Numerical analysis of real gas MHD flow on two-dimensional self-field MPD thrusters

NASA Astrophysics Data System (ADS)

Xisto, Carlos M.; Páscoa, José C.; Oliveira, Paulo J.

2015-07-01

A self-field magnetoplasmadynamic (MPD) thruster is a low-thrust electric propulsion space-system that enables the usage of magnetohydrodynamic (MHD) principles for accelerating a plasma flow towards high speed exhaust velocities. It can produce an high specific impulse, making it suitable for long duration interplanetary space missions. In this paper numerical results obtained with a new code, which is being developed at C-MAST (Centre for Mechanical and Aerospace Technologies), for a two-dimensional self-field MPD thruster are presented. The numerical model is based on the macroscopic MHD equations for compressible and electrically resistive flow and is able to predict the two most important thrust mechanisms that are associated with this kind of propulsion system, namely the thermal thrust and the electromagnetic thrust. Moreover, due to the range of very high temperatures that could occur during the operation of the MPD, it also includes a real gas model for argon.

Numerical modeling of consolidation processes in hydraulically deposited soils

NASA Astrophysics Data System (ADS)

Brink, Nicholas Robert

Hydraulically deposited soils are encountered in many common engineering applications including mine tailing and geotextile tube fills, though the consolidation process for such soils is highly nonlinear and requires the use of advanced numerical techniques to provide accurate predictions. Several commercially available finite element codes poses the ability to model soil consolidation, and it was the goal of this research to assess the ability of two of these codes, ABAQUS and PLAXIS, to model the large-strain, two-dimensional consolidation processes which occur in hydraulically deposited soils. A series of one- and two-dimensionally drained rectangular models were first created to assess the limitations of ABAQUS and PLAXIS when modeling consolidation of highly compressible soils. Then, geotextile tube and TSF models were created to represent actual scenarios which might be encountered in engineering practice. Several limitations were discovered, including the existence of a minimum preconsolidation stress below which numerical solutions become unstable.

Stripe order in the underdoped region of the two-dimensional Hubbard model

NASA Astrophysics Data System (ADS)

Zheng, Bo-Xiao; Chung, Chia-Min; Corboz, Philippe; Ehlers, Georg; Qin, Ming-Pu; Noack, Reinhard M.; Shi, Hao; White, Steven R.; Zhang, Shiwei; Chan, Garnet Kin-Lic

2017-12-01

Competing inhomogeneous orders are a central feature of correlated electron materials, including the high-temperature superconductors. The two-dimensional Hubbard model serves as the canonical microscopic physical model for such systems. Multiple orders have been proposed in the underdoped part of the phase diagram, which corresponds to a regime of maximum numerical difficulty. By combining the latest numerical methods in exhaustive simulations, we uncover the ordering in the underdoped ground state. We find a stripe order that has a highly compressible wavelength on an energy scale of a few kelvin, with wavelength fluctuations coupled to pairing order. The favored filled stripe order is different from that seen in real materials. Our results demonstrate the power of modern numerical methods to solve microscopic models, even in challenging settings.

Analytical Approach to (2+1)-Dimensional Boussinesq Equation and (3+1)-Dimensional Kadomtsev-Petviashvili Equation

NASA Astrophysics Data System (ADS)

Sarıaydın, Selin; Yıldırım, Ahmet

2010-05-01

In this paper, we studied the solitary wave solutions of the (2+1)-dimensional Boussinesq equation utt -uxx-uyy-(u2)xx-uxxxx = 0 and the (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation uxt -6ux 2 +6uuxx -uxxxx -uyy -uzz = 0. By using this method, an explicit numerical solution is calculated in the form of a convergent power series with easily computable components. To illustrate the application of this method numerical results are derived by using the calculated components of the homotopy perturbation series. The numerical solutions are compared with the known analytical solutions. Results derived from our method are shown graphically.

Numerical abilities in fish: A methodological review.

PubMed

Agrillo, Christian; Miletto Petrazzini, Maria Elena; Bisazza, Angelo

2017-08-01

The ability to utilize numerical information can be adaptive in a number of ecological contexts including foraging, mating, parental care, and anti-predator strategies. Numerical abilities of mammals and birds have been studied both in natural conditions and in controlled laboratory conditions using a variety of approaches. During the last decade this ability was also investigated in some fish species. Here we reviewed the main methods used to study this group, highlighting the strengths and weaknesses of each of the methods used. Fish have only been studied under laboratory conditions and among the methods used with other species, only two have been systematically used in fish-spontaneous choice tests and discrimination learning procedures. In the former case, the choice between two options is observed in a biologically relevant situation and the degree of preference for the larger/smaller group is taken as a measure of the capacity to discriminate the two quantities (e.g., two shoals differing in number). In discrimination learning tasks, fish are trained to select the larger or the smaller of two sets of abstract objects, typically two-dimensional geometric figures, using food or social companions as reward. Beyond methodological differences, what emerges from the literature is a substantial similarity of the numerical abilities of fish with those of other vertebrates studied. Copyright © 2017 Elsevier B.V. All rights reserved.

Two-dimensional numerical study of two counter-propagating helium plasma jets in air at atmospheric pressure

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

Yan, Wen; Sang, Chaofeng; Wang, Dezhen, E-mail: wangdez@dlut.edu.cn

In this paper, a computational study of two counter-propagating helium plasma jets in ambient air is presented. A two-dimensional fluid model is applied to investigate the physical processes of the two plasma jets interaction (PJI) driven by equal and unequal voltages, respectively. In all studied cases, the PJI results in a decrease of both plasma bullets propagation velocity. When the two plasma jets are driven by equal voltages, they never merge but rather approach each other around the middle of the gas gap at a minimum approach distance, and the minimal distance decreases with the increase of both the appliedmore » voltages and initial electron density, but increases with the increase of the relative permittivity. When the two plasma jets are driven by unequal voltages, we observe the two plasma jets will merge at the position away from the middle of the gas gap. The effect of applied voltage difference on the PJI is also studied.« less

Wave-induced response of a floating two-dimensional body with a moonpool

PubMed Central

Fredriksen, Arnt G.; Kristiansen, Trygve; Faltinsen, Odd M.

2015-01-01

Regular wave-induced behaviour of a floating stationary two-dimensional body with a moonpool is studied. The focus is on resonant piston-mode motion in the moonpool and rigid-body motions. Dedicated two-dimensional experiments have been performed. Two numerical hybrid methods, which have previously been applied to related problems, are further developed. Both numerical methods couple potential and viscous flow. The semi-nonlinear hybrid method uses linear free-surface and body-boundary conditions. The other one uses fully nonlinear free-surface and body-boundary conditions. The harmonic polynomial cell method solves the Laplace equation in the potential flow domain, while the finite volume method solves the Navier–Stokes equations in the viscous flow domain near the body. Results from the two codes are compared with the experimental data. The nonlinear hybrid method compares well with the data, while certain discrepancies are observed for the semi-nonlinear method. In particular, the roll motion is over-predicted by the semi-nonlinear hybrid method. Error sources in the semi-nonlinear hybrid method are discussed. The moonpool strongly affects heave motions in a frequency range around the piston-mode resonance frequency of the moonpool. No resonant water motions occur in the moonpool at the piston-mode resonance frequency. Instead large moonpool motions occur at a heave natural frequency associated with small damping near the piston-mode resonance frequency. PMID:25512594

Two-dimensional thermal modeling of power monolithic microwave integrated circuits (MMIC's)

NASA Technical Reports Server (NTRS)

Fan, Mark S.; Christou, Aris; Pecht, Michael G.

1992-01-01

Numerical simulations of the two-dimensional temperature distributions for a typical GaAs MMIC circuit are conducted, aiming at understanding the heat conduction process of the circuit chip and providing temperature information for device reliability analysis. The method used is to solve the two-dimensional heat conduction equation with a control-volume-based finite difference scheme. In particular, the effects of the power dissipation and the ambient temperature are examined, and the criterion for the worst operating environment is discussed in terms of the allowed highest device junction temperature.

Flow of rarefied gases over two-dimensional bodies

NASA Technical Reports Server (NTRS)

Jeng, Duen-Ren; De Witt, Kenneth J.; Keith, Theo G., Jr.; Chung, Chan-Hong

1989-01-01

A kinetic-theory analysis is made of the flow of rarefied gases over two-dimensional bodies of arbitrary curvature. The Boltzmann equation simplified by a model collision integral is written in an arbitrary orthogonal curvilinear coordinate system, and solved by means of finite-difference approximation with the discrete ordinate method. A numerical code is developed which can be applied to any two-dimensional submerged body of arbitrary curvature for the flow regimes from free-molecular to slip at transonic Mach numbers. Predictions are made for the case of a right circular cylinder.

Particle Interactions Mediated by Dynamical Networks: Assessment of Macroscopic Descriptions

NASA Astrophysics Data System (ADS)

Barré, J.; Carrillo, J. A.; Degond, P.; Peurichard, D.; Zatorska, E.

2018-02-01

We provide a numerical study of the macroscopic model of Barré et al. (Multiscale Model Simul, 2017, to appear) derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodeling process is very fast, the macroscopic model takes the form of a single aggregation-diffusion equation for the density of particles. The theoretical study of the macroscopic model gives precise criteria for the phase transitions of the steady states, and in the one-dimensional case, we show numerically that the stationary solutions of the microscopic model undergo the same phase transitions and bifurcation types as the macroscopic model. In the two-dimensional case, we show that the numerical simulations of the macroscopic model are in excellent agreement with the predicted theoretical values. This study provides a partial validation of the formal derivation of the macroscopic model from a microscopic formulation and shows that the former is a consistent approximation of an underlying particle dynamics, making it a powerful tool for the modeling of dynamical networks at a large scale.

Particle Interactions Mediated by Dynamical Networks: Assessment of Macroscopic Descriptions.

PubMed

Barré, J; Carrillo, J A; Degond, P; Peurichard, D; Zatorska, E

2018-01-01

We provide a numerical study of the macroscopic model of Barré et al. (Multiscale Model Simul, 2017, to appear) derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodeling process is very fast, the macroscopic model takes the form of a single aggregation-diffusion equation for the density of particles. The theoretical study of the macroscopic model gives precise criteria for the phase transitions of the steady states, and in the one-dimensional case, we show numerically that the stationary solutions of the microscopic model undergo the same phase transitions and bifurcation types as the macroscopic model. In the two-dimensional case, we show that the numerical simulations of the macroscopic model are in excellent agreement with the predicted theoretical values. This study provides a partial validation of the formal derivation of the macroscopic model from a microscopic formulation and shows that the former is a consistent approximation of an underlying particle dynamics, making it a powerful tool for the modeling of dynamical networks at a large scale.

The two-stroke poppet valve engine. Part 2: Numerical investigations of intake and exhaust flow behaviour

NASA Astrophysics Data System (ADS)

Kamili Zahidi, M.; Razali Hanipah, M.

2017-10-01

A two-stroke poppet valve engine is developed to overcome the common problems in conventional two-stroke engine designs. However, replacing piston control port with poppet valve will resulted different flow behaviour. This paper presents the model and simulation result of three-dimensional (3D) port flow investigation of a two-stroke poppet valve engine. The objective of the investigation is to conduct a numerical investigation on port flow performance of two-stroke poppet valve engine and compare the results obtained from the experimental investigation. The model is to be used for the future numerical study of the engine. The volume flow rate results have been compared with the results obtained experimentally as presented in first part of this paper. The model has shown good agreement in terms of the flow rate at initial and final valve lifts but reduced by about 50% during half-lift region.

Numerical methods for multi-scale modeling of non-Newtonian flows

NASA Astrophysics Data System (ADS)

Symeonidis, Vasileios

This work presents numerical methods for the simulation of Non-Newtonian fluids in the continuum as well as the mesoscopic level. The former is achieved with Direct Numerical Simulation (DNS) spectral h/p methods, while the latter employs the Dissipative Particle Dynamics (DPD) technique. Physical results are also presented as a motivation for a clear understanding of the underlying numerical approaches. The macroscopic simulations employ two non-Newtonian models, namely the Reiner-Ravlin (RR) and the viscoelastic FENE-P model. (1) A spectral viscosity method defined by two parameters ε, M is used to stabilize the FENE-P conformation tensor c. Convergence studies are presented for different combinations of these parameters. Two boundary conditions for the tensor c are also investigated. (2) Agreement is achieved with other works for Stokes flow of a two-dimensional cylinder in a channel. Comparison of the axial normal stress and drag coefficient on the cylinder is presented. Further, similar results from unsteady two- and three-dimensional turbulent flows past a flat plate in a channel are shown. (3) The RR problem is formulated for nearly incompressible flows, with the introduction of a mathematically equivalent tensor formulation. A spectral viscosity method and polynomial over-integration are studied. Convergence studies, including a three-dimensional channel flow with a parallel slot, investigate numerical problems arising from elemental boundaries and sharp corners. (4) The round hole pressure problem is presented for Newtonian and RR fluids in geometries with different hole sizes. Comparison with experimental data is made for the Newtonian case. The flaw in the experimental assumptions of undisturbed pressure opposite the hole is revealed, while good agreement with the data is shown. The Higashitani-Pritchard kinematical theory for RR, fluids is recovered for round holes and an approximate formula for the RR Stokes hole pressure is presented. The mesoscopic simulations assume bead-spring representations of polymer chains and investigate different integrating schemes of the DPD equations and different intra-polymer force combinations. (1) A novel family of time-staggered integrators is presented, taking advantage of the time-scale disparity between polymer-solvent and solvent-solvent interactions. Convergence tests for relaxation parameters for the velocity-Verlet and Lowe's schemes are presented. (2) Wormlike chains simulating lambda- DNA molecules subject to constant shear are studied, and direct comparison with Brownian Dynamics and experimental results is made. The effect of the number of beads per chain is examined through the extension autocorrelation function. (3) The Schmidt number (Sc) for each numerical scheme is investigated and the dependence on the scheme's parameters is shown. Re-visiting the wormlike chain problem under shear, we recover a better agreement with the experimental data through proper adjustment of Sc.

Parallel 3-D numerical simulation of dielectric barrier discharge plasma actuators

NASA Astrophysics Data System (ADS)

Houba, Tomas

Dielectric barrier discharge plasma actuators have shown promise in a range of applications including flow control, sterilization and ozone generation. Developing numerical models of plasma actuators is of great importance, because a high-fidelity parallel numerical model allows new design configurations to be tested rapidly. Additionally, it provides a better understanding of the plasma actuator physics which is useful for further innovation. The physics of plasma actuators is studied numerically. A loosely coupled approach is utilized for the coupling of the plasma to the neutral fluid. The state of the art in numerical plasma modeling is advanced by the development of a parallel, three-dimensional, first-principles model with detailed air chemistry. The model incorporates 7 charged species and 18 reactions, along with a solution of the electron energy equation. To the author's knowledge, a parallel three-dimensional model of a gas discharge with a detailed air chemistry model and the solution of electron energy is unique. Three representative geometries are studied using the gas discharge model. The discharge of gas between two parallel electrodes is used to validate the air chemistry model developed for the gas discharge code. The gas discharge model is then applied to the discharge produced by placing a dc powered wire and grounded plate electrodes in a channel. Finally, a three-dimensional simulation of gas discharge produced by electrodes placed inside a riblet is carried out. The body force calculated with the gas discharge model is loosely coupled with a fluid model to predict the induced flow inside the riblet.

Numerical study of the radiometric phenomenon exhibited by a rotating Crookes radiometer

NASA Astrophysics Data System (ADS)

Anikin, Yu. A.

2011-11-01

The two-dimensional rarefied gas flow around a rotating Crookes radiometer and the arising radiometric forces are studied by numerically solving the Boltzmann kinetic equation. The computations are performed in a noninertial frame of reference rotating together with the radiometer. The collision integral is directly evaluated using a projection method, while second- and third-order accurate TVD schemes are used to solve the advection equation and the equation for inertia-induced transport in the velocity space, respectively. The radiometric forces are found as functions of the rotation frequency.

G-Jitter Effects in Protein Crystal Growth - A Numerical Study

NASA Technical Reports Server (NTRS)

Ramachandran, N.; Baugher, C. R.

1995-01-01

The impact of spacecraft acceleration environment on Protein Crystal Growth (PCG) is studied. A brief overview of the Space Shuttle acceleration environment is provided followed by a simple scaling procedure used to obtain estimates of the flow and concentration field characteristics in PCG. A detailed two-dimensional numerical model is then used to simulate the PCG system response to different disturbance scenarios; viz. residual g effects, impulse type disturbances and oscillatory inputs. The results show that PCG is susceptible to g-jitter and is a good candidate for vibration isolation.

Analytical solutions of the two-dimensional Dirac equation for a topological channel intersection

NASA Astrophysics Data System (ADS)

Anglin, J. R.; Schulz, A.

2017-01-01

Numerical simulations in a tight-binding model have shown that an intersection of topologically protected one-dimensional chiral channels can function as a beam splitter for noninteracting fermions on a two-dimensional lattice [Qiao, Jung, and MacDonald, Nano Lett. 11, 3453 (2011), 10.1021/nl201941f; Qiao et al., Phys. Rev. Lett. 112, 206601 (2014), 10.1103/PhysRevLett.112.206601]. Here we confirm this result analytically in the corresponding continuum k .p model, by solving the associated two-dimensional Dirac equation, in the presence of a "checkerboard" potential that provides a right-angled intersection between two zero-line modes. The method by which we obtain our analytical solutions is systematic and potentially generalizable to similar problems involving intersections of one-dimensional systems.

A numerical study of the effects of a large sandbar upon sea breeze development

NASA Technical Reports Server (NTRS)

Kessler, R. C.; Pielke, R. A.; Mcqueen, J.; Eppel, D.

1985-01-01

Two-dimensional numerical simulations of sea breeze development over a large sandbar on the North Sea coast of Germany are reported. The numerical model used in these experiments contains a detailed treatment of soil moisture, which allows evaluation of the effects of differential surface characteristics on the airflow pattern. Results of the simulations indicate that the contrast between the moist sandbar and adjacent dry land, the tidal inundation of the sandbar, and the westward penetration of the Baltic sea breeze play important roles in the development of mesoscale airflow patterns in the sandbar region.

Three-dimensional discrete-time Lotka-Volterra models with an application to industrial clusters

NASA Astrophysics Data System (ADS)

Bischi, G. I.; Tramontana, F.

2010-10-01

We consider a three-dimensional discrete dynamical system that describes an application to economics of a generalization of the Lotka-Volterra prey-predator model. The dynamic model proposed is used to describe the interactions among industrial clusters (or districts), following a suggestion given by [23]. After studying some local and global properties and bifurcations in bidimensional Lotka-Volterra maps, by numerical explorations we show how some of them can be extended to their three-dimensional counterparts, even if their analytic and geometric characterization becomes much more difficult and challenging. We also show a global bifurcation of the three-dimensional system that has no two-dimensional analogue. Besides the particular economic application considered, the study of the discrete version of Lotka-Volterra dynamical systems turns out to be a quite rich and interesting topic by itself, i.e. from a purely mathematical point of view.

Random gauge models of the superconductor-insulator transition in two-dimensional disordered superconductors

NASA Astrophysics Data System (ADS)

Granato, Enzo

2017-11-01

We study numerically the superconductor-insulator transition in two-dimensional inhomogeneous superconductors with gauge disorder, described by four different quantum rotor models: a gauge glass, a flux glass, a binary phase glass, and a Gaussian phase glass. The first two models describe the combined effect of geometrical disorder in the array of local superconducting islands and a uniform external magnetic field, while the last two describe the effects of random negative Josephson-junction couplings or π junctions. Monte Carlo simulations in the path-integral representation of the models are used to determine the critical exponents and the universal conductivity at the quantum phase transition. The gauge- and flux-glass models display the same critical behavior, within the estimated numerical uncertainties. Similar agreement is found for the binary and Gaussian phase-glass models. Despite the different symmetries and disorder correlations, we find that the universal conductivity of these models is approximately the same. In particular, the ratio of this value to that of the pure model agrees with recent experiments on nanohole thin-film superconductors in a magnetic field, in the large disorder limit.

Data Acquisition Using Xbox Kinect Sensor

ERIC Educational Resources Information Center

Ballester, Jorge; Pheatt, Charles B.

2012-01-01

The study of motion is central in physics education and has taken many forms as technology has provided numerous methods to acquire data. For example, the analysis of still or moving images is particularly effective in discussions of two-dimensional motion. Introductory laboratory measurement methods have progressed through water clocks, spark…

SIMULATING TEMPORAL VARIATIONS IN NUTRIENT, PHYTOPLANKTON, AND ZOOPLANKTON ON THE INNER OREGON SHELF

EPA Science Inventory

The objective of this study is to use a numerical model to examine the linkages between physical processes and temporal variability in the plankton dynamics in a coastal upwelling system. We used a nutrient-phytoplankton-zooplankton model coupled to a two-dimensional circulation...

Two-dimensional simulation of a two-phase, regenerative pumped radiator loop utilizing direct contact heat transfer with phase change

NASA Astrophysics Data System (ADS)

Rhee, Hyop S.; Begg, Lester L.; Wetch, Joseph R.; Jang, Jong H.; Juhasz, Albert J.

An innovative pumped loop concept for 600 K space power system radiators utilizing direct contact heat transfer, which facilitates repeated startup/shutdown of the power system without complex and time-consuming coolant thawing during power startup, is under development. The heat transfer process with melting/freezing of Li in an NaK flow was studied through two-dimensional time-dependent numerical simulations to characterize and predict the Li/NaK radiator performance during startup (thawing) and shutdown (cold-trapping). Effects of system parameters and the criteria for the plugging domain are presented together with temperature distribution patterns in solid Li and subsequent melting surface profile variations in time.

Numerical simulation of groundwater flow in strongly anisotropic aquifers using multiple-point flux approximation method

NASA Astrophysics Data System (ADS)

Lin, S. T.; Liou, T. S.

2017-12-01

Numerical simulation of groundwater flow in anisotropic aquifers usually suffers from the lack of accuracy of calculating groundwater flux across grid blocks. Conventional two-point flux approximation (TPFA) can only obtain the flux normal to the grid interface but completely neglects the one parallel to it. Furthermore, the hydraulic gradient in a grid block estimated from TPFA can only poorly represent the hydraulic condition near the intersection of grid blocks. These disadvantages are further exacerbated when the principal axes of hydraulic conductivity, global coordinate system, and grid boundary are not parallel to one another. In order to refine the estimation the in-grid hydraulic gradient, several multiple-point flux approximation (MPFA) methods have been developed for two-dimensional groundwater flow simulations. For example, the MPFA-O method uses the hydraulic head at the junction node as an auxiliary variable which is then eliminated using the head and flux continuity conditions. In this study, a three-dimensional MPFA method will be developed for numerical simulation of groundwater flow in three-dimensional and strongly anisotropic aquifers. This new MPFA method first discretizes the simulation domain into hexahedrons. Each hexahedron is further decomposed into a certain number of tetrahedrons. The 2D MPFA-O method is then extended to these tetrahedrons, using the unknown head at the intersection of hexahedrons as an auxiliary variable along with the head and flux continuity conditions to solve for the head at the center of each hexahedron. Numerical simulations using this new MPFA method have been successfully compared with those obtained from a modified version of TOUGH2.

Computation of Reacting Flows in Combustion Processes

NASA Technical Reports Server (NTRS)

Keith, Theo G., Jr.; Chen, K.-H.

2001-01-01

The objective of this research is to develop an efficient numerical algorithm with unstructured grids for the computation of three-dimensional chemical reacting flows that are known to occur in combustion components of propulsion systems. During the grant period (1996 to 1999), two companion codes have been developed and various numerical and physical models were implemented into the two codes.

Numerical studies of unsteady two dimensional subsonic flows using the ICE method. Ph.D. Thesis - Toledo Univ.

NASA Technical Reports Server (NTRS)

Wieber, P. R.

1973-01-01

A numerical program was developed to compute transient compressible and incompressible laminar flows in two dimensions with multicomponent mixing and chemical reaction. The algorithm used the Los Alamos Scientific Laboratory ICE (Implicit Continuous-Fluid Eulerian) method as its base. The program can compute both high and low speed compressible flows. The numerical program incorporating the stabilization techniques was quite successful in treating both old and new problems. Detailed calculations of coaxial flow very close to the entry plane were possible. The program treated complex flows such as the formation and downstream growth of a recirculation cell. An implicit solution of the species equation predicted mixing and reaction rates which compared favorably with the literature.

Magnetic dynamo action in two-dimensional turbulent magneto-hydrodynamics

NASA Technical Reports Server (NTRS)

Fyfe, D.; Joyce, G.; Montgomery, D.

1977-01-01

Two-dimensional magnetohydrodynamic turbulence is explored by means of numerical simulation. Previous analytical theory, based on non-dissipative constants of the motion in a truncated Fourier representation, is verified by following the evolution of highly non-equilibrium initial conditions numerically. Dynamo action (conversion of a significant fraction of turbulent kinetic energy into long-wavelength magnetic field energy) is observed. It is conjectured that in the presence of dissipation and external forcing, a dual cascade will be observed for zero-helicity situations. Energy will cascade to higher wavenumbers simultaneously with a cascade of mean square vector potential to lower wavenumbers, leading to an omni-directional magnetic energy spectrum.

Numerical procedure to determine geometric view factors for surfaces occluded by cylinders

NASA Technical Reports Server (NTRS)

Sawyer, P. L.

1978-01-01

A numerical procedure was developed to determine geometric view factors between connected infinite strips occluded by any number of infinite circular cylinders. The procedure requires a two-dimensional cross-sectional model of the configuration of interest. The two-dimensional model consists of a convex polygon enclosing any number of circles. Each side of the polygon represents one strip, and each circle represents a circular cylinder. A description and listing of a computer program based on this procedure are included in this report. The program calculates geometric view factors between individual strips and between individual strips and the collection of occluding cylinders.

Real gas flow fields about three dimensional configurations

NASA Technical Reports Server (NTRS)

Balakrishnan, A.; Lombard, C. K.; Davy, W. C.

1983-01-01

Real gas, inviscid supersonic flow fields over a three-dimensional configuration are determined using a factored implicit algorithm. Air in chemical equilibrium is considered and its local thermodynamic properties are computed by an equilibrium composition method. Numerical solutions are presented for both real and ideal gases at three different Mach numbers and at two different altitudes. Selected results are illustrated by contour plots and are also tabulated for future reference. Results obtained compare well with existing tabulated numerical solutions and hence validate the solution technique.

Scaling characteristics of one-dimensional fractional diffusion processes in the presence of power-law distributed random noise

NASA Astrophysics Data System (ADS)

Nezhadhaghighi, Mohsen Ghasemi

2017-08-01

Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ -stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α . We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ -stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.

Three-dimensional numerical investigation of the separation process in a vortex tube at different operating conditions

NASA Astrophysics Data System (ADS)

Rafiee, Seyed Ehsan; Sadeghiazad, M. M.

2016-06-01

Air separators provide safe, clean, and appropriate air flow to engines and are widely used in vehicles with large engines such as ships and submarines. In this operational study, the separation process inside a Ranque-Hilsch vortex tube cleaning (cooling) system is investigated to analyze the impact of the operating gas type on the vortex tube performance; the operating gases used are air, nitrogen, oxygen, carbon dioxide and nitrogen dioxide. The computational fluid dynamic model used is equipped with a three-dimensional structure, and the steady-state condition is applied during computations. The standard k-ɛ turbulence model is employed to resolve nonlinear flow equations, and various key parameters, such as hot and cold exhaust thermal drops, and power separation rates, are described numerically. The results show that nitrogen dioxide creates the greatest separation power out of all gases tested, and the numerical results are validated by good agreement with available experimental data. In addition, a comparison is made between the use of two different boundary conditions, the pressure-far-field and the pressure-outlet, when analyzing complex turbulent flows inside the air separators. Results present a comprehensive and practical solution for use in future numerical studies.

Scaling characteristics of one-dimensional fractional diffusion processes in the presence of power-law distributed random noise.

PubMed

Nezhadhaghighi, Mohsen Ghasemi

2017-08-01

Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ-stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α. We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ-stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.

Tachyon condensation due to domain-wall annihilation in Bose-Einstein condensates.

PubMed

Takeuchi, Hiromitsu; Kasamatsu, Kenichi; Tsubota, Makoto; Nitta, Muneto

2012-12-14

We show theoretically that a domain-wall annihilation in two-component Bose-Einstein condensates causes tachyon condensation accompanied by spontaneous symmetry breaking in a two-dimensional subspace. Three-dimensional vortex formation from domain-wall annihilations is considered a kink formation in subspace. Numerical experiments reveal that the subspatial dynamics obey the dynamic scaling law of phase-ordering kinetics. This model is experimentally feasible and provides insights into how the extra dimensions influence subspatial phase transition in higher-dimensional space.

Particle-tracking analysis of contributing areas of public-supply wells in simple and complex flow systems, Cape Cod, Massachusetts

USGS Publications Warehouse

Barlow, Paul M.

1997-01-01

Steady-state, two- and three-dimensional, ground-water-flow models coupled with particle tracking were evaluated to determine their effectiveness in delineating contributing areas of wells pumping from stratified-drift aquifers of Cape Cod, Massachusetts. Several contributing areas delineated by use of the three-dimensional models do not conform to simple ellipsoidal shapes that are typically delineated by use of two-dimensional analytical and numerical modeling techniques and included discontinuous areas of the water table.

Multi-dimensional rheology-based two-phase model for sediment transport and applications to sheet flow and pipeline scour

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

Lee, Cheng-Hsien; Department of Water Resources and Environmental Engineering, Tamkang University, New Taipei City 25137, Taiwan; Low, Ying Min, E-mail: ceelowym@nus.edu.sg

2016-05-15

Sediment transport is fundamentally a two-phase phenomenon involving fluid and sediments; however, many existing numerical models are one-phase approaches, which are unable to capture the complex fluid-particle and inter-particle interactions. In the last decade, two-phase models have gained traction; however, there are still many limitations in these models. For example, several existing two-phase models are confined to one-dimensional problems; in addition, the existing two-dimensional models simulate only the region outside the sand bed. This paper develops a new three-dimensional two-phase model for simulating sediment transport in the sheet flow condition, incorporating recently published rheological characteristics of sediments. The enduring-contact, inertial,more » and fluid viscosity effects are considered in determining sediment pressure and stresses, enabling the model to be applicable to a wide range of particle Reynolds number. A k − ε turbulence model is adopted to compute the Reynolds stresses. In addition, a novel numerical scheme is proposed, thus avoiding numerical instability caused by high sediment concentration and allowing the sediment dynamics to be computed both within and outside the sand bed. The present model is applied to two classical problems, namely, sheet flow and scour under a pipeline with favorable results. For sheet flow, the computed velocity is consistent with measured data reported in the literature. For pipeline scour, the computed scour rate beneath the pipeline agrees with previous experimental observations. However, the present model is unable to capture vortex shedding; consequently, the sediment deposition behind the pipeline is overestimated. Sensitivity analyses reveal that model parameters associated with turbulence have strong influence on the computed results.« less

Numerical and Physical Modeling of the Response of Resonator Liners to Intense Sound and Grazing Flow

NASA Technical Reports Server (NTRS)

Hersh, Alan S.; Tam, Christopher

2009-01-01

Two significant advances have been made in the application of computational aeroacoustics methodology to acoustic liner technology. The first is that temperature effects for discrete sound are not the same as for broadband noise. For discrete sound, the normalized resistance appears to be insensitive to temperature except at high SPL. However, reactance is lower, significantly lower in absolute value, at high temperature. The second is the numerical investigation the acoustic performance of a liner by direct numerical simulation. Liner impedance is affected by the non-uniformity of the incident sound waves. This identifies the importance of pressure gradient. Preliminary design one and two-dimensional impedance models were developed to design sound absorbing liners in the presence of intense sound and grazing flow. The two-dimensional model offers the potential to empirically determine incident sound pressure face-plate distance from resonator orifices. This represents an important initial step in improving our understanding of how to effectively use the Dean Two-Microphone impedance measurement method.

Role of thermal two-phonon scattering for impurity dynamics in a low-dimensional Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Lausch, Tobias; Widera, Artur; Fleischhauer, Michael

2018-03-01

We numerically study the relaxation dynamics of a single, heavy impurity atom interacting with a finite one- or two-dimensional, ultracold Bose gas. While there is a clear separation of time scales between processes resulting from single- and two-phonon scattering in three spatial dimensions, the thermalization in lower dimensions is dominated by two-phonon processes. This is due to infrared divergences in the corresponding scattering rates in the thermodynamic limit, which are a manifestation of the Mermin-Wagner-Hohenberg theorem. This makes it necessary to include second-order phonon scattering above a crossover temperature T2ph . T2ph scales inversely with the system size and is much smaller than currently experimentally accessible.

Alignment dynamics of diffusive scalar gradient in a two-dimensional model flow

NASA Astrophysics Data System (ADS)

Gonzalez, M.

2018-04-01

The Lagrangian two-dimensional approach of scalar gradient kinematics is revisited accounting for molecular diffusion. Numerical simulations are performed in an analytic, parameterized model flow, which enables considering different regimes of scalar gradient dynamics. Attention is especially focused on the influence of molecular diffusion on Lagrangian statistical orientations and on the dynamics of scalar gradient alignment.

Numerically simulated two-dimensional auroral double layers

NASA Technical Reports Server (NTRS)

Borovsky, J. E.; Joyce, G.

1983-01-01

A magnetized 2 1/2-dimensional particle-in-cell system which is periodic in one direction and bounded by reservoirs of Maxwellian plasma in the other is used to numerically simulate electrostatic plasma double layers. For the cases of both oblique and two-dimensional double layers, the present results indicate periodic instability, Debye length rather than gyroradii scaling, and low frequency electrostatic turbulence together with electron beam-excited electrostatatic electron-cyclotron waves. Estimates are given for the thickness of auroral doule layers, as well as the separations within multiple auroral arcs. Attention is given to the temporal modulation of accelerated beams, and the possibilities for ion precipitation and ion conic production by the double layer are hypothesized. Simulations which include the atmospheric backscattering of electrons imply the action of an ionospheric sheath which accelerates ionospheric ions upward.

Numerical simulations - Some results for the 2- and 3-D Hubbard models and a 2-D electron phonon model

NASA Technical Reports Server (NTRS)

Scalapino, D. J.; Sugar, R. L.; White, S. R.; Bickers, N. E.; Scalettar, R. T.

1989-01-01

Numerical simulations on the half-filled three-dimensional Hubbard model clearly show the onset of Neel order. Simulations of the two-dimensional electron-phonon Holstein model show the competition between the formation of a Peierls-CDW state and a superconducting state. However, the behavior of the partly filled two-dimensional Hubbard model is more difficult to determine. At half-filling, the antiferromagnetic correlations grow as T is reduced. Doping away from half-filling suppresses these correlations, and it is found that there is a weak attractive pairing interaction in the d-wave channel. However, the strength of the pair field susceptibility is weak at the temperatures and lattice sizes that have been simulated, and the nature of the low-temperature state of the nearly half-filled Hubbard model remains open.

One-dimensional analysis of supersonic two-stage HVOF process

NASA Astrophysics Data System (ADS)

Katanoda, Hiroshi; Hagi, Junichi; Fukuhara, Minoru

2009-12-01

The one-dimensional calculation of the gas/particle flows of a supersonic two-stage high-velocity oxy-fuel (HVOF) thermal spray process was performed. The internal gas flow was solved by numerically integrating the equations of the quasi-one-dimensional flow including the effects of pipe friction and heat transfer. As for the supersonic jet flow, semi-empirical equations were used to obtain the gas velocity and temperature along the center line. The velocity and temperature of the particle were obtained by an one-way coupling method. The material of the spray particle selected in this study is ultra high molecular weight polyethylene (UHMWPE). The temperature distributions in the spherical UHMWPE particles of 50 and 150µm accelerated and heated by the supersonic gas flow was clarified.

Thermal conductivity in one-dimensional nonlinear systems

NASA Astrophysics Data System (ADS)

Politi, Antonio; Giardinà, Cristian; Livi, Roberto; Vassalli, Massimo

2000-03-01

Thermal conducitivity of one-dimensional nonlinear systems typically diverges in the thermodynamic limit, whenever the momentum is conserved (i.e. in the absence of interactions with an external substrate). Evidence comes from detailed studies of Fermi-Pasta-Ulam and diatomic Toda chains. Here, we discuss the first example of a one-dimensional system obeying Fourier law : a chain of coupled rotators. Numerical estimates of the thermal conductivity obtained by simulating a chain in contact with two thermal baths at different temperatures are found to be consistent with those ones based on linear response theory. The dynamics of the Fourier modes provides direct evidence of energy diffusion. The finiteness of the conductivity is traced back to the occurrence of phase-jumps. Our conclusions are confirmed by the analysis of two variants of the rotator model.

Analytic reconstruction of magnetic resonance imaging signal obtained from a periodic encoding field.

PubMed

Rybicki, F J; Hrovat, M I; Patz, S

2000-09-01

We have proposed a two-dimensional PERiodic-Linear (PERL) magnetic encoding field geometry B(x,y) = g(y)y cos(q(x)x) and a magnetic resonance imaging pulse sequence which incorporates two fields to image a two-dimensional spin density: a standard linear gradient in the x dimension, and the PERL field. Because of its periodicity, the PERL field produces a signal where the phase of the two dimensions is functionally different. The x dimension is encoded linearly, but the y dimension appears as the argument of a sinusoidal phase term. Thus, the time-domain signal and image spin density are not related by a two-dimensional Fourier transform. They are related by a one-dimensional Fourier transform in the x dimension and a new Bessel function integral transform (the PERL transform) in the y dimension. The inverse of the PERL transform provides a reconstruction algorithm for the y dimension of the spin density from the signal space. To date, the inverse transform has been computed numerically by a Bessel function expansion over its basis functions. This numerical solution used a finite sum to approximate an infinite summation and thus introduced a truncation error. This work analytically determines the basis functions for the PERL transform and incorporates them into the reconstruction algorithm. The improved algorithm is demonstrated by (1) direct comparison between the numerically and analytically computed basis functions, and (2) reconstruction of a known spin density. The new solution for the basis functions also lends proof of the system function for the PERL transform under specific conditions.

Stability of a flow down an incline with respect to two-dimensional and three-dimensional disturbances for Newtonian and non-Newtonian fluids.

PubMed

Allouche, M H; Millet, S; Botton, V; Henry, D; Ben Hadid, H; Rousset, F

2015-12-01

Squire's theorem, which states that the two-dimensional instabilities are more dangerous than the three-dimensional instabilities, is revisited here for a flow down an incline, making use of numerical stability analysis and Squire relationships when available. For flows down inclined planes, one of these Squire relationships involves the slopes of the inclines. This means that the Reynolds number associated with a two-dimensional wave can be shown to be smaller than that for an oblique wave, but this oblique wave being obtained for a larger slope. Physically speaking, this prevents the possibility to directly compare the thresholds at a given slope. The goal of the paper is then to reach a conclusion about the predominance or not of two-dimensional instabilities at a given slope, which is of practical interest for industrial or environmental applications. For a Newtonian fluid, it is shown that, for a given slope, oblique wave instabilities are never the dominant instabilities. Both the Squire relationships and the particular variations of the two-dimensional wave critical curve with regard to the inclination angle are involved in the proof of this result. For a generalized Newtonian fluid, a similar result can only be obtained for a reduced stability problem where some term connected to the perturbation of viscosity is neglected. For the general stability problem, however, no Squire relationships can be derived and the numerical stability results show that the thresholds for oblique waves can be smaller than the thresholds for two-dimensional waves at a given slope, particularly for large obliquity angles and strong shear-thinning behaviors. The conclusion is then completely different in that case: the dominant instability for a generalized Newtonian fluid flowing down an inclined plane with a given slope can be three dimensional.

An Exponential Finite Difference Technique for Solving Partial Differential Equations. M.S. Thesis - Toledo Univ., Ohio

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.

Numerical modeling of surface wave development under the action of wind

NASA Astrophysics Data System (ADS)

Chalikov, Dmitry

2018-06-01

The numerical modeling of two-dimensional surface wave development under the action of wind is performed. The model is based on three-dimensional equations of potential motion with a free surface written in a surface-following nonorthogonal curvilinear coordinate system in which depth is counted from a moving surface. A three-dimensional Poisson equation for the velocity potential is solved iteratively. A Fourier transform method, a second-order accuracy approximation of vertical derivatives on a stretched vertical grid and fourth-order Runge-Kutta time stepping are used. Both the input energy to waves and dissipation of wave energy are calculated on the basis of earlier developed and validated algorithms. A one-processor version of the model for PC allows us to simulate an evolution of the wave field with thousands of degrees of freedom over thousands of wave periods. A long-time evolution of a two-dimensional wave structure is illustrated by the spectra of wave surface and the input and output of energy.

exponential finite difference technique for solving partial differential equations

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

Handschuh, R.F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that weremore » more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.« less

Numerical simulation of two-dimensional flow over a heated carbon surface with coupled heterogeneous and homogeneous reactions

NASA Astrophysics Data System (ADS)

Johnson, Ryan Federick; Chelliah, Harsha Kumar

2017-01-01

For a range of flow and chemical timescales, numerical simulations of two-dimensional laminar flow over a reacting carbon surface were performed to understand further the complex coupling between heterogeneous and homogeneous reactions. An open-source computational package (OpenFOAM®) was used with previously developed lumped heterogeneous reaction models for carbon surfaces and a detailed homogeneous reaction model for CO oxidation. The influence of finite-rate chemical kinetics was explored by varying the surface temperatures from 1800 to 2600 K, while flow residence time effects were explored by varying the free-stream velocity up to 50 m/s. The reacting boundary layer structure dependence on the residence time was analysed by extracting the ratio of chemical source and species diffusion terms. The important contributions of radical species reactions on overall carbon removal rate, which is often neglected in multi-dimensional simulations, are highlighted. The results provide a framework for future development and validation of lumped heterogeneous reaction models based on multi-dimensional reacting flow configurations.

A 2.5D Computational Method to Simulate Cylindrical Fluidized Beds

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

Li, Tingwen; Benyahia, Sofiane; Dietiker, Jeff

2015-02-17

In this paper, the limitations of axisymmetric and Cartesian two-dimensional (2D) simulations of cylindrical gas-solid fluidized beds are discussed. A new method has been proposed to carry out pseudo-two-dimensional (2.5D) simulations of a cylindrical fluidized bed by appropriately combining computational domains of Cartesian 2D and axisymmetric simulations. The proposed method was implemented in the open-source code MFIX and applied to the simulation of a lab-scale bubbling fluidized bed with necessary sensitivity study. After a careful grid study to ensure the numerical results are grid independent, detailed comparisons of the flow hydrodynamics were presented against axisymmetric and Cartesian 2D simulations. Furthermore,more » the 2.5D simulation results have been compared to the three-dimensional (3D) simulation for evaluation. This new approach yields better agreement with the 3D simulation results than with axisymmetric and Cartesian 2D simulations.« less

Numerical study of core formation of asymmetrically driven cone-guided targets

DOE PAGES

Sawada, Hiroshi; Sakagami, Hitoshi

2017-09-22

Compression of a directly driven fast ignition cone-sphere target with a finite number of laser beams is numerically studied using a three-dimensional hydrodynamics code IMPACT-3D. The formation of a dense plasma core is simulated for 12-, 9-, 6-, and 4-beam configurations of the GEKKO XII laser. The complex 3D shapes of the cores are analyzed by elucidating synthetic 2D x-ray radiographic images in two orthogonal directions. Finally, the simulated x-ray images show significant differences in the core shape between the two viewing directions and rotation of the stagnating core axis in the top view for the axisymmetric 9- and 6-beammore » configurations.« less

Numerical study of core formation of asymmetrically driven cone-guided targets

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

Sawada, Hiroshi; Sakagami, Hitoshi

Compression of a directly driven fast ignition cone-sphere target with a finite number of laser beams is numerically studied using a three-dimensional hydrodynamics code IMPACT-3D. The formation of a dense plasma core is simulated for 12-, 9-, 6-, and 4-beam configurations of the GEKKO XII laser. The complex 3D shapes of the cores are analyzed by elucidating synthetic 2D x-ray radiographic images in two orthogonal directions. Finally, the simulated x-ray images show significant differences in the core shape between the two viewing directions and rotation of the stagnating core axis in the top view for the axisymmetric 9- and 6-beammore » configurations.« less

Thermal smearing and screening in a strong magnetic field for Dirac materials in comparison with the two dimensional electron liquid

NASA Astrophysics Data System (ADS)

Gumbs, Godfrey; Balassis, Antonios; Dahal, Dipendra; Lawrence Glasser, M.

2016-10-01

We compute and compare the effects due to a uniform perpendicular magnetic field as well as temperature on the static polarization functions for monolayer graphene (MLG), associated with the Dirac point, with that for the two-dimensional electron liquid (2DEL) with the use of comprehensive numerical calculations. The relevance of our study to the Friedel oscillations for the screening of the potential for a dilute distribution of impurities is reported too. Our results show substantial differences due to screening for the 2DEL and MLG which have not been given adequate attention previously.

Numerical study of natural convection in a horizontal cylinder filled with water-based alumina nanofluid.

PubMed

Meng, Xiangyin; Li, Yan

2015-01-01

Natural heat convection of water-based alumina (Al2O3/water) nanofluids (with volume fraction 1% and 4%) in a horizontal cylinder is numerically investigated. The whole three-dimensional computational fluid dynamics (CFD) procedure is performed in a completely open-source way. Blender, enGrid, OpenFOAM and ParaView are employed for geometry creation, mesh generation, case simulation and post process, respectively. Original solver 'buoyantBoussinesqSimpleFoam' is selected for the present study, and a temperature-dependent solver 'buoyantBoussinesqSimpleTDFoam' is developed to ensure the simulation is more realistic. The two solvers are used for same cases and compared to corresponding experimental results. The flow regime in these cases is laminar (Reynolds number is 150) and the Rayleigh number range is 0.7 × 10(7) ~ 5 × 10(7). By comparison, the average natural Nusselt numbers of water and Al2O3/water nanofluids are found to increase with the Rayleigh number. At the same Rayleigh number, the Nusselt number is found to decrease with nanofluid volume fraction. The temperature-dependent solver is found better for water and 1% Al2O3/water nanofluid cases, while the original solver is better for 4% Al2O3/water nanofluid cases. Furthermore, due to strong three-dimensional flow features in the horizontal cylinder, three-dimensional CFD simulation is recommended instead of two-dimensional simplifications.

A volume-of-fluid method for simulation of compressible axisymmetric multi-material flow

NASA Astrophysics Data System (ADS)

de Niem, D.; Kührt, E.; Motschmann, U.

2007-02-01

A two-dimensional Eulerian hydrodynamic method for the numerical simulation of inviscid compressible axisymmetric multi-material flow in external force fields for the situation of pure fluids separated by macroscopic interfaces is presented. The method combines an implicit Lagrangian step with an explicit Eulerian advection step. Individual materials obey separate energy equations, fulfill general equations of state, and may possess different temperatures. Material volume is tracked using a piecewise linear volume-of-fluid method. An overshoot-free logically simple and economic material advection algorithm for cylinder coordinates is derived, in an algebraic formulation. New aspects arising in the case of more than two materials such as the material ordering strategy during transport are presented. One- and two-dimensional numerical examples are given.

Numerical study on characteristic of two-dimensional metal/dielectric photonic crystals

NASA Astrophysics Data System (ADS)

Zong, Yi-Xin; Xia, Jian-Bai; Wu, Hai-Bin

2017-04-01

An improved plan-wave expansion method is adopted to theoretically study the photonic band diagrams of two-dimensional (2D) metal/dielectric photonic crystals. Based on the photonic band structures, the dependence of flat bands and photonic bandgaps on two parameters (dielectric constant and filling factor) are investigated for two types of 2D metal/dielectric (M/D) photonic crystals, hole and cylinder photonic crystals. The simulation results show that band structures are affected greatly by these two parameters. Flat bands and bandgaps can be easily obtained by tuning these parameters and the bandgap width may reach to the maximum at certain parameters. It is worth noting that the hole-type photonic crystals show more bandgaps than the corresponding cylinder ones, and the frequency ranges of bandgaps also depend strongly on these parameters. Besides, the photonic crystals containing metallic medium can obtain more modulation of photonic bands, band gaps, and large effective refractive index, etc. than the dielectric/dielectric ones. According to the numerical results, the needs of optical devices for flat bands and bandgaps can be met by selecting the suitable geometry and material parameters. Project supported by the National Basic Research Program of China (Grant No. 2011CB922200) and the National Natural Science Foundation of China (Grant No. 605210010).

An application of a two-equation model of turbulence to three-dimensional chemically reacting flows

NASA Technical Reports Server (NTRS)

Lee, J.

1994-01-01

A numerical study of three dimensional chemically reacting and non-reacting flowfields is conducted using a two-equation model of turbulence. A generalized flow solver using an implicit Lower-Upper (LU) diagonal decomposition numerical technique and finite-rate chemistry has been coupled with a low-Reynolds number two-equation model of turbulence. This flow solver is then used to study chemically reacting turbulent supersonic flows inside combustors with synergetic fuel injectors. The reacting and non-reacting turbulent combustor solutions obtained are compared with zero-equation turbulence model solutions and with available experimental data. The hydrogen-air chemistry is modeled using a nine-species/eighteen reaction model. A low-Reynolds number k-epsilon model was used to model the effect of turbulence because, in general, the low-Reynolds number k-epsilon models are easier to implement numerically and are far more general than algebraic models. However, low-Reynolds number k-epsilon models require a much finer near-wall grid resolution than high-Reynolds number models to resolve accurately the near-wall physics. This is especially true in complex flowfields, where the stiff nature of the near-wall turbulence must be resolved. Therefore, the limitations imposed by the near-wall characteristics and compressible model corrections need to be evaluated further. The gradient-diffusion hypothesis is used to model the effects of turbulence on the mass diffusion process. The influence of this low-Reynolds number turbulence model on the reacting flowfield predictions was studied parametrically.

Numerical method for predicting flow characteristics and performance of nonaxisymmetric nozzles. Part 2: Applications

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.

Excitonic effects in two-dimensional semiconductors: Path integral Monte Carlo approach

DOE PAGES

Velizhanin, Kirill A.; Saxena, Avadh

2015-11-01

The most striking features of novel two-dimensional semiconductors (e.g., transition metal dichalcogenide monolayers or phosphorene) is a strong Coulomb interaction between charge carriers resulting in large excitonic effects. In particular, this leads to the formation of multicarrier bound states upon photoexcitation (e.g., excitons, trions, and biexcitons), which could remain stable at near-room temperatures and contribute significantly to the optical properties of such materials. In our work we have used the path integral Monte Carlo methodology to numerically study properties of multicarrier bound states in two-dimensional semiconductors. Specifically, we have accurately investigated and tabulated the dependence of single-exciton, trion, and biexcitonmore » binding energies on the strength of dielectric screening, including the limiting cases of very strong and very weak screening. Our results of this work are potentially useful in the analysis of experimental data and benchmarking of theoretical and computational models.« less

An approximate theoretical method for modeling the static thrust performance of non-axisymmetric two-dimensional convergent-divergent nozzles. M.S. Thesis - George Washington Univ.

NASA Technical Reports Server (NTRS)

Hunter, Craig A.

1995-01-01

An analytical/numerical method has been developed to predict the static thrust performance of non-axisymmetric, two-dimensional convergent-divergent exhaust nozzles. Thermodynamic nozzle performance effects due to over- and underexpansion are modeled using one-dimensional compressible flow theory. Boundary layer development and skin friction losses are calculated using an approximate integral momentum method based on the classic karman-Polhausen solution. Angularity effects are included with these two models in a computational Nozzle Performance Analysis Code, NPAC. In four different case studies, results from NPAC are compared to experimental data obtained from subscale nozzle testing to demonstrate the capabilities and limitations of the NPAC method. In several cases, the NPAC prediction matched experimental gross thrust efficiency data to within 0.1 percent at a design NPR, and to within 0.5 percent at off-design conditions.

Study of the hydrodynamics of the formation of flows caused by the interaction of a shock wave with two-dimensional density perturbations on the Iskra-5 laser facility

NASA Astrophysics Data System (ADS)

Babanov, A. V.; Barinov, M. A.; Barinov, S. P.; Garanin, R. V.; Zhidkov, N. V.; Kalmykov, N. A.; Kovalenko, V. P.; Kokorin, S. N.; Pinegin, A. V.; Solomatina, E. Yu.; Solomatin, I. I.; Suslov, N. A.

2017-03-01

The hydrodynamics of the flow formation due to the interaction of a shock wave with two-dimensional density perturbations is experimentally investigated on the Iskra-5 laser facility. Shadow images of a jet arising as a result of the impact of a shock wave (formed by a soft X-ray pulse from a target-illuminator) on a flat aluminium target with a blind cylindrical cavity are recorded in experiments with point-like X-ray backlighting having a photon energy of ~4.5 keV. The sizes and mass of the jet ejected from the aluminium cavity by this shock wave are estimated. The experimental data are compared with the results of numerical simulation of the jet formation and dynamics according to the two-dimensional MID-ND2D code.

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

NASA Technical Reports Server (NTRS)

Schallhorn, Paul; Majumdar, Alok

2012-01-01

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

Numerical solution to the glancing sidewall oblique shock wave/turbulent boundary layer interaction in three dimension

NASA Technical Reports Server (NTRS)

Anderson, B. H.; Benson, T. J.

1983-01-01

A supersonic three-dimensional viscous forward-marching computer design code called PEPSIS is used to obtain a numerical solution of the three-dimensional problem of the interaction of a glancing sidewall oblique shock wave and a turbulent boundary layer. Very good results are obtained for a test case that was run to investigate the use of the wall-function boundary-condition approximation for a highly complex three-dimensional shock-boundary layer interaction. Two additional test cases (coarse mesh and medium mesh) are run to examine the question of near-wall resolution when no-slip boundary conditions are applied. A comparison with experimental data shows that the PEPSIS code gives excellent results in general and is practical for three-dimensional supersonic inlet calculations.

Numerical solution to the glancing sidewall oblique shock wave/turbulent boundary layer interaction in three-dimension

NASA Technical Reports Server (NTRS)

Anderson, B. H.; Benson, T. J.

1983-01-01

A supersonic three-dimensional viscous forward-marching computer design code called PEPSIS is used to obtain a numerical solution of the three-dimensional problem of the interaction of a glancing sidewall oblique shock wave and a turbulent boundary layer. Very good results are obtained for a test case that was run to investigate the use of the wall-function boundary-condition approximation for a highly complex three-dimensional shock-boundary layer interaction. Two additional test cases (coarse mesh and medium mesh) are run to examine the question of near-wall resolution when no-slip boundary conditions are applied. A comparison with experimental data shows that the PEPSIS code gives excellent results in general and is practical for three-dimensional supersonic inlet calculations.

An equivalent domain integral for analysis of two-dimensional mixed mode problems

NASA Technical Reports Server (NTRS)

Raju, I. S.; Shivakumar, K. N.

1989-01-01

An equivalent domain integral (EDI) method for calculating J-integrals for two-dimensional cracked elastic bodies subjected to mixed mode loading is presented. The total and product integrals consist of the sum of an area or domain integral and line integrals on the crack faces. The EDI method gave accurate values of the J-integrals for two mode I and two mixed mode problems. Numerical studies showed that domains consisting of one layer of elements are sufficient to obtain accurate J-integral values. Two procedures for separating the individual modes from the domain integrals are presented. The procedure that uses the symmetric and antisymmetric components of the stress and displacement fields to calculate the individual modes gave accurate values of the integrals for all the problems analyzed.

Numerical Modeling of Three-Dimensional Fluid Flow with Phase Change

NASA Technical Reports Server (NTRS)

Esmaeeli, Asghar; Arpaci, Vedat

1999-01-01

We present a numerical method to compute phase change dynamics of three-dimensional deformable bubbles. The full Navier-Stokes and energy equations are solved for both phases by a front tracking/finite difference technique. The fluid boundary is explicitly tracked by discrete points that are connected by triangular elements to form a front that is used to keep the stratification of material properties sharp and to calculate the interfacial source terms. Two simulations are presented to show robustness of the method in handling complex phase boundaries. In the first case, growth of a vapor bubble in zero gravity is studied where large volume increase of the bubble is managed by adaptively increasing the front resolution. In the second case, growth of a bubble under high gravity is studied where indentation at the rear of the bubble results in a region of large curvature which challenges the front tracking in three dimensions.

Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-01-01

The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.

Cold spray nozzle mach number limitation

NASA Astrophysics Data System (ADS)

Jodoin, B.

2002-12-01

The classic one-dimensional isentropic flow approach is used along with a two-dimensional axisymmetric numerical model to show that the exit Mach number of a cold spray nozzle should be limited due to two factors. To show this, the two-dimensional model is validated with experimental data. Although both models show that the stagnation temperature is an important limiting factor, the one-dimensional approach fails to show how important the shock-particle interactions are at limiting the nozzle Mach number. It is concluded that for an air nozzle spraying solid powder particles, the nozzle Mach number should be set between 1.5 and 3 to limit the negative effects of the high stagnation temperature and of the shock-particle interactions.

Direct numerical simulation of a compressible boundary-layer flow past an isolated three-dimensional hump in a high-speed subsonic regime

NASA Astrophysics Data System (ADS)

De Grazia, D.; Moxey, D.; Sherwin, S. J.; Kravtsova, M. A.; Ruban, A. I.

2018-02-01

In this paper we study the boundary-layer separation produced in a high-speed subsonic boundary layer by a small wall roughness. Specifically, we present a direct numerical simulation (DNS) of a two-dimensional boundary-layer flow over a flat plate encountering a three-dimensional Gaussian-shaped hump. This work was motivated by the lack of DNS data of boundary-layer flows past roughness elements in a similar regime which is typical of civil aviation. The Mach and Reynolds numbers are chosen to be relevant for aeronautical applications when considering small imperfections at the leading edge of wings. We analyze different heights of the hump: The smaller heights result in a weakly nonlinear regime, while the larger result in a fully nonlinear regime with an increasing laminar separation bubble arising downstream of the roughness element and the formation of a pair of streamwise counterrotating vortices which appear to support themselves.

On the Solution of the Three-Dimensional Flowfield About a Flow-Through Nacelle. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Compton, William Bernard

1985-01-01

The solution of the three dimensional flow field for a flow through nacelle was studied. Both inviscid and viscous inviscid interacting solutions were examined. Inviscid solutions were obtained with two different computational procedures for solving the three dimensional Euler equations. The first procedure employs an alternating direction implicit numerical algorithm, and required the development of a complete computational model for the nacelle problem. The second computational technique employs a fourth order Runge-Kutta numerical algorithm which was modified to fit the nacelle problem. Viscous effects on the flow field were evaluated with a viscous inviscid interacting computational model. This model was constructed by coupling the explicit Euler solution procedure with a flag entrainment boundary layer solution procedure in a global iteration scheme. The computational techniques were used to compute the flow field for a long duct turbofan engine nacelle at free stream Mach numbers of 0.80 and 0.94 and angles of attack of 0 and 4 deg.

Numerical Zooming Between a NPSS Engine System Simulation and a One-Dimensional High Compressor Analysis Code

NASA Technical Reports Server (NTRS)

Follen, Gregory; auBuchon, M.

2000-01-01

Within NASA's High Performance Computing and Communication (HPCC) program, NASA Glenn Research Center is developing an environment for the analysis/design of aircraft engines called the Numerical Propulsion System Simulation (NPSS). NPSS focuses on the integration of multiple disciplines such as aerodynamics, structures, and heat transfer along with the concept of numerical zooming between zero-dimensional to one-, two-, and three-dimensional component engine codes. In addition, the NPSS is refining the computing and communication technologies necessary to capture complex physical processes in a timely and cost-effective manner. The vision for NPSS is to create a "numerical test cell" enabling full engine simulations overnight on cost-effective computing platforms. Of the different technology areas that contribute to the development of the NPSS Environment, the subject of this paper is a discussion on numerical zooming between a NPSS engine simulation and higher fidelity representations of the engine components (fan, compressor, burner, turbines, etc.). What follows is a description of successfully zooming one-dimensional (row-by-row) high-pressure compressor analysis results back to a zero-dimensional NPSS engine simulation and a discussion of the results illustrated using an advanced data visualization tool. This type of high fidelity system-level analysis, made possible by the zooming capability of the NPSS, will greatly improve the capability of the engine system simulation and increase the level of virtual test conducted prior to committing the design to hardware.

Approximation and Numerical Analysis of Nonlinear Equations of Evolution.

DTIC Science & Technology

1980-01-31

dominant convective terms, or Stefan type problems such as the flow of fluids through porous media or the melting and freezing of ice. Such problems...means of formulating time-dependent Stefan problems was initiated. Classes of problems considered here include the one-phase and two-phase Stefan ...some new numerical methods were 2 developed for two dimensional, two-phase Stefan problems with time dependent boundary conditions. A variety of example

An Assessment of Five Modeling Approaches for Thermo-Mechanical Stress Analysis of Laminated Composite Panels

NASA Technical Reports Server (NTRS)

Noor, A. K.; Malik, M.

2000-01-01

A study is made of the effects of variation in the lamination and geometric parameters, and boundary conditions of multi-layered composite panels on the accuracy of the detailed response characteristics obtained by five different modeling approaches. The modeling approaches considered include four two-dimensional models, each with five parameters to characterize the deformation in the thickness direction, and a predictor-corrector approach with twelve displacement parameters. The two-dimensional models are first-order shear deformation theory, third-order theory; a theory based on trigonometric variation of the transverse shear stresses through the thickness, and a discrete layer theory. The combination of the following four key elements distinguishes the present study from previous studies reported in the literature: (1) the standard of comparison is taken to be the solutions obtained by using three-dimensional continuum models for each of the individual layers; (2) both mechanical and thermal loadings are considered; (3) boundary conditions other than simply supported edges are considered; and (4) quantities compared include detailed through-the-thickness distributions of transverse shear and transverse normal stresses. Based on the numerical studies conducted, the predictor-corrector approach appears to be the most effective technique for obtaining accurate transverse stresses, and for thermal loading, none of the two-dimensional models is adequate for calculating transverse normal stresses, even when used in conjunction with three-dimensional equilibrium equations.

A 3-dimensional mass conserving element for compressible flows

NASA Technical Reports Server (NTRS)

Fix, G.; Suri, M.

1985-01-01

A variety of finite element schemes has been used in the numerical approximation of compressible flows particularly in underwater acoustics. In many instances instabilities have been generated due to the lack of mass conservation. Two- and three-dimensional elements are developed which avoid these problems.

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Jiang, Yi-Tsann

1993-01-01

A general solution adaptive scheme-based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Jiang, Yi-Tsann; Usab, William J., Jr.

1993-01-01

A general solution adaptive scheme based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

Translation and integration of numerical atomic orbitals in linear molecules

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

Heinäsmäki, Sami, E-mail: sami.heinasmaki@gmail.com

2014-02-14

We present algorithms for translation and integration of atomic orbitals for LCAO calculations in linear molecules. The method applies to arbitrary radial functions given on a numerical mesh. The algorithms are based on pseudospectral differentiation matrices in two dimensions and the corresponding two-dimensional Gaussian quadratures. As a result, multicenter overlap and Coulomb integrals can be evaluated effectively.

Fractional calculus phenomenology in two-dimensional plasma models

NASA Astrophysics Data System (ADS)

Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill

2006-10-01

Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).

Numerical Limitations of 1D Hydraulic Models Using MIKE11 or HEC-RAS software - Case study of Baraolt River, Romania

NASA Astrophysics Data System (ADS)

Andrei, Armas; Robert, Beilicci; Erika, Beilicci

2017-10-01

MIKE 11 is an advanced hydroinformatic tool, a professional engineering software package for simulation of one-dimensional flows in estuaries, rivers, irrigation systems, channels and other water bodies. MIKE 11 is a 1-dimensional river model. It was developed by DHI Water · Environment · Health, Denmark. The basic computational procedure of HEC-RAS for steady flow is based on the solution of the one-dimensional energy equation. Energy losses are evaluated by friction and contraction / expansion. The momentum equation may be used in situations where the water surface profile is rapidly varied. These situations include hydraulic jumps, hydraulics of bridges, and evaluating profiles at river confluences. For unsteady flow, HEC-RAS solves the full, dynamic, 1-D Saint Venant Equation using an implicit, finite difference method. The unsteady flow equation solver was adapted from Dr. Robert L. Barkau’s UNET package. Fluid motion is controlled by the basic principles of conservation of mass, energy and momentum, which form the basis of fluid mechanics and hydraulic engineering. Complex flow situations must be solved using empirical approximations and numerical models, which are based on derivations of the basic principles (backwater equation, Navier-Stokes equation etc.). All numerical models are required to make some form of approximation to solve these principles, and consequently all have their limitations. The study of hydraulics and fluid mechanics is founded on the three basic principles of conservation of mass, energy and momentum. Real-life situations are frequently too complex to solve without the aid of numerical models. There is a tendency among some engineers to discard the basic principles taught at university and blindly assume that the results produced by the model are correct. Regardless of the complexity of models and despite the claims of their developers, all numerical models are required to make approximations. These may be related to geometric limitations, numerical simplification, or the use of empirical correlations. Some are obvious: one-dimensional models must average properties over the two remaining directions. It is the less obvious and poorly advertised approximations that pose the greatest threat to the novice user. Some of these, such as the inability of one-dimensional unsteady models to simulate supercritical flow can cause significant inaccuracy in the model predictions.

Structure and Dynamics of the Solar Corona

NASA Technical Reports Server (NTRS)

Schnack, D. D.

1994-01-01

Advanced computational techniques were used to study solar coronal heating and coronal mass ejections. A three dimensional, time dependent resistive magnetohydrodynamic code was used to study the dynamic response of a model corona to continuous, slow, random magnetic footpoint displacements in the photosphere. Three dimensional numerical simulations of the response of the corona to simple smooth braiding flows in the photosphere were calculated to illustrate and understand the spontaneous formation of current filaments. Two dimensional steady state helmet streamer configurations were obtained by determining the time asymptotic state of the interaction of an initially one dimensinal transponic solar wind with a spherical potential dipole field. The disruption of the steady state helmet streamer configuration was studied as a response to shearing of the magnetic footpoints of the closed field lines under the helmet.

Analytical three-dimensional neutron transport benchmarks for verification of nuclear engineering codes. Final report

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

Ganapol, B.D.; Kornreich, D.E.

Because of the requirement of accountability and quality control in the scientific world, a demand for high-quality analytical benchmark calculations has arisen in the neutron transport community. The intent of these benchmarks is to provide a numerical standard to which production neutron transport codes may be compared in order to verify proper operation. The overall investigation as modified in the second year renewal application includes the following three primary tasks. Task 1 on two dimensional neutron transport is divided into (a) single medium searchlight problem (SLP) and (b) two-adjacent half-space SLP. Task 2 on three-dimensional neutron transport covers (a) pointmore » source in arbitrary geometry, (b) single medium SLP, and (c) two-adjacent half-space SLP. Task 3 on code verification, includes deterministic and probabilistic codes. The primary aim of the proposed investigation was to provide a suite of comprehensive two- and three-dimensional analytical benchmarks for neutron transport theory applications. This objective has been achieved. The suite of benchmarks in infinite media and the three-dimensional SLP are a relatively comprehensive set of one-group benchmarks for isotropically scattering media. Because of time and resource limitations, the extensions of the benchmarks to include multi-group and anisotropic scattering are not included here. Presently, however, enormous advances in the solution for the planar Green`s function in an anisotropically scattering medium have been made and will eventually be implemented in the two- and three-dimensional solutions considered under this grant. Of particular note in this work are the numerical results for the three-dimensional SLP, which have never before been presented. The results presented were made possible only because of the tremendous advances in computing power that have occurred during the past decade.« less

Investigation of the complex electroviscous effects on electrolyte (single and multiphase) flow in porous medi.

NASA Astrophysics Data System (ADS)

Bolet, A. J. S.; Linga, G.; Mathiesen, J.

2017-12-01

Surface charge is an important control parameter for wall-bounded flow of electrolyte solution. The electroviscous effect has been studied theoretically in model geometries such as infinite capillaries. However, in more complex geometries a quantification of the electroviscous effect is a non-trival task due to strong non-linarites of the underlying equations. In general, one has to rely on numerical methods. Here we present numerical studies of the full three-dimensional steady state Stokes-Poisson-Nernst-Planck problem in order to model electrolyte transport in artificial porous samples. The simulations are performed using the finite element method. From the simulation, we quantity how the electroviscous effect changes the general flow permeability in complex three-dimensional porous media. The porous media we consider are mostly generated artificially by connecting randomly dispersed cylindrical pores. Furthermore, we present results of electric driven two-phase immiscible flow in two dimensions. The simulations are performed by augmenting the above equations with a phase field model to handle and track the interaction between the two fluids (using parameters corresponding to oil-water interfaces, where oil non-polar). In particular, we consider the electro-osmotic effect on imbibition due to charged walls and electrolyte-solution.

A Numerical Study of Cirrus Clouds. Part I: Model Description.

NASA Astrophysics Data System (ADS)

Liu, Hui-Chun; Wang, Pao K.; Schlesinger, Robert E.

2003-04-01

This article, the first of a two-part series, presents a detailed description of a two-dimensional numerical cloud model directed toward elucidating the physical processes governing the evolution of cirrus clouds. The two primary scientific purposes of this work are (a) to determine the evolution and maintenance mechanisms of cirrus clouds and try to explain why some cirrus can persist for a long time; and (b) to investigate the influence of certain physical factors such as radiation, ice crystal habit, latent heat, ventilation effects, and aggregation mechanisms on the evolution of cirrus. The second part will discuss sets of model experiments that were run to address objectives (a) and (b), respectively.As set forth in this paper, the aforementioned two-dimensional numerical model, which comprises the research tool for this study, is organized into three modules that embody dynamics, microphysics, and radiation. The dynamic module develops a set of equations to describe shallow moist convection, also parameterizing turbulence by using a 1.5-order closure scheme. The microphysical module uses a double-moment scheme to simulate the evolution of the size distribution of ice particles. Heterogeneous and homogeneous nucleation of haze particles are included, along with other ice crystal processes such as diffusional growth, sedimentation, and aggregation. The radiation module uses a two-stream radiative transfer scheme to determine the radiative fluxes and heating rates, while the cloud optical properties are determined by the modified anomalous diffraction theory (MADT) for ice particles. One of the main advantages of this cirrus model is its explicit formulation of the microphysical and radiative properties as functions of ice crystal habit.

EFFECTS OF ELECTROOSMOSIS ON SOIL TEMPERATURE AND HYDRAULIC HEAD: II. NUMERICAL SIMULATION

EPA Science Inventory

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...

Boundary shape identification problems in two-dimensional domains related to thermal testing of materials

NASA Technical Reports Server (NTRS)

Banks, H. T.; Kojima, Fumio

1988-01-01

The identification of the geometrical structure of the system boundary for a two-dimensional diffusion system is reported. The domain identification problem treated here is converted into an optimization problem based on a fit-to-data criterion and theoretical convergence results for approximate identification techniques are discussed. Results of numerical experiments to demonstrate the efficacy of the theoretical ideas are reported.

Long-time states of inverse cascades in the presence of a maximum length scale

NASA Technical Reports Server (NTRS)

Hossain, M.; Matthaeus, W. H.; Montgomery, D.

1983-01-01

It is shown numerically, both for the two-dimensional Navier-Stokes (guiding-center plasma) equations and for two-dimensional magnetohydrodynamics, that the long-time asymptotic state in a forced inverse-cascade situation is one in which the spectrum is completely dominated by its own fundamental. The growth continues until the fundamental is dissipatively limited by its own dissipation rate.

A two-dimensional finite-difference solution for the temperature distribution in a radial gas turbine guide vane blade

NASA Technical Reports Server (NTRS)

Hosny, W. M.; Tabakoff, W.

1975-01-01

A two-dimensional finite difference numerical technique is presented to determine the temperature distribution in a solid blade of a radial guide vane. A computer program is written in Fortran IV for IBM 370/165 computer. The computer results obtained from these programs have a similar behavior and trend as those obtained by experimental results.

A nominally second-order cell-centered Lagrangian scheme for simulating elastic-plastic flows on two-dimensional unstructured grids

NASA Astrophysics Data System (ADS)

Maire, Pierre-Henri; Abgrall, Rémi; Breil, Jérôme; Loubère, Raphaël; Rebourcet, Bernard

2013-02-01

In this paper, we describe a cell-centered Lagrangian scheme devoted to the numerical simulation of solid dynamics on two-dimensional unstructured grids in planar geometry. This numerical method, utilizes the classical elastic-perfectly plastic material model initially proposed by Wilkins [M.L. Wilkins, Calculation of elastic-plastic flow, Meth. Comput. Phys. (1964)]. In this model, the Cauchy stress tensor is decomposed into the sum of its deviatoric part and the thermodynamic pressure which is defined by means of an equation of state. Regarding the deviatoric stress, its time evolution is governed by a classical constitutive law for isotropic material. The plasticity model employs the von Mises yield criterion and is implemented by means of the radial return algorithm. The numerical scheme relies on a finite volume cell-centered method wherein numerical fluxes are expressed in terms of sub-cell force. The generic form of the sub-cell force is obtained by requiring the scheme to satisfy a semi-discrete dissipation inequality. Sub-cell force and nodal velocity to move the grid are computed consistently with cell volume variation by means of a node-centered solver, which results from total energy conservation. The nominally second-order extension is achieved by developing a two-dimensional extension in the Lagrangian framework of the Generalized Riemann Problem methodology, introduced by Ben-Artzi and Falcovitz [M. Ben-Artzi, J. Falcovitz, Generalized Riemann Problems in Computational Fluid Dynamics, Cambridge Monogr. Appl. Comput. Math. (2003)]. Finally, the robustness and the accuracy of the numerical scheme are assessed through the computation of several test cases.

Robust Multigrid Smoothers for Three Dimensional Elliptic Equations with Strong Anisotropies

NASA Technical Reports Server (NTRS)

Llorente, Ignacio M.; Melson, N. Duane

1998-01-01

We discuss the behavior of several plane relaxation methods as multigrid smoothers for the solution of a discrete anisotropic elliptic model problem on cell-centered grids. The methods compared are plane Jacobi with damping, plane Jacobi with partial damping, plane Gauss-Seidel, plane zebra Gauss-Seidel, and line Gauss-Seidel. Based on numerical experiments and local mode analysis, we compare the smoothing factor of the different methods in the presence of strong anisotropies. A four-color Gauss-Seidel method is found to have the best numerical and architectural properties of the methods considered in the present work. Although alternating direction plane relaxation schemes are simpler and more robust than other approaches, they are not currently used in industrial and production codes because they require the solution of a two-dimensional problem for each plane in each direction. We verify the theoretical predictions of Thole and Trottenberg that an exact solution of each plane is not necessary and that a single two-dimensional multigrid cycle gives the same result as an exact solution, in much less execution time. Parallelization of the two-dimensional multigrid cycles, the kernel of the three-dimensional implicit solver, is also discussed. Alternating-plane smoothers are found to be highly efficient multigrid smoothers for anisotropic elliptic problems.

A three-dimensional dual potential procedure with applications to wind tunnel inlets and interacting boundary layers

NASA Technical Reports Server (NTRS)

Rao, K. V.; Pletcher, R. H.; Steger, J. L.; Vandalsem, W. R.

1987-01-01

A dual potential decomposition of the velocity field into a scalar and a vector potential function is extended to three dimensions and used in the finite-difference simulation of steady three-dimensional inviscid rotational flows and viscous flow. The finite-difference procedure was used to simulate the flow through the 80 by 120 ft wind tunnel at NASA Ames Research Center. Rotational flow produced by the stagnation pressure drop across vanes and screens which are located at the entrance of the inlet is modeled using actuator disk theory. Results are presented for two different inlet vane and screen configurations. The numerical predictions are in good agreement with experimental data. The dual potential procedure was also applied to calculate the viscous flow along two and three dimensional troughs. Viscous effects are simulated by injecting vorticity which is computed from a boundary layer algorithm. For attached flow over a three dimensional trough, the present calculations are in good agreement with other numerical predictions. For separated flow, it is shown from a two dimensional analysis that the boundary layer approximation provides an accurate measure of the vorticity in regions close to the wall; whereas further away from the wall, caution has to be exercised in using the boundary-layer equations to supply vorticity to the dual potential formulation.

A modelling approach to vaccination and contraception programmes for rabies control in fox populations.

PubMed Central

Suppo, C; Naulin, J M; Langlais, M; Artois, M

2000-01-01

In a previous study, three of the authors designed a one-dimensional model to simulate the propagation of rabies within a growing fox population; the influence of various parameters on the epidemic model was studied, including oral-vaccination programmes. In this work, a two-dimensional model of a fox population having either an exponential or a logistic growth pattern was considered. Using numerical simulations, the efficiencies of two prophylactic methods (fox contraception and vaccination against rabies) were assessed, used either separately or jointly. It was concluded that far lower rates of administration are necessary to eradicate rabies, and that the undesirable side-effects of each programme disappear, when both are used together. PMID:11007334

Ameba-like diffusion in two-dimensional polymer melts: how critical exponents determine the structural relaxation

NASA Astrophysics Data System (ADS)

Kreer, Torsten; Meyer, Hendrik; Baschnagel, Joerg

2008-03-01

By means of numerical investigations we demonstrate that the structural relaxation of linear polymers in two dimensional (space-filling) melts is characterized by ameba-like diffusion, where the chains relax via frictional dissipation at their interfacial contact lines. The perimeter length of the contact line determines a new length scale, which does not exist in three dimensions. We show how this length scale follows from the critical exponents, which hence characterize not only the static but also the dynamic properties of the melt. Our data is in agreement with recent theoretical predictions, concerning the time-dependence of single-monomer mean-square displacements and the scaling of concomitant relaxation times with the degree of polymerization. For the latter we demonstrate a density crossover-scaling as an additional test for ameba-like relaxation. We compare our results to the conceptually different Rouse model, which predicts numerically close exponents. Our data can clearly rule out the classical picture as the relevant relaxation mechanism in two-dimensional polymer melts.

Nature of self-diffusion in two-dimensional fluids

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

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

Nature of self-diffusion in two-dimensional fluids

DOE PAGES

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; ...

2017-12-18

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

Cratering mechanics

NASA Technical Reports Server (NTRS)

Ivanov, B. A.

1986-01-01

Main concepts and theoretical models which are used for studying the mechanics of cratering are discussed. Numerical two-dimensional calculations are made of explosions near a surface and high-speed impact. Models are given for the motion of a medium during cratering. Data from laboratory modeling are given. The effect of gravitational force and scales of cratering phenomena is analyzed.

Assessment of Static Delamination Propagation Capabilities in Commercial Finite Element Codes Using Benchmark Analysis

NASA Technical Reports Server (NTRS)

Orifici, Adrian C.; Krueger, Ronald

2010-01-01

With capabilities for simulating delamination growth in composite materials becoming available, the need for benchmarking and assessing these capabilities is critical. In this study, benchmark analyses were performed to assess the delamination propagation simulation capabilities of the VCCT implementations in Marc TM and MD NastranTM. Benchmark delamination growth results for Double Cantilever Beam, Single Leg Bending and End Notched Flexure specimens were generated using a numerical approach. This numerical approach was developed previously, and involves comparing results from a series of analyses at different delamination lengths to a single analysis with automatic crack propagation. Specimens were analyzed with three-dimensional and two-dimensional models, and compared with previous analyses using Abaqus . The results demonstrated that the VCCT implementation in Marc TM and MD Nastran(TradeMark) was capable of accurately replicating the benchmark delamination growth results and that the use of the numerical benchmarks offers advantages over benchmarking using experimental and analytical results.

A numerical study of coarsening in the two-dimensional complex Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Liu, Weigang; Tauber, Uwe

The complex Ginzburg-Landau equation with additive noise is a stochastic partial differential equation that describes a remarkably wide range of physical systems: coupled non-linear oscillators subject to external noise near a Hopf bifurcation instability; spontaneous structure formation in non-equilibrium systems, e.g., in cyclically competing populations; and driven-dissipative Bose-Einstein condensation, realized in open systems on the interface of quantum optics and many-body physics. We employ a finite-difference method to numerically solve the noisy complex Ginzburg-Landau equation on a two-dimensional domain with the goal to investigate the coarsening dynamics following a quench from a strongly fluctuating defect turbulence phase to a long-range ordered phase. We start from a simplified amplitude equation, solve it numerically, and then study the spatio-temporal behavior characterized by the spontaneous creation and annihilation of topological defects (spiral waves). We check our simulation results against the known dynamical phase diagram in this non-equilibrium system, tentatively analyze the coarsening kinetics following sudden quenches, and characterize the ensuing aging scaling behavior. In addition, we aim to use Voronoi triangulation to study the cellular structure in the phase turbulence and frozen states. This research is supported by the U. S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering under Award DE-FG02-09ER46613.

Carbon nanotube thin film strain sensors: comparison between experimental tests and numerical simulations

NASA Astrophysics Data System (ADS)

Lee, Bo Mi; Loh, Kenneth J.

2017-04-01

Carbon nanotubes can be randomly deposited in polymer thin film matrices to form nanocomposite strain sensors. However, a computational framework that enables the direct design of these nanocomposite thin films is still lacking. The objective of this study is to derive an experimentally validated and two-dimensional numerical model of carbon nanotube-based thin film strain sensors. This study consisted of two parts. First, multi-walled carbon nanotube (MWCNT)-Pluronic strain sensors were fabricated using vacuum filtration, and their physical, electrical, and electromechanical properties were evaluated. Second, scanning electron microscope images of the films were used for identifying topological features of the percolated MWCNT network, where the information obtained was then utilized for developing the numerical model. Validation of the numerical model was achieved by ensuring that the area ratios (of MWCNTs relative to the polymer matrix) were equivalent for both the experimental and modeled cases. Strain sensing behavior of the percolation-based model was simulated and then compared to experimental test results.

Numerical solution of 2D-vector tomography problem using the method of approximate inverse

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

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.

Nonlinearity-dependent asymmetric transmission in a sawtooth photonic lattice with defects

NASA Astrophysics Data System (ADS)

Ji, Kaiwen; Qi, Xinyuan; Li, Shasha; Han, Kun; Wen, Zengrun; Zhang, Guoquan; Bai, Jintao

2018-04-01

We study both theoretically and numerically the asymetric transmission of a Gaussian beam in a two-dimensional nonlinear sawtooth lattice with two defects. The results show that quasi-total reflection, asymmetric propagation and asymmetric reflection can all be achieved in such a system by adjusting the input intensity, the magnitude of defects and the number of nonlinear waveguides. This study may provide a new way to realize an optical switch and optical diode.

Neural Network Machine Learning and Dimension Reduction for Data Visualization

NASA Technical Reports Server (NTRS)

Liles, Charles A.

2014-01-01

Neural network machine learning in computer science is a continuously developing field of study. Although neural network models have been developed which can accurately predict a numeric value or nominal classification, a general purpose method for constructing neural network architecture has yet to be developed. Computer scientists are often forced to rely on a trial-and-error process of developing and improving accurate neural network models. In many cases, models are constructed from a large number of input parameters. Understanding which input parameters have the greatest impact on the prediction of the model is often difficult to surmise, especially when the number of input variables is very high. This challenge is often labeled the "curse of dimensionality" in scientific fields. However, techniques exist for reducing the dimensionality of problems to just two dimensions. Once a problem's dimensions have been mapped to two dimensions, it can be easily plotted and understood by humans. The ability to visualize a multi-dimensional dataset can provide a means of identifying which input variables have the highest effect on determining a nominal or numeric output. Identifying these variables can provide a better means of training neural network models; models can be more easily and quickly trained using only input variables which appear to affect the outcome variable. The purpose of this project is to explore varying means of training neural networks and to utilize dimensional reduction for visualizing and understanding complex datasets.

Numerical solutions of 2-D multi-stage rotor/stator unsteady flow interactions

NASA Astrophysics Data System (ADS)

Yang, R.-J.; Lin, S.-J.

1991-01-01

The Rai method of single-stage rotor/stator flow interaction is extended to handle multistage configurations. In this study, a two-dimensional Navier-Stokes multi-zone approach was used to investigate unsteady flow interactions within two multistage axial turbines. The governing equations are solved by an iterative, factored, implicit finite-difference, upwind algorithm. Numerical accuracy is checked by investigating the effect of time step size, the effect of subiteration in the Newton-Raphson technique, and the effect of full viscous versus thin-layer approximation. Computer results compared well with experimental data. Unsteady flow interactions, wake cutting, and the associated evolution of vortical entities are discussed.

Numerical Studies of Three-dimensional Breakdown in Trailing Vortex Wakes

NASA Technical Reports Server (NTRS)

Evans, P. F.; Hackett, J. E.

1976-01-01

Finite element, three dimensional relaxation methods are used to calculate the development of vortex wakes behind aircraft for a considerable downstream distance. The inclusion of a self-induction term in the solution, dependent upon local curvature and vortex core radius, permits calculation of finite lifetimes for systems for which infinite life would be predicted two dimensionally. The associated computer program is described together with single-pair, twin-pair, and multiple-pair studies carried out using it. It is found, in single-pair studies, that there is a lower limit to the wavelengths at which the Crow-type of instability can occur. Below this limit, self-induction effects cause the plane of the disturbance waves to rotate counter to the vortex direction. Self induction in two dimensionally generated twin spiral waves causes an increase in axial length which becomes more marked with decreasing initial wavelength. The time taken for vortex convergence toward the center plane is correspondingly increased. The limited parametric twin-pair study performed suggests that time-to-converge increases with increasing flap span. Limited studies of Boeing 747 configurations show correct qualitative response to removal of the outer flap and to gear deployment, as compared with wind tunnel and flight test experience.

Three-dimensional cellular deformation analysis with a two-photon magnetic manipulator workstation.

PubMed

Huang, Hayden; Dong, Chen Y; Kwon, Hyuk-Sang; Sutin, Jason D; Kamm, Roger D; So, Peter T C

2002-04-01

The ability to apply quantifiable mechanical stresses at the microscopic scale is critical for studying cellular responses to mechanical forces. This necessitates the use of force transducers that can apply precisely controlled forces to cells while monitoring the responses noninvasively. This paper describes the development of a micromanipulation workstation integrating two-photon, three-dimensional imaging with a high-force, uniform-gradient magnetic manipulator. The uniform-gradient magnetic field applies nearly uniform forces to a large cell population, permitting statistical quantification of select molecular responses to mechanical stresses. The magnetic transducer design is capable of exerting over 200 pN of force on 4.5-microm-diameter paramagnetic particles and over 800 pN on 5.0-microm ferromagnetic particles. These forces vary within +/-10% over an area 500 x 500 microm2. The compatibility with the use of high numerical aperture (approximately 1.0) objectives is an integral part of the workstation design allowing submicron-resolution, three-dimensional, two-photon imaging. Three-dimensional analyses of cellular deformation under localized mechanical strain are reported. These measurements indicate that the response of cells to large focal stresses may contain three-dimensional global deformations and show the suitability of this workstation to further studying cellular response to mechanical stresses.

Reaction-Infiltration Instabilities in Fractured and Porous Rocks

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

Ladd, Anthony

In this project we are developing a multiscale analysis of the evolution of fracture permeability, using numerical simulations and linear stability analysis. Our simulations include fully three-dimensional simulations of the fracture topography, fluid flow, and reactant transport, two-dimensional simulations based on aperture models, and linear stability analysis.

Three-dimensional numerical modeling of water quality and sediment-associated processes in natural lakes

USDA-ARS?s Scientific Manuscript database

This chapter presents the development and application of a three-dimensional water quality model for predicting the distributions of nutrients, phytoplankton, dissolved oxygen, etc., in natural lakes. In this model, the computational domain was divided into two parts: the water column and the bed se...

Semiclassical propagation of Wigner functions.

PubMed

Dittrich, T; Gómez, E A; Pachón, L A

2010-06-07

We present a comprehensive study of semiclassical phase-space propagation in the Wigner representation, emphasizing numerical applications, in particular as an initial-value representation. Two semiclassical approximation schemes are discussed. The propagator of the Wigner function based on van Vleck's approximation replaces the Liouville propagator by a quantum spot with an oscillatory pattern reflecting the interference between pairs of classical trajectories. Employing phase-space path integration instead, caustics in the quantum spot are resolved in terms of Airy functions. We apply both to two benchmark models of nonlinear molecular potentials, the Morse oscillator and the quartic double well, to test them in standard tasks such as computing autocorrelation functions and propagating coherent states. The performance of semiclassical Wigner propagation is very good even in the presence of marked quantum effects, e.g., in coherent tunneling and in propagating Schrodinger cat states, and of classical chaos in four-dimensional phase space. We suggest options for an effective numerical implementation of our method and for integrating it in Monte-Carlo-Metropolis algorithms suitable for high-dimensional systems.

Lorentz force particle analyzer

NASA Astrophysics Data System (ADS)

Wang, Xiaodong; Thess, André; Moreau, René; Tan, Yanqing; Dai, Shangjun; Tao, Zhen; Yang, Wenzhi; Wang, Bo

2016-07-01

A new contactless technique is presented for the detection of micron-sized insulating particles in the flow of an electrically conducting fluid. A transverse magnetic field brakes this flow and tends to become entrained in the flow direction by a Lorentz force, whose reaction force on the magnetic-field-generating system can be measured. The presence of insulating particles suspended in the fluid produce changes in this Lorentz force, generating pulses in it; these pulses enable the particles to be counted and sized. A two-dimensional numerical model that employs a moving mesh method demonstrates the measurement principle when such a particle is present. Two prototypes and a three-dimensional numerical model are used to demonstrate the feasibility of a Lorentz force particle analyzer (LFPA). The findings of this study conclude that such an LFPA, which offers contactless and on-line quantitative measurements, can be applied to an extensive range of applications. These applications include measurements of the cleanliness of high-temperature and aggressive molten metal, such as aluminum and steel alloys, and the clean manufacturing of semiconductors.

Numerical study of the flow in a three-dimensional thermally driven cavity

NASA Astrophysics Data System (ADS)

Rauwoens, Pieter; Vierendeels, Jan; Merci, Bart

2008-06-01

Solutions for the fully compressible Navier-Stokes equations are presented for the flow and temperature fields in a cubic cavity with large horizontal temperature differences. The ideal-gas approximation for air is assumed and viscosity is computed using Sutherland's law. The three-dimensional case forms an extension of previous studies performed on a two-dimensional square cavity. The influence of imposed boundary conditions in the third dimension is investigated as a numerical experiment. Comparison is made between convergence rates in case of periodic and free-slip boundary conditions. Results with no-slip boundary conditions are presented as well. The effect of the Rayleigh number is studied. Results are computed using a finite volume method on a structured, collocated grid. An explicit third-order discretization for the convective part and an implicit central discretization for the acoustic part and for the diffusive part are used. To stabilize the scheme an artificial dissipation term for the pressure and the temperature is introduced. The discrete equations are solved using a time-marching method with restrictions on the timestep corresponding to the explicit parts of the solver. Multigrid is used as acceleration technique.

Common aero vehicle autonomous reentry trajectory optimization satisfying waypoint and no-fly zone constraints

NASA Astrophysics Data System (ADS)

Jorris, Timothy R.

2007-12-01

To support the Air Force's Global Reach concept, a Common Aero Vehicle is being designed to support the Global Strike mission. "Waypoints" are specified for reconnaissance or multiple payload deployments and "no-fly zones" are specified for geopolitical restrictions or threat avoidance. Due to time critical targets and multiple scenario analysis, an autonomous solution is preferred over a time-intensive, manually iterative one. Thus, a real-time or near real-time autonomous trajectory optimization technique is presented to minimize the flight time, satisfy terminal and intermediate constraints, and remain within the specified vehicle heating and control limitations. This research uses the Hypersonic Cruise Vehicle (HCV) as a simplified two-dimensional platform to compare multiple solution techniques. The solution techniques include a unique geometric approach developed herein, a derived analytical dynamic optimization technique, and a rapidly emerging collocation numerical approach. This up-and-coming numerical technique is a direct solution method involving discretization then dualization, with pseudospectral methods and nonlinear programming used to converge to the optimal solution. This numerical approach is applied to the Common Aero Vehicle (CAV) as the test platform for the full three-dimensional reentry trajectory optimization problem. The culmination of this research is the verification of the optimality of this proposed numerical technique, as shown for both the two-dimensional and three-dimensional models. Additionally, user implementation strategies are presented to improve accuracy and enhance solution convergence. Thus, the contributions of this research are the geometric approach, the user implementation strategies, and the determination and verification of a numerical solution technique for the optimal reentry trajectory problem that minimizes time to target while satisfying vehicle dynamics and control limitation, and heating, waypoint, and no-fly zone constraints.

Oil adsorption ability of three-dimensional epicuticular wax coverages in plants

NASA Astrophysics Data System (ADS)

Gorb, Elena V.; Hofmann, Philipp; Filippov, Alexander E.; Gorb, Stanislav N.

2017-04-01

Primary aerial surfaces of terrestrial plants are very often covered with three-dimensional epicuticular waxes. Such wax coverages play an important role in insect-plant interactions. Wax blooms have been experimentally shown in numerous previous studies to be impeding locomotion and reducing attachment of insects. Among the mechanisms responsible for these effects, a possible adsorption of insect adhesive fluid by highly porous wax coverage has been proposed (adsorption hypothesis). Recently, a great decrease in insect attachment force on artificial adsorbing materials was revealed in a few studies. However, adsorption ability of plant wax blooms was still not tested. Using a cryo scanning electron microscopy approach and high-speed video recordings of fluid drops behavior, followed by numerical analysis of experimental data, we show here that the three-dimensional epicuticular wax coverage in the waxy zone of Nepenthes alata pitcher adsorbs oil: we detected changes in the base, height, and volume of the oil drops. The wax layer thickness, differing in samples with untreated two-layered wax coverage and treated one-layered wax, did not significantly affect the drop behavior. These results provide strong evidence that three-dimensional plant wax coverages due to their adsorption capability are in general anti-adhesive for insects, which rely on wet adhesion.

Numerical study on wave loads and motions of two ships advancing in waves by using three-dimensional translating-pulsating source

NASA Astrophysics Data System (ADS)

Xu, Yong; Dong, Wen-Cai

2013-08-01

A frequency domain analysis method based on the three-dimensional translating-pulsating (3DTP) source Green function is developed to investigate wave loads and free motions of two ships advancing on parallel course in waves. Two experiments are carried out respectively to measure the wave loads and the freemotions for a pair of side-byside arranged ship models advancing with an identical speed in head regular waves. For comparison, each model is also tested alone. Predictions obtained by the present solution are found in favorable agreement with the model tests and are more accurate than the traditional method based on the three dimensional pulsating (3DP) source Green function. Numerical resonances and peak shift can be found in the 3DP predictions, which result from the wave energy trapped in the gap between two ships and the extremely inhomogeneous wave load distribution on each hull. However, they can be eliminated by 3DTP, in which the speed affects the free surface and most of the wave energy can be escaped from the gap. Both the experiment and the present prediction show that hydrodynamic interaction effects on wave loads and free motions are significant. The present solver may serve as a validated tool to predict wave loads and motions of two vessels under replenishment at sea, and may help to evaluate the hydrodynamic interaction effects on the ships safety in replenishment operation.

Wave-induced response of a floating two-dimensional body with a moonpool.

PubMed

Fredriksen, Arnt G; Kristiansen, Trygve; Faltinsen, Odd M

2015-01-28

Regular wave-induced behaviour of a floating stationary two-dimensional body with a moonpool is studied. The focus is on resonant piston-mode motion in the moonpool and rigid-body motions. Dedicated two-dimensional experiments have been performed. Two numerical hybrid methods, which have previously been applied to related problems, are further developed. Both numerical methods couple potential and viscous flow. The semi-nonlinear hybrid method uses linear free-surface and body-boundary conditions. The other one uses fully nonlinear free-surface and body-boundary conditions. The harmonic polynomial cell method solves the Laplace equation in the potential flow domain, while the finite volume method solves the Navier-Stokes equations in the viscous flow domain near the body. Results from the two codes are compared with the experimental data. The nonlinear hybrid method compares well with the data, while certain discrepancies are observed for the semi-nonlinear method. In particular, the roll motion is over-predicted by the semi-nonlinear hybrid method. Error sources in the semi-nonlinear hybrid method are discussed. The moonpool strongly affects heave motions in a frequency range around the piston-mode resonance frequency of the moonpool. No resonant water motions occur in the moonpool at the piston-mode resonance frequency. Instead large moonpool motions occur at a heave natural frequency associated with small damping near the piston-mode resonance frequency. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Freels, J. D.

1989-01-01

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

PIFEX: An advanced programmable pipelined-image processor

NASA Technical Reports Server (NTRS)

Gennery, D. B.; Wilcox, B.

1985-01-01

PIFEX is a pipelined-image processor being built in the JPL Robotics Lab. It will operate on digitized raster-scanned images (at 60 frames per second for images up to about 300 by 400 and at lesser rates for larger images), performing a variety of operations simultaneously under program control. It thus is a powerful, flexible tool for image processing and low-level computer vision. It also has applications in other two-dimensional problems such as route planning for obstacle avoidance and the numerical solution of two-dimensional partial differential equations (although its low numerical precision limits its use in the latter field). The concept and design of PIFEX are described herein, and some examples of its use are given.

A second-order accurate kinetic-theory-based method for inviscid compressible flows

NASA Technical Reports Server (NTRS)

Deshpande, Suresh M.

1986-01-01

An upwind method for the numerical solution of the Euler equations is presented. This method, called the kinetic numerical method (KNM), is based on the fact that the Euler equations are moments of the Boltzmann equation of the kinetic theory of gases when the distribution function is Maxwellian. The KNM consists of two phases, the convection phase and the collision phase. The method is unconditionally stable and explicit. It is highly vectorizable and can be easily made total variation diminishing for the distribution function by a suitable choice of the interpolation strategy. The method is applied to a one-dimensional shock-propagation problem and to a two-dimensional shock-reflection problem.

Three-dimensional Numerical Simulations of Rayleigh-Taylor Unstable Flames in Type Ia Supernovae

NASA Astrophysics Data System (ADS)

Zingale, M.; Woosley, S. E.; Rendleman, C. A.; Day, M. S.; Bell, J. B.

2005-10-01

Flame instabilities play a dominant role in accelerating the burning front to a large fraction of the speed of sound in a Type Ia supernova. We present a three-dimensional numerical simulation of a Rayleigh-Taylor unstable carbon flame, following its evolution through the transition to turbulence. A low-Mach number hydrodynamics method is used, freeing us from the harsh time step restrictions imposed by sound waves. We fully resolve the thermal structure of the flame and its reaction zone, eliminating the need for a flame model. A single density is considered, 1.5×107 g cm-3, and half-carbon, half-oxygen fuel: conditions under which the flame propagated in the flamelet regime in our related two-dimensional study. We compare to a corresponding two-dimensional simulation and show that while fire polishing keeps the small features suppressed in two dimensions, turbulence wrinkles the flame on far smaller scales in the three-dimensional case, suggesting that the transition to the distributed burning regime occurs at higher densities in three dimensions. Detailed turbulence diagnostics are provided. We show that the turbulence follows a Kolmogorov spectrum and is highly anisotropic on the large scales, with a much larger integral scale in the direction of gravity. Furthermore, we demonstrate that it becomes more isotropic as it cascades down to small scales. On the basis of the turbulent statistics and the flame properties of our simulation, we compute the Gibson scale. We show the progress of the turbulent flame through a classic combustion regime diagram, indicating that the flame just enters the distributed burning regime near the end of our simulation.

Ejection mechanisms in the sublayer of a turbulent channel

NASA Technical Reports Server (NTRS)

Jimenez, Javier; Moin, P.; Moser, R.; Keefe, L.

1988-01-01

The structure of the vorticity field in the viscous wall layer of a turbulent channel is studied by examining the results of a fully resolved direct numerical simulation. It is shown that this region is dominated by intense three-dimensional shear layers in which the dominant vorticity component is spanwise. The advection and reproduction processes of these structures are examined and shown to be consistent with the classical generation mechanism for two-dimensional Tollmien-Schlichting waves. This process is fundamentally different from the usually accepted mechanism involving hairpin vortices.

Two-dimensional solitons in conservative and parity-time-symmetric triple-core waveguides with cubic-quintic nonlinearity

NASA Astrophysics Data System (ADS)

Feijoo, David; Zezyulin, Dmitry A.; Konotop, Vladimir V.

2015-12-01

We analyze a system of three two-dimensional nonlinear Schrödinger equations coupled by linear terms and with the cubic-quintic (focusing-defocusing) nonlinearity. We consider two versions of the model: conservative and parity-time (PT ) symmetric. These models describe triple-core nonlinear optical waveguides, with balanced gain and losses in the PT -symmetric case. We obtain families of soliton solutions and discuss their stability. The latter study is performed using a linear stability analysis and checked with direct numerical simulations of the evolutional system of equations. Stable solitons are found in the conservative and PT -symmetric cases. Interactions and collisions between the conservative and PT -symmetric solitons are briefly investigated, as well.

A time-implicit numerical method and benchmarks for the relativistic Vlasov–Ampere equations

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

Carrie, Michael; Shadwick, B. A.

2016-01-04

Here, we present a time-implicit numerical method to solve the relativistic Vlasov–Ampere system of equations on a two dimensional phase space grid. The time-splitting algorithm we use allows the generalization of the work presented here to higher dimensions keeping the linear aspect of the resulting discrete set of equations. The implicit method is benchmarked against linear theory results for the relativistic Landau damping for which analytical expressions using the Maxwell-Juttner distribution function are derived. We note that, independently from the shape of the distribution function, the relativistic treatment features collective behaviors that do not exist in the non relativistic case.more » The numerical study of the relativistic two-stream instability completes the set of benchmarking tests.« less

A Comparison of Numerical and Analytical Radiative-Transfer Solutions for Plane Albedo of Natural Waters

EPA Science Inventory

Three numerical algorithms were compared to provide a solution of a radiative transfer equation (RTE) for plane albedo (hemispherical reflectance) in semi-infinite one-dimensional plane-parallel layer. Algorithms were based on the invariant imbedding method and two different var...

Numerical studies of nonspherical carbon combustion models

NASA Astrophysics Data System (ADS)

Mueller, E.; Arnett, W. D.

1982-10-01

First results of axisymmetric numerical studies of the final evolution of degenerate C + O cores are reported. The two-dimensional convective flow is treated without a phenomenological theory of convection. The computations show that, in the beginning, the nuclear burning propagates slowly outward from the center of the star in a spherical combustion front. Small-scale eddies form, giving rise to bumps in the front. The bumps grow into blobs and eventually into fingers, which steadily elongate relative to the rest of the combustion front. This behavior is not well described by either the detonation or deflagration models, being more complex than either.

Dynamics of one- and two-dimensional fronts in a bistable equation with time-delayed global feedback: Propagation failure and control mechanisms

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

Boubendir, Yassine; Mendez, Vicenc; Rotstein, Horacio G.

2010-09-15

We study the evolution of fronts in a bistable equation with time-delayed global feedback in the fast reaction and slow diffusion regime. This equation generalizes the Hodgkin-Grafstein and Allen-Cahn equations. We derive a nonlinear equation governing the motion of fronts, which includes a term with delay. In the one-dimensional case this equation is linear. We study the motion of one- and two-dimensional fronts, finding a much richer dynamics than for the previously studied cases (without time-delayed global feedback). We explain the mechanism by which localized fronts created by inhibitory global coupling loose stability in a Hopf bifurcation as the delaymore » time increases. We show that for certain delay times, the prevailing phase is different from that corresponding to the system in the absence of global coupling. Numerical simulations of the partial differential equation are in agreement with the analytical predictions.« less

Spinon confinement in a quasi-one-dimensional XXZ Heisenberg antiferromagnet

NASA Astrophysics Data System (ADS)

Lake, Bella; Bera, Anup K.; Essler, Fabian H. L.; Vanderstraeten, Laurens; Hubig, Claudius; Schollwock, Ulrich; Islam, A. T. M. Nazmul; Schneidewind, Astrid; Quintero-Castro, Diana L.

Half-integer spin Heisenberg chains constitute a key paradigm for quantum number fractionalization: flipping a spin creates a minimum of two elementary spinon excitations. These have been observed in numerous experiments. We report on inelastic neutron scattering experiments on the quasi-one-dimensional anisotropic spin-1/2 Heisenberg antiferromagnet SrCo2V2O8. These reveal a mechanism for temperature-induced spinon confinement, manifesting itself in the formation of sequences of spinon bound states. A theoretical description of this effect is achieved by a combination of analytical and numerical methods.

Schramm-Loewner (SLE) analysis of quasi two-dimensional turbulent flows

NASA Astrophysics Data System (ADS)

Thalabard, Simon

2012-02-01

Quasi two-dimensional turbulence can be observed in several cases: for example, in the laboratory using liquid soap films, or as the result of a strong imposed rotation as obtained in three-dimensional large direct numerical simulations. We study and contrast SLE properties of such flows, in the former case in the inverse cascade of energy to large scale, and in the latter in the direct cascade of energy to small scales in the presence of a fully-helical forcing. We thus examine the geometric properties of these quasi 2D regimes in the context of stochastic geometry, as was done for the 2D inverse cascade by Bernard et al. (2006). We show that in both cases the data is compatible with self-similarity and with SLE behaviors, whose different diffusivities can be heuristically determined.

Three-Dimensional Upward Flame Spreading in Partial-Gravity Buoyant Flows

NASA Technical Reports Server (NTRS)

Sacksteder, Kurt R.; Feier, Ioan I.; Shih, Hsin-Yi; T'ien, James S.

2001-01-01

Reduced-gravity environments have been used to establish low-speed, purely forced flows for both opposed- and concurrent-flow flame spread studies. Altenkirch's group obtained spacebased experimental results and developed unsteady, two-dimensional numerical simulations of opposed-flow flame spread including gas-phase radiation, primarily away from the flammability limit for thin fuels, but including observations of thick fuel quenching in quiescent environments. T'ien's group contributed some early flame spreading results for thin fuels both in opposed flow and concurrent flow regimes, with more focus on near-limit conditions. T'ien's group also developed two- and three-dimensional numerical simulations of concurrent-flow flame spread incorporating gas-phase radiative models, including predictions of a radiatively-induced quenching limit reached in very low-speed air flows. Radiative quenching has been subsequently observed in other studies of combustion in very low-speed flows including other flame spread investigations, droplet combustion and homogeneous diffusion flames, and is the subject of several contemporary studies reported in this workshop. Using NASA aircraft flying partial-gravity "parabolic" trajectories, flame spreading in purely buoyant, opposed-flow (downward burning) has been studied. These results indicated increases in flame spread rates and enhanced flammability (lower limiting atmospheric oxygen content) as gravity levels were reduced from normal Earth gravity, and were consistent with earlier data obtained by Altenkirch using a centrifuge. In this work, experimental results and a three-dimensional numerical simulation of upward flame spreading in variable partial-gravity environments were obtained including some effects of reduced pressure and variable sample width. The simulation provides physical insight for interpreting the experimental results and shows the intrinsic 3-D nature of buoyant, upward flame spreading. This study is intended to link the evolving understanding of flame spreading in purely-forced flows to the purely-buoyant flow environment, particularly in the concurrent flow regime; provide additional insight into the existence of steady flame spread in concurrent flows; and stimulate direct comparisons between opposed- and concurrent-flow flame spread. Additionally, this effort is intended to provide direct practical understanding applicable to fire protection planning for the habitable facilities in partial gravity environments of anticipated Lunar and Martian explorations.

Uniform high order spectral methods for one and two dimensional Euler equations

NASA Technical Reports Server (NTRS)

Cai, Wei; Shu, Chi-Wang

1991-01-01

Uniform high order spectral methods to solve multi-dimensional Euler equations for gas dynamics are discussed. Uniform high order spectral approximations with spectral accuracy in smooth regions of solutions are constructed by introducing the idea of the Essentially Non-Oscillatory (ENO) polynomial interpolations into the spectral methods. The authors present numerical results for the inviscid Burgers' equation, and for the one dimensional Euler equations including the interactions between a shock wave and density disturbance, Sod's and Lax's shock tube problems, and the blast wave problem. The interaction between a Mach 3 two dimensional shock wave and a rotating vortex is simulated.

Effects of the approximations of light propagation on quantitative photoacoustic tomography using two-dimensional photon diffusion equation and linearization

NASA Astrophysics Data System (ADS)

Okawa, Shinpei; Hirasawa, Takeshi; Kushibiki, Toshihiro; Ishihara, Miya

2017-12-01

Quantitative photoacoustic tomography (QPAT) employing a light propagation model will play an important role in medical diagnoses by quantifying the concentration of hemoglobin or a contrast agent. However, QPAT by the light propagation model with the three-dimensional (3D) radiative transfer equation (RTE) requires a huge computational load in the iterative forward calculations involved in the updating process to reconstruct the absorption coefficient. The approximations of the light propagation improve the efficiency of the image reconstruction for the QPAT. In this study, we compared the 3D/two-dimensional (2D) photon diffusion equation (PDE) approximating 3D RTE with the Monte Carlo simulation based on 3D RTE. Then, the errors in a 2D PDE-based linearized image reconstruction caused by the approximations were quantitatively demonstrated and discussed in the numerical simulations. It was clearly observed that the approximations affected the reconstructed absorption coefficient. The 2D PDE-based linearized algorithm succeeded in the image reconstruction of the region with a large absorption coefficient in the 3D phantom. The value reconstructed in the phantom experiment agreed with that in the numerical simulation, so that it was validated that the numerical simulation of the image reconstruction predicted the relationship between the true absorption coefficient of the target in the 3D medium and the reconstructed value with the 2D PDE-based linearized algorithm. Moreover, the the true absorption coefficient in 3D medium was estimated from the 2D reconstructed image on the basis of the prediction by the numerical simulation. The estimation was successful in the phantom experiment, although some limitations were revealed.

Gravity-Driven Thin Film Flow of an Ellis Fluid.

PubMed

Kheyfets, Vitaly O; Kieweg, Sarah L

2013-12-01

The thin film lubrication approximation has been studied extensively for moving contact lines of Newtonian fluids. However, many industrial and biological applications of the thin film equation involve shear-thinning fluids, which often also exhibit a Newtonian plateau at low shear. This study presents new numerical simulations of the three-dimensional (i.e. two-dimensional spreading), constant-volume, gravity-driven, free surface flow of an Ellis fluid. The numerical solution was validated with a new similarity solution, compared to previous experiments, and then used in a parametric study. The parametric study centered around rheological data for an example biological application of thin film flow: topical drug delivery of anti-HIV microbicide formulations, e.g. hydroxyethylcellulose (HEC) polymer solutions. The parametric study evaluated how spreading length and front velocity saturation depend on Ellis parameters. A lower concentration polymer solution with smaller zero shear viscosity ( η 0 ), τ 1/2 , and λ values spread further. However, when comparing any two fluids with any possible combinations of Ellis parameters, the impact of changing one parameter on spreading length depends on the direction and magnitude of changes in the other two parameters. In addition, the isolated effect of the shear-thinning parameter, λ , on the front velocity saturation depended on τ 1/2 . This study highlighted the relative effects of the individual Ellis parameters, and showed that the shear rates in this flow were in both the shear-thinning and plateau regions of rheological behavior, emphasizing the importance of characterizing the full range of shear-rates in rheological measurements. The validated numerical model and parametric study provides a useful tool for future steps to optimize flow of a fluid with rheological behavior well-described by the Ellis constitutive model, in a range of industrial and biological applications.

Multiple steady solutions in a driven cavity

NASA Astrophysics Data System (ADS)

Osman, Kahar; McHugh, John

2004-11-01

The symmetric driven cavity (Farias and McHugh, Phys. Fluids, 2002) in two and three dimensions is considered. Results are obtained via numerical computations of the Navier-Stokes equations, assuming constant density. The numerical algorithm is a splitting method, using finite differences. The forcing at the top is sinusoidal, and the forcing wavelength is allowed to vary in subsequent trials. The two dimensional results with 2, 4, and 6 oscillations in the forcing show a subcritical bifurcation to an asymmetric solution, with the Reynolds number as the important parameter. The symmetric solution is found to have vortex flow with streamlines that conform to the boundary shape. The asymmetric solution has vortex flow with streamlines that are approximately circular near the vortex center. Two dimensional results with 8 or more oscillations in the forcing show a supercritical bifurcation to an asymmetric solution. Three dimensional simulations show that the length ratios play a critical role, and the depth of the cavity must be large compared to the height in order to acheive the same subcritical bifurcation as with two dimensions.

Experimental and numerical studies on three dimensional GTA weld pool convection: Non-axisymmetric effects

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

Joshi, Y.; Dutta, P.; Schupp, P.E.

1995-12-31

Observations of surface flow patterns of steel and aluminum GTAW pools have been made using a pulsed laser visualization system. The weld pool convection is found to be three dimensional, with the azimuthal circulation depending on the location of the clamp with respect to the torch. Oscillation of steel pools and undulating motion in aluminum weld pools are also observed even with steady process parameters. Current axisymmetric numerical models are unable to explain such phenomena. A three dimensional computational study is carried out in this study to explain the rotational flow in aluminum weld pools.

Buckling of a growing tissue and the emergence of two-dimensional patterns☆

PubMed Central

Nelson, M.R.; King, J.R.; Jensen, O.E.

2013-01-01

The process of biological growth and the associated generation of residual stress has previously been considered as a driving mechanism for tissue buckling and pattern selection in numerous areas of biology. Here, we develop a two-dimensional thin plate theory to simulate the growth of cultured intestinal epithelial cells on a deformable substrate, with the goal of elucidating how a tissue engineer might best recreate the regular array of invaginations (crypts of Lieberkühn) found in the wall of the mammalian intestine. We extend the standard von Kármán equations to incorporate inhomogeneity in the plate’s mechanical properties and surface stresses applied to the substrate by cell proliferation. We determine numerically the configurations of a homogeneous plate under uniform cell growth, and show how tethering to an underlying elastic foundation can be used to promote higher-order buckled configurations. We then examine the independent effects of localised softening of the substrate and spatial patterning of cellular growth, demonstrating that (within a two-dimensional framework, and contrary to the predictions of one-dimensional models) growth patterning constitutes a more viable mechanism for control of crypt distribution than does material inhomogeneity. PMID:24128749

Buckling of a growing tissue and the emergence of two-dimensional patterns.

PubMed

Nelson, M R; King, J R; Jensen, O E

2013-12-01

The process of biological growth and the associated generation of residual stress has previously been considered as a driving mechanism for tissue buckling and pattern selection in numerous areas of biology. Here, we develop a two-dimensional thin plate theory to simulate the growth of cultured intestinal epithelial cells on a deformable substrate, with the goal of elucidating how a tissue engineer might best recreate the regular array of invaginations (crypts of Lieberkühn) found in the wall of the mammalian intestine. We extend the standard von Kármán equations to incorporate inhomogeneity in the plate's mechanical properties and surface stresses applied to the substrate by cell proliferation. We determine numerically the configurations of a homogeneous plate under uniform cell growth, and show how tethering to an underlying elastic foundation can be used to promote higher-order buckled configurations. We then examine the independent effects of localised softening of the substrate and spatial patterning of cellular growth, demonstrating that (within a two-dimensional framework, and contrary to the predictions of one-dimensional models) growth patterning constitutes a more viable mechanism for control of crypt distribution than does material inhomogeneity. Copyright © 2013 Elsevier Inc. All rights reserved.

Two-Dimensional Failure Waves and Ignition Fronts in Premixed Combustion

NASA Technical Reports Server (NTRS)

Vedarajan, T. G.; Buckmaster J.; Ronney, P.

1998-01-01

This paper is a continuation of our work on edge-flames in premixed combustion. An edge-flame is a two-dimensional structure constructed from a one-dimensional configuration that has two stable solutions (bistable equilibrium). Edge-flames can display wavelike behavior, advancing as ignition fronts or retreating as failure waves. Here we consider two one-dimensional configurations: twin deflagrations in a straining flow generated by the counterflow of fresh streams of mixture: and a single deflagration subject to radiation losses. The edge-flames constructed from the first configuration have positive or negative speeds, according to the value of the strain rate. But our numerical solutions strongly suggest that only positive speeds (corresponding to ignition fronts) can exist for the second configuration. We show that this phenomenon can also occur in diffusion flames when the Lewis numbers are small. And we discuss the asymptotics of the one-dimensional twin deflagration configuration. an overlooked problem from the 70s.

STAN5: A program for numerical computation of two-dimensional internal and external boundary layer flows

NASA Technical Reports Server (NTRS)

Crawford, M. E.; Kays, W. M.

1976-01-01

A large variety of two dimensional flows can be accommodated by the program, including boundary layers on a flat plate, flow inside nozzles and diffusers (for a prescribed potential flow distribution), flow over axisymmetric bodies, and developing and fully developed flow inside circular pipes and flat ducts. The flows may be laminar or turbulent, and provision is made to handle transition.

Simulation of confined magnetohydrodynamic flows with Dirichlet boundary conditions using a pseudo-spectral method with volume penalization

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

Morales, Jorge A.; Leroy, Matthieu; Bos, Wouter J.T.

A volume penalization approach to simulate magnetohydrodynamic (MHD) flows in confined domains is presented. Here the incompressible visco-resistive MHD equations are solved using parallel pseudo-spectral solvers in Cartesian geometries. The volume penalization technique is an immersed boundary method which is characterized by a high flexibility for the geometry of the considered flow. In the present case, it allows to use other than periodic boundary conditions in a Fourier pseudo-spectral approach. The numerical method is validated and its convergence is assessed for two- and three-dimensional hydrodynamic (HD) and MHD flows, by comparing the numerical results with results from literature and analyticalmore » solutions. The test cases considered are two-dimensional Taylor–Couette flow, the z-pinch configuration, three dimensional Orszag–Tang flow, Ohmic-decay in a periodic cylinder, three-dimensional Taylor–Couette flow with and without axial magnetic field and three-dimensional Hartmann-instabilities in a cylinder with an imposed helical magnetic field. Finally, we present a magnetohydrodynamic flow simulation in toroidal geometry with non-symmetric cross section and imposing a helical magnetic field to illustrate the potential of the method.« less

Lattice Wigner equation.

PubMed

Solórzano, S; Mendoza, M; Succi, S; Herrmann, H J

2018-01-01

We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.

Electroelastic fields in a layered piezoelectric cylindrical shell under dynamic load

NASA Astrophysics Data System (ADS)

Saviz, M. R.; Shakeri, M.; Yas, M. H.

2007-10-01

The objective of this paper is to demonstrate layerwise theory for the analysis of thick laminated piezoelectric shell structures. A general finite element formulation using the layerwise theory is developed for a laminated cylindrical shell with piezoelectric layers, subjected to dynamic loads. The quadratic approximation of the displacement and electric potential in the thickness direction is considered. The governing equations are reduced to two-dimensional (2D) differential equations. The three-dimensional (3D) elasticity solution is also presented. The resulting equations are solved by a proper finite element method. The numerical results for static loading are compared with exact solutions of benchmark problems. Numerical examples of the dynamic problem are presented. The convergence is studied, as is the influence of the electromechanical coupling on the axisymmetric free-vibration characteristics of a thick cylinder.

Lattice Wigner equation

NASA Astrophysics Data System (ADS)

Solórzano, S.; Mendoza, M.; Succi, S.; Herrmann, H. J.

2018-01-01

We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.

Localization and mobility edges in one-dimensional deterministic potentials

NASA Astrophysics Data System (ADS)

Tong, Peiqing

1994-10-01

In this paper, we study the localization properties of the wave function of a one-dimensional tight-binding electron moving in an asymptotic periodic potential, Vn=λ cos(2πQn+παnν), where n is the site index and 0<ν<1. For Q rational, the electronic energy band consists of many subbands, and the number of subbands is determined by Q. For λ<2, there are two mobility edges where the eigenstates at the subband center are all extended, whereas the subband-edge states are all localized in every subband. We develop some heuristic arguments to calculate exactly the mobility edges for this model and carry out numerical work to study the localization properties of the model. Our theoretical results are essentially in exact agreement with the numerical results. We calculate the critical exponents δ and β at mobility edges. We also study the nature of the localized, extended eigenstates and mobility edges of this system as a function of λ, α, and ν.

3DFEMWATER/3DLEWASTE: NUMERICAL CODES FOR DELINEATING WELLHEAD PROTECTION AREAS IN AGRICULTURAL REGIONS BASED ON THE ASSIMILATIVE CAPACITY CRITERION

EPA Science Inventory

Two related numerical codes, 3DFEMWATER and 3DLEWASTE, are presented sed to delineate wellhead protection areas in agricultural regions using the assimilative capacity criterion. DFEMWATER (Three-dimensional Finite Element Model of Water Flow Through Saturated-Unsaturated Media) ...

SURFACTANT ENHANCED RECOVERY OF TETRACHLOROETHYLENE FROM A POROUS MEDIUM CONTAINING LOW PERMEABILITY LENSES. 2. NUMERICAL SIMULATION. (R825409)

EPA Science Inventory

Abstract

A numerical model of surfactant enhanced solubilization was developed and applied to the simulation of nonaqueous phase liquid recovery in two-dimensional heterogeneous laboratory sand tank systems. Model parameters were derived from independent, small-scale, ...

Streamline integration as a method for two-dimensional elliptic grid generation

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

Wiesenberger, M., E-mail: Matthias.Wiesenberger@uibk.ac.at; Held, M.; Einkemmer, L.

We propose a new numerical algorithm to construct a structured numerical elliptic grid of a doubly connected domain. Our method is applicable to domains with boundaries defined by two contour lines of a two-dimensional function. Furthermore, we can adapt any analytically given boundary aligned structured grid, which specifically includes polar and Cartesian grids. The resulting coordinate lines are orthogonal to the boundary. Grid points as well as the elements of the Jacobian matrix can be computed efficiently and up to machine precision. In the simplest case we construct conformal grids, yet with the help of weight functions and monitor metricsmore » we can control the distribution of cells across the domain. Our algorithm is parallelizable and easy to implement with elementary numerical methods. We assess the quality of grids by considering both the distribution of cell sizes and the accuracy of the solution to elliptic problems. Among the tested grids these key properties are best fulfilled by the grid constructed with the monitor metric approach. - Graphical abstract: - Highlights: • Construct structured, elliptic numerical grids with elementary numerical methods. • Align coordinate lines with or make them orthogonal to the domain boundary. • Compute grid points and metric elements up to machine precision. • Control cell distribution by adaption functions or monitor metrics.« less

Numerical Model of Flame Spread Over Solids in Microgravity: A Supplementary Tool for Designing a Space Experiment

NASA Technical Reports Server (NTRS)

Shih, Hsin-Yi; Tien, James S.; Ferkul, Paul (Technical Monitor)

2001-01-01

The recently developed numerical model of concurrent-flow flame spread over thin solids has been used as a simulation tool to help the designs of a space experiment. The two-dimensional and three-dimensional, steady form of the compressible Navier-Stokes equations with chemical reactions are solved. With the coupled multi-dimensional solver of the radiative heat transfer, the model is capable of answering a number of questions regarding the experiment concept and the hardware designs. In this paper, the capabilities of the numerical model are demonstrated by providing the guidance for several experimental designing issues. The test matrix and operating conditions of the experiment are estimated through the modeling results. The three-dimensional calculations are made to simulate the flame-spreading experiment with realistic hardware configuration. The computed detailed flame structures provide the insight to the data collection. In addition, the heating load and the requirements of the product exhaust cleanup for the flow tunnel are estimated with the model. We anticipate that using this simulation tool will enable a more efficient and successful space experiment to be conducted.

Numerical simulation of drop impact on a thin film: the origin of the droplets in the splashing regime

NASA Astrophysics Data System (ADS)

Xie, Zhihua; Che, Zhizhao; Ismail, Renad; Pain, Chris; Matar, Omar

2015-11-01

Drop impact on a liquid layer is a feature of numerous multiphase flow problems, and has been the subject of numerous theoretical, experimental and numerical investigations. In the splashing regime, however, little attention has been focused on the origin of the droplets that are formed during the splashing process. The objective of this study is to investigate this issue numerically in order to improve our understanding of the mechanisms underlying splashing as a function of the relevant system parameters. In contrast to the conventional two-phase flow approach, commonly used to simulate splashing, here, a three-dimensional, three-phase flow model, with adaptive, unstructured meshing, is employed to study the liquid (droplet) - gas (surrounding air) - liquid (thin film) system. In the cases to be presented, both liquid phases have the same fluid property, although, clearly, our method can be used in the more general case of two different liquids. Numerical results of droplet impact on a thin film are analysed to determine whether the origin of the droplets following impact corresponds to the mother drop, or the thin film, or both. EPSRC Programme Grant, MEMPHIS, EP/K0039761/1.

Energy-level repulsion by spin-orbit coupling in two-dimensional Rydberg excitons

NASA Astrophysics Data System (ADS)

Stephanovich, V. A.; Sherman, E. Ya.; Zinner, N. T.; Marchukov, O. V.

2018-05-01

We study the effects of Rashba spin-orbit coupling on two-dimensional Rydberg exciton systems. Using analytical and numerical arguments we demonstrate that this coupling considerably modifies the wave functions and leads to a level repulsion that results in a deviation from the Poissonian statistics of the adjacent level distance distribution. This signifies the crossover to nonintegrability of the system and hints at the possibility of quantum chaos emerging. Such behavior strongly differs from the classical realization, where spin-orbit coupling produces highly entangled, chaotic electron trajectories in an exciton. We also calculate the oscillator strengths and show that randomization appears in the transitions between states with different total momenta.

Drag of two-dimensional small-amplitude symmetric and asymmetric wavy walls in turbulent boundary layers

NASA Technical Reports Server (NTRS)

Lin, J. C.; Walsh, M. J.; Balasubramanian, R.

1984-01-01

Included are results of an experimental investigation of low-speed turbulent flow over multiple two-dimensional transverse rigid wavy surfaces having a wavelength on the order of the boundary-layer thickness. Data include surface pressure and total drag measurements on symmetric and asymmetric wall waves under a low-speed turbulent boundary-layer flow. Several asymmetric wave configurations exhibited drag levels below the equivalent symmetric (sine) wave. The experimental results compare favorably with numerical predictions from a Reynolds-averaged Navier-Stokes spectral code. The reported results are of particular interest for the estimation of drag, the minimization of fabrication waviness effects, and the study of wind-wave interactions.

The flashing Brownian ratchet and Parrondo's paradox.

PubMed

Ethier, S N; Lee, Jiyeon

2018-01-01

A Brownian ratchet is a one-dimensional diffusion process that drifts towards a minimum of a periodic asymmetric sawtooth potential. A flashing Brownian ratchet is a process that alternates between two regimes, a one-dimensional Brownian motion and a Brownian ratchet, producing directed motion. These processes have been of interest to physicists and biologists for nearly 25 years. The flashing Brownian ratchet is the process that motivated Parrondo's paradox, in which two fair games of chance, when alternated, produce a winning game. Parrondo's games are relatively simple, being discrete in time and space. The flashing Brownian ratchet is rather more complicated. We show how one can study the latter process numerically using a random walk approximation.

Application of finite difference techniques to noise propagation in jet engine ducts

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1973-01-01

A finite difference formulation is presented for wave propagation in a rectangular two-dimensional duct without steady flow. The difference technique, which should be used in the study of acoustically treated inlet and exhausts ducts used in turbofan engines, can readily handle acoustical flow field complications such as axial variations in wall impedance and cross-section area. In the numerical analysis, the continuous acoustic field is lumped into a series of grid points in which the pressure and velocity at each grid point are separated into real and imaginary terms. An example calculation is also presented for the sound attenuation in a two-dimensional straight soft-walled suppressor.

Application of finite difference techniques to noise propagation in jet engine ducts

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1973-01-01

A finite difference formulation is presented for wave propagation in a rectangular two-dimensional duct without steady flow. The difference technique, which should be useful in the study of acoustically treated inlet and exhausts ducts used in turbofan engines, can readily handle acoustical flow field complications such as axial variations in wall impedance and cross section area. In the numerical analysis, the continuous acoustic field is lumped into a series of grid points in which the pressure and velocity at each grid point are separated into real and imaginary terms. An example calculation is also presented for the sound attenuation in a two-dimensional straight soft-walled suppressor.

Time-accurate simulations of a shear layer forced at a single frequency

NASA Technical Reports Server (NTRS)

Claus, R. W.; Huang, P. G.; Macinnes, J. M.

1988-01-01

Calculations are presented for the forced shear layer studied experimentally by Oster and Wygnanski, and Weisbrot. Two different computational approaches are examined: Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES). The DNS approach solves the full three dimensional Navier-Stokes equations for a temporally evolving mixing layer, while the LES approach solves the two dimensional Navier-Stokes equations with a subgrid scale turbulence model. While the comparison between these calculations and experimental data was hampered by a lack of information on the inflow boundary conditions, the calculations are shown to qualitatively agree with several aspects of the experiment. The sensitivity of these calculations to factors such as mesh refinement and Reynolds number is illustrated.

Morphodynamic Responses of a River-Floodplain System to a Chute Cutoff: Numerical Experiments to Investigate the Role of Multiple Active Factors

NASA Astrophysics Data System (ADS)

Li, Z.; Garcia, M. H.

2017-12-01

Unlike neck cutoffs, which are caused by meander migration to an over-mature stage, a chute cutoff is governed by many more factors. A chute cutoff always occurs when there is over-bank flow caused by floods. During this process, the river-floodplain system characteristics will determine the newly formed cutoff channel location and extent. Hence, a comprehensive study of the influence which different active factors have on a cutoff channel is necessary. Numerical experiments are well suited in this case because of the possibility of studying a large number of scenarios and also the practical and econocmical challenges of collecting high quality data during floods in the field. Numerical simulations were performed using the open TELEMAC-MASCARET modeling suite, which can solve the two-dimensional Shallow Water Equations, the three-dimensional, Reynolds-averaged Navier-Stokes equations (RANS). It can also be coupled with sediment transport equations. It is implemented on unstructured meshes using the Finite Element Method (FEM). The modeling results show the great detail the morphodynamic response attributed to each active factor (flow magnitude, sediment erosive properties, channel sinuosity, etc.), as well as paving the way and showing how to use the dimensionless relations obtained with the numerical experiments.

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

Kaufman, Allan N.; Tracy, Eugene R.; Brizard, Alain J.

The process of resonant wave conversion (often called linear mode conversion) has traditionally been analyzed with a spatially one-dimensional slab model, for which the rays propagate in a two-dimensional phase space. However, it has recently been shown [E. R. Tracy and A. N. Kaufman, Phys. Rev. Lett. 91, 130402 (2003)] that multidimensional rays have a helical structure for conversion in two or more spatial dimensions (if their dispersion matrix is generic). In that case, a one-dimensional model is inadequate; a correct analysis requires two spatial dimensions and, thus, four-dimensional phase space. A cold-plasma model is introduced in this paper whichmore » exhibits ray helicity in conversion regions where the density and magnetic field gradients are significantly nonparallel. For illustration, such regions are identified in a model of the poloidal plane of a deuterium-tritium tokamak plasma. In each conversion region, characterized by a six-sector topology, rays in the sector for incident and reflected magnetosonic waves exhibit significant helicity. A detailed analytic and numerical study of helical rays in this sector is developed for a 'symmetric-wedge' model.« less

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

Kaufman, Allan N.; Tracy, Eugene R.; Brizard, Alain J.

The process of resonant wave conversion (often called linear mode conversion) has traditionally been analyzed with a spatially one-dimensional slab model, for which the rays propagate in a two-dimensional phase space. However, it has recently been shown [E.R. Tracy and A.N. Kaufman, Phys. Rev. Lett. 91, 130402 (2003)] that multidimensional rays have a helical structure for conversion in two or more spatial dimensions (if their dispersion matrix is generic). In that case, a one-dimensional model is inadequate; a correct analysis requires two spatial dimensions and, thus, four-dimensional phase space. In this paper we show that a cold plasma model willmore » exhibit ray helicity in conversion regions where the density and magnetic field gradients are significantly non-parallel. For illustration, we examine a model of the poloidal plane of a deuterium-tritium tokamak plasma, and identify such a region. In this region, characterized by a six-sector topology, rays in the sector for incident and reflected magnetosonic waves exhibit significant helicity. We introduce a ''symmetric-wedge'' model, to develop a detailed analytic and numerical study of helical rays in this sector.« less

The effects of detailed chemistry and transport on microgravity droplet combustion

NASA Technical Reports Server (NTRS)

Marchese, A. J.; Lee, J. C.; Held, T. J.; Dryer, F. L.

1995-01-01

A brief overview of recent advances in the theoretical study of microgravity droplet combustion is presented. Much of this work has centered on the development and utilization of sphero-symmetric transient numerical models which consider detailed gas phase chemistry and transport as well as energy and/or species transport within a regressing condensed phase. Numerical results for microgravity combustion and vaporization of methanol, methanol/water, heptane, and heptane/hexadecane droplets are summarized along with refinements in chemical kinetics and the development of a new two-dimensional axi-symmetric model.

Numerical simulation of two-dimensional Rayleigh-Benard convection

NASA Astrophysics Data System (ADS)

Grigoriev, Vasiliy V.; Zakharov, Petr E.

2017-11-01

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

Coupled boundary and finite element analysis of vibration from railway tunnels—a comparison of two- and three-dimensional models

NASA Astrophysics Data System (ADS)

Andersen, L.; Jones, C. J. C.

2006-06-01

The analysis of vibration from railway tunnels is of growing interest as new and higher-speed railways are built under the ground to address the transport problems of growing modern urban areas. Such analysis can be carried out using numerical methods but models and therefore computing times can be large. There is a need to be able to apply very fast calculations that can be used in tunnel design and studies of environmental impacts. Taking advantage of the fact that tunnels often have a two-dimensional geometry in the sense that the cross section is constant along the tunnel axis, it is useful to evaluate the potential uses of two-dimensional models before committing to much more costly three-dimensional approaches. The vibration forces in the track due to the passage of a train are by nature three-dimensional and a complete analysis undoubtedly requires a model of three-dimensional wave propagation. The aim of this paper is to investigate the quality of the information that can be gained from a two-dimensional model of a railway tunnel. The vibration transmission from the tunnel floor to the ground surface is analysed for the frequency range relevant to the perception of whole body vibration (about 4-80 Hz). A coupled finite element and boundary element scheme is applied in both two and three dimensions. Two tunnel designs are considered: a cut-and-cover tunnel for a double track and a single-track tunnel dug with the New Austrian tunnelling method (NATM).

Phase diagram of two-dimensional hard rods from fundamental mixed measure density functional theory

NASA Astrophysics Data System (ADS)

Wittmann, René; Sitta, Christoph E.; Smallenburg, Frank; Löwen, Hartmut

2017-10-01

A density functional theory for the bulk phase diagram of two-dimensional orientable hard rods is proposed and tested against Monte Carlo computer simulation data. In detail, an explicit density functional is derived from fundamental mixed measure theory and freely minimized numerically for hard discorectangles. The phase diagram, which involves stable isotropic, nematic, smectic, and crystalline phases, is obtained and shows good agreement with the simulation data. Our functional is valid for a multicomponent mixture of hard particles with arbitrary convex shapes and provides a reliable starting point to explore various inhomogeneous situations of two-dimensional hard rods and their Brownian dynamics.

Robust PRNG based on homogeneously distributed chaotic dynamics

NASA Astrophysics Data System (ADS)

Garasym, Oleg; Lozi, René; Taralova, Ina

2016-02-01

This paper is devoted to the design of new chaotic Pseudo Random Number Generator (CPRNG). Exploring several topologies of network of 1-D coupled chaotic mapping, we focus first on two dimensional networks. Two topologically coupled maps are studied: TTL rc non-alternate, and TTL SC alternate. The primary idea of the novel maps has been based on an original coupling of the tent and logistic maps to achieve excellent random properties and homogeneous /uniform/ density in the phase plane, thus guaranteeing maximum security when used for chaos base cryptography. In this aim two new nonlinear CPRNG: MTTL 2 sc and NTTL 2 are proposed. The maps successfully passed numerous statistical, graphical and numerical tests, due to proposed ring coupling and injection mechanisms.

Numerical investigation of fluid mud motion using a three-dimensional hydrodynamic and two-dimensional fluid mud coupling model

NASA Astrophysics Data System (ADS)

Yang, Xiaochen; Zhang, Qinghe; Hao, Linnan

2015-03-01

A water-fluid mud coupling model is developed based on the unstructured grid finite volume coastal ocean model (FVCOM) to investigate the fluid mud motion. The hydrodynamics and sediment transport of the overlying water column are solved using the original three-dimensional ocean model. A horizontal two-dimensional fluid mud model is integrated into the FVCOM model to simulate the underlying fluid mud flow. The fluid mud interacts with the water column through the sediment flux, current, and shear stress. The friction factor between the fluid mud and the bed, which is traditionally determined empirically, is derived with the assumption that the vertical distribution of shear stress below the yield surface of fluid mud is identical to that of uniform laminar flow of Newtonian fluid in the open channel. The model is validated by experimental data and reasonable agreement is found. Compared with numerical cases with fixed friction factors, the results simulated with the derived friction factor exhibit the best agreement with the experiment, which demonstrates the necessity of the derivation of the friction factor.

Graphical and Numerical Descriptive Analysis: Exploratory Tools Applied to Vietnamese Data

ERIC Educational Resources Information Center

Haughton, Dominique; Phong, Nguyen

2004-01-01

This case study covers several exploratory data analysis ideas, the histogram and boxplot, kernel density estimates, the recently introduced bagplot--a two-dimensional extension of the boxplot--as well as the violin plot, which combines a boxplot with a density shape plot. We apply these ideas and demonstrate how to interpret the output from these…

Multi-dimensional high order essentially non-oscillatory finite difference methods in generalized coordinates

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

1992-01-01

The nonlinear stability of compact schemes for shock calculations is investigated. In recent years compact schemes were used in various numerical simulations including direct numerical simulation of turbulence. However to apply them to problems containing shocks, one has to resolve the problem of spurious numerical oscillation and nonlinear instability. A framework to apply nonlinear limiting to a local mean is introduced. The resulting scheme can be proven total variation (1D) or maximum norm (multi D) stable and produces nice numerical results in the test cases. The result is summarized in the preprint entitled 'Nonlinearly Stable Compact Schemes for Shock Calculations', which was submitted to SIAM Journal on Numerical Analysis. Research was continued on issues related to two and three dimensional essentially non-oscillatory (ENO) schemes. The main research topics include: parallel implementation of ENO schemes on Connection Machines; boundary conditions; shock interaction with hydrogen bubbles, a preparation for the full combustion simulation; and direct numerical simulation of compressible sheared turbulence.

Numerical solution of supersonic three-dimensional free-mixing flows using the parabolic-elliptic Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Hirsh, R. S.

1976-01-01

A numerical method is presented for solving the parabolic-elliptic Navier-Stokes equations. The solution procedure is applied to three-dimensional supersonic laminar jet flow issuing parallel with a supersonic free stream. A coordinate transformation is introduced which maps the boundaries at infinity into a finite computational domain in order to eliminate difficulties associated with the imposition of free-stream boundary conditions. Results are presented for an approximate circular jet, a square jet, varying aspect ratio rectangular jets, and interacting square jets. The solution behavior varies from axisymmetric to nearly two-dimensional in character. For cases where comparisons of the present results with those obtained from shear layer calculations could be made, agreement was good.

Simulation of wave propagation in three-dimensional random media

NASA Technical Reports Server (NTRS)

Coles, William A.; Filice, J. P.; Frehlich, R. G.; Yadlowsky, M.

1993-01-01

Quantitative error analysis for simulation of wave propagation in three dimensional random media assuming narrow angular scattering are presented for the plane wave and spherical wave geometry. This includes the errors resulting from finite grid size, finite simulation dimensions, and the separation of the two-dimensional screens along the propagation direction. Simple error scalings are determined for power-law spectra of the random refractive index of the media. The effects of a finite inner scale are also considered. The spatial spectra of the intensity errors are calculated and compared to the spatial spectra of intensity. The numerical requirements for a simulation of given accuracy are determined for realizations of the field. The numerical requirements for accurate estimation of higher moments of the field are less stringent.

Simplified dragonfly airfoil aerodynamics at Reynolds numbers below 8000

NASA Astrophysics Data System (ADS)

Levy, David-Elie; Seifert, Avraham

2009-07-01

Effective aerodynamics at Reynolds numbers lower than 10 000 is of great technological interest and a fundamental scientific challenge. The current study covers a Reynolds number range of 2000-8000. At these Reynolds numbers, natural insect flight could provide inspiration for technology development. Insect wings are commonly characterized by corrugated airfoils. In particular, the airfoil of the dragonfly, which is able to glide, can be used for two-dimensional aerodynamic study of fixed rigid wings. In this study, a simplified dragonfly airfoil is numerically analyzed in a steady free-stream flow. The aerodynamic performance (such as mean and fluctuating lift and drag), are first compared to a "traditional" low Reynolds number airfoil: the Eppler-E61. The numerical results demonstrate superior performances of the corrugated airfoil. A series of low-speed wind and water tunnel experiments were performed on the corrugated airfoil, to validate the numerical results. The findings indicate quantitative agreement with the mean wake velocity profiles and shedding frequencies while validating the two dimensionality of the flow. A flow physics numerical study was performed in order to understand the underlying mechanism of corrugated airfoils at these Reynolds numbers. Airfoil shapes based on the flow field characteristics of the corrugated airfoil were built and analyzed. Their performances were compared to those of the corrugated airfoil, stressing the advantages of the latter. It was found that the flow which separates from the corrugations and forms spanwise vortices intermittently reattaches to the aft-upper arc region of the airfoil. This mechanism is responsible for the relatively low intensity of the vortices in the airfoil wake, reducing the drag and increasing the flight performances of this kind of corrugated airfoil as compared to traditional low Reynolds number airfoils such as the Eppler E-61.

Two-dimensional patterns in bacterial veils arise from self-generated, three-dimensional fluid flows.

PubMed

Cogan, N G; Wolgemuth, C W

2011-01-01

The behavior of collections of oceanic bacteria is controlled by metabolic (chemotaxis) and physical (fluid motion) processes. Some sulfur-oxidizing bacteria, such as Thiovulum majus, unite these two processes via a material interface produced by the bacteria and upon which the bacteria are transiently attached. This interface, termed a bacterial veil, is formed by exo-polymeric substances (EPS) produced by the bacteria. By adhering to the veil while continuing to rotate their flagella, the bacteria are able to exert force on the fluid surroundings. This behavior induces a fluid flow that, in turn, causes the bacteria to aggregate leading to the formation of a physical pattern in the veil. These striking patterns are very similar in flavor to the classic convection instability observed when a shallow fluid is heated from below. However, the physics are very different since the flow around the veil is mediated by the bacteria and affects the bacterial densities. In this study, we extend a model of a one-dimensional veil in a two-dimensional fluid to the more realistic two-dimensional veil in a three-dimensional fluid. The linear stability analysis indicates that the Peclet number serves as a bifurcation parameter, which is consistent with experimental observations. We also solve the nonlinear problem numerically and are able to obtain patterns that are similar to those observed in the experiments.

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

McHugh, P.R.; Ramshaw, J.D.

MAGMA is a FORTRAN computer code designed to viscous flow in in situ vitrification melt pools. It models three-dimensional, incompressible, viscous flow and heat transfer. The momentum equation is coupled to the temperature field through the buoyancy force terms arising from the Boussinesq approximation. All fluid properties, except density, are assumed variable. Density is assumed constant except in the buoyancy force terms in the momentum equation. A simple melting model based on the enthalpy method allows the study of the melt front progression and latent heat effects. An indirect addressing scheme used in the numerical solution of the momentum equationmore » voids unnecessary calculations in cells devoid of liquid. Two-dimensional calculations can be performed using either rectangular or cylindrical coordinates, while three-dimensional calculations use rectangular coordinates. All derivatives are approximated by finite differences. The incompressible Navier-Stokes equations are solved using a new fully implicit iterative technique, while the energy equation is differenced explicitly in time. Spatial derivatives are written in conservative form using a uniform, rectangular, staggered mesh based on the marker and cell placement of variables. Convective terms are differenced using a weighted average of centered and donor cell differencing to ensure numerical stability. Complete descriptions of MAGMA governing equations, numerics, code structure, and code verification are provided. 14 refs.« less

Dynamics of a neuron model in different two-dimensional parameter-spaces

NASA Astrophysics Data System (ADS)

Rech, Paulo C.

2011-03-01

We report some two-dimensional parameter-space diagrams numerically obtained for the multi-parameter Hindmarsh-Rose neuron model. Several different parameter planes are considered, and we show that regardless of the combination of parameters, a typical scenario is preserved: for all choice of two parameters, the parameter-space presents a comb-shaped chaotic region immersed in a large periodic region. We also show that exist regions close these chaotic region, separated by the comb teeth, organized themselves in period-adding bifurcation cascades.

A nominally second-order cell-centered Lagrangian scheme for simulating elastic–plastic flows on two-dimensional unstructured grids

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

Maire, Pierre-Henri, E-mail: maire@celia.u-bordeaux1.fr; Abgrall, Rémi, E-mail: remi.abgrall@math.u-bordeau1.fr; Breil, Jérôme, E-mail: breil@celia.u-bordeaux1.fr

2013-02-15

In this paper, we describe a cell-centered Lagrangian scheme devoted to the numerical simulation of solid dynamics on two-dimensional unstructured grids in planar geometry. This numerical method, utilizes the classical elastic-perfectly plastic material model initially proposed by Wilkins [M.L. Wilkins, Calculation of elastic–plastic flow, Meth. Comput. Phys. (1964)]. In this model, the Cauchy stress tensor is decomposed into the sum of its deviatoric part and the thermodynamic pressure which is defined by means of an equation of state. Regarding the deviatoric stress, its time evolution is governed by a classical constitutive law for isotropic material. The plasticity model employs themore » von Mises yield criterion and is implemented by means of the radial return algorithm. The numerical scheme relies on a finite volume cell-centered method wherein numerical fluxes are expressed in terms of sub-cell force. The generic form of the sub-cell force is obtained by requiring the scheme to satisfy a semi-discrete dissipation inequality. Sub-cell force and nodal velocity to move the grid are computed consistently with cell volume variation by means of a node-centered solver, which results from total energy conservation. The nominally second-order extension is achieved by developing a two-dimensional extension in the Lagrangian framework of the Generalized Riemann Problem methodology, introduced by Ben-Artzi and Falcovitz [M. Ben-Artzi, J. Falcovitz, Generalized Riemann Problems in Computational Fluid Dynamics, Cambridge Monogr. Appl. Comput. Math. (2003)]. Finally, the robustness and the accuracy of the numerical scheme are assessed through the computation of several test cases.« less

Flow Visualization and Pattern Formation in Vertically Falling Liquid Films

NASA Astrophysics Data System (ADS)

Balakotaiah, Vemuri; Malamataris, Nikolaos

2008-11-01

Analytical results of a low-dimensional two equation h-q model and results of a direct numerical simulation of the transient two-dimensional Navier Stokes equations are presented for vertically falling liquid films along a solid wall. The numerical study aims at the elucidation of the hydrodynamics of the falling film. The analytical study aims at the calculation of the parameter space where pattern formation occurs for this flow. It has been found that when the wave amplitude exceeds a certain magnitude, flow reversal occurs in the film underneath the minimum of the waves [1]. The instantaneous vortical structures possess two hyperbolic points on the vertical wall and an elliptic point in the film. As the wave amplitude increases further, the elliptic point reaches the free surface of the film and two more hyperbolic points are formed in the free surface that replace the elliptic point. Between the two hyperbolic points on the free surface, the streamwise component of velocity is negative and the film is divided into asymmetric patterns of up and down flows. Depending on the value of the Kapitza number, these patterns are either stationary or oscillatory. Physical reasons for the influence of the Kapitza number on pattern formation are given. Movies are shown where the pattern formation is demonstrated. [1] N.A.Malamataris and V.Balakotaiah (2008), AIChE J., 54(7), p. 1725-1740

A numerical experiment that provides new results regarding the inception of separation in the flow around a circular cylinder

NASA Astrophysics Data System (ADS)

Malamataris, Nikolaos; Liakos, Anastasios

2015-11-01

The exact value of the Reynolds number regarding the inception of separation in the flow around a circular cylinder is still a matter of research. This work connects the inception of separation with the calculation of a positive pressure gradient around the circumference of the cylinder. The hypothesis is that inception of separation occurs when the pressure gradient becomes positive around the circumference. From the most cited laboratory experiments that have dealt with that subject of inception of separation only Thom has measured the pressure gradient there at very low Reynolds numbers (up to Re=3.5). For this reason, the experimental conditions of his tunnel are simulated in a new numerical experiment. The full Navier Stokes equations in both two and three dimensions are solved with a home made code that utilizes Galerkin finite elements. In the two dimensional numerical experiment, inception of separation is observed at Re=4.3, which is the lowest Reynolds number where inception has been reported computationally. Currently, the three dimensional experiment is under way, in order to compare if there are effects of three dimensional theory of separation in the conditions of Thom's experiments.

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

NASA Astrophysics Data System (ADS)

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

2016-08-01

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

A new numerical formulation of gas leakage and spread into a residential space in terms of hazard analysis.

PubMed

Nagaosa, Ryuichi S

2014-04-30

This study proposes a new numerical formulation of the spread of a flammable gas leakage. A new numerical approach has been applied to establish fundamental data for a hazard assessment of flammable gas spread in an enclosed residential space. The approach employs an extended version of a two-compartment concept, and determines the leakage concentration of gas using a mass-balance based formulation. The study also introduces a computational fluid dynamics (CFD) technique for calculating three-dimensional details of the gas spread by resolving all the essential scales of fluid motions without a turbulent model. The present numerical technique promises numerical solutions with fewer uncertainties produced by the model equations while maintaining high accuracy. The study examines the effect of gas density on the concentration profiles of flammable gas spread. It also discusses the effect of gas leakage rate on gas concentration profiles. Copyright © 2014 The Authors. Published by Elsevier B.V. All rights reserved.

High-Order Central WENO Schemes for Multi-Dimensional Hamilton-Jacobi Equations

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron; Biegel, Bryan (Technical Monitor)

2002-01-01

We present new third- and fifth-order Godunov-type central schemes for approximating solutions of the Hamilton-Jacobi (HJ) equation in an arbitrary number of space dimensions. These are the first central schemes for approximating solutions of the HJ equations with an order of accuracy that is greater than two. In two space dimensions we present two versions for the third-order scheme: one scheme that is based on a genuinely two-dimensional Central WENO reconstruction, and another scheme that is based on a simpler dimension-by-dimension reconstruction. The simpler dimension-by-dimension variant is then extended to a multi-dimensional fifth-order scheme. Our numerical examples in one, two and three space dimensions verify the expected order of accuracy of the schemes.

Simulation of variable-density flow and transport of reactive and nonreactive solutes during a tracer test at Cape Cod, Massachusetts

USGS Publications Warehouse

Zhang, Hubao; Schwartz, Frank W.; Wood, Warren W.; Garabedian, S.P.; LeBlanc, D.R.

1998-01-01

A multispecies numerical code was developed to simulate flow and mass transport with kinetic adsorption in variable-density flow systems. The two-dimensional code simulated the transport of bromide (Br−), a nonreactive tracer, and lithium (Li+), a reactive tracer, in a large-scale tracer test performed in a sand-and-gravel aquifer at Cape Cod, Massachusetts. A two-fraction kinetic adsorption model was implemented to simulate the interaction of Li+ with the aquifer solids. Initial estimates for some of the transport parameters were obtained from a nonlinear least squares curve-fitting procedure, where the breakthrough curves from column experiments were matched with one-dimensional theoretical models. The numerical code successfully simulated the basic characteristics of the two plumes in the tracer test. At early times the centers of mass of Br− and Li+ sank because the two plumes were closely coupled to the density-driven velocity field. At later times the rate of downward movement in the Br− plume due to gravity slowed significantly because of dilution by dispersion. The downward movement of the Li+ plume was negligible because the two plumes moved in locally different velocity regimes, where Li+ transport was retarded relative to Br−. The maximum extent of downward transport of the Li+ plume was less than that of the Br− plume. This study also found that at early times the downward movement of a plume created by a three-dimensional source could be much more extensive than the case with a two-dimensional source having the same cross-sectional area. The observed shape of the Br− plume at Cape Cod was simulated by adding two layers with different hydraulic conductivities at shallow depth across the region. The large dispersion and asymmetrical shape of the Li+ plume were simulated by including kinetic adsorption-desorption reactions.

Two-dimensional analytic weighting functions for limb scattering

NASA Astrophysics Data System (ADS)

Zawada, D. J.; Bourassa, A. E.; Degenstein, D. A.

2017-10-01

Through the inversion of limb scatter measurements it is possible to obtain vertical profiles of trace species in the atmosphere. Many of these inversion methods require what is often referred to as weighting functions, or derivatives of the radiance with respect to concentrations of trace species in the atmosphere. Several radiative transfer models have implemented analytic methods to calculate weighting functions, alleviating the computational burden of traditional numerical perturbation methods. Here we describe the implementation of analytic two-dimensional weighting functions, where derivatives are calculated relative to atmospheric constituents in a two-dimensional grid of altitude and angle along the line of sight direction, in the SASKTRAN-HR radiative transfer model. Two-dimensional weighting functions are required for two-dimensional inversions of limb scatter measurements. Examples are presented where the analytic two-dimensional weighting functions are calculated with an underlying one-dimensional atmosphere. It is shown that the analytic weighting functions are more accurate than ones calculated with a single scatter approximation, and are orders of magnitude faster than a typical perturbation method. Evidence is presented that weighting functions for stratospheric aerosols calculated under a single scatter approximation may not be suitable for use in retrieval algorithms under solar backscatter conditions.

The P1-RKDG method for two-dimensional Euler equations of gas dynamics

NASA Technical Reports Server (NTRS)

Cockburn, Bernardo; Shu, Chi-Wang

1991-01-01

A class of nonlinearly stable Runge-Kutta local projection discontinuous Galerkin (RKDG) finite element methods for conservation laws is investigated. Two dimensional Euler equations for gas dynamics are solved using P1 elements. The generalization of the local projections, which for scalar nonlinear conservation laws was designed to satisfy a local maximum principle, to systems of conservation laws such as the Euler equations of gas dynamics using local characteristic decompositions is discussed. Numerical examples include the standard regular shock reflection problem, the forward facing step problem, and the double Mach reflection problem. These preliminary numerical examples are chosen to show the capacity of the approach to obtain nonlinearly stable results comparable with the modern nonoscillatory finite difference methods.

Inverse energy cascade in three-dimensional isotropic turbulence.

PubMed

Biferale, Luca; Musacchio, Stefano; Toschi, Federico

2012-04-20

We study the statistical properties of homogeneous and isotropic three-dimensional (3D) turbulent flows. By introducing a novel way to make numerical investigations of Navier-Stokes equations, we show that all 3D flows in nature possess a subset of nonlinear evolution leading to a reverse energy transfer: from small to large scales. Up to now, such an inverse cascade was only observed in flows under strong rotation and in quasi-two-dimensional geometries under strong confinement. We show here that energy flux is always reversed when mirror symmetry is broken, leading to a distribution of helicity in the system with a well-defined sign at all wave numbers. Our findings broaden the range of flows where the inverse energy cascade may be detected and rationalize the role played by helicity in the energy transfer process, showing that both 2D and 3D properties naturally coexist in all flows in nature. The unconventional numerical methodology here proposed, based on a Galerkin decimation of helical Fourier modes, paves the road for future studies on the influence of helicity on small-scale intermittency and the nature of the nonlinear interaction in magnetohydrodynamics.

LBQ2D, Extending the Line Broadened Quasilinear Model to TAE-EP Interaction

NASA Astrophysics Data System (ADS)

Ghantous, Katy; Gorelenkov, Nikolai; Berk, Herbert

2012-10-01

The line broadened quasilinear model was proposed and tested on the one dimensional electrostatic case of the bump on tailfootnotetextH.L Berk, B. Breizman and J. Fitzpatrick, Nucl. Fusion, 35:1661, 1995 to study the wave particle interaction. In conventional quasilinear theory, the sea of overlapping modes evolve with time as the particle distribution function self consistently undergo diffusion in phase space. The line broadened quasilinear model is an extension to the conventional theory in a way that allows treatment of isolated modes as well as overlapping modes by broadening the resonant line in phase space. This makes it possible to treat the evolution of modes self consistently from onset to saturation in either case. We describe here the model denoted by LBQ2D which is an extension of the proposed one dimensional line broadened quasilinear model to the case of TAEs interacting with energetic particles in two dimensional phase space, energy as well as canonical angular momentum. We study the saturation of isolated modes in various regimes and present the analytical derivation and numerical results. Finally, we present, using ITER parameters, the case where multiple modes overlap and describe the techniques used for the numerical treatment.

A dynamic-solver-consistent minimum action method: With an application to 2D Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Wan, Xiaoliang; Yu, Haijun

2017-02-01

This paper discusses the necessity and strategy to unify the development of a dynamic solver and a minimum action method (MAM) for a spatially extended system when employing the large deviation principle (LDP) to study the effects of small random perturbations. A dynamic solver is used to approximate the unperturbed system, and a minimum action method is used to approximate the LDP, which corresponds to solving an Euler-Lagrange equation related to but more complicated than the unperturbed system. We will clarify possible inconsistencies induced by independent numerical approximations of the unperturbed system and the LDP, based on which we propose to define both the dynamic solver and the MAM on the same approximation space for spatial discretization. The semi-discrete LDP can then be regarded as the exact LDP of the semi-discrete unperturbed system, which is a finite-dimensional ODE system. We achieve this methodology for the two-dimensional Navier-Stokes equations using a divergence-free approximation space. The method developed can be used to study the nonlinear instability of wall-bounded parallel shear flows, and be generalized straightforwardly to three-dimensional cases. Numerical experiments are presented.

A computer program for fitting smooth surfaces to three-dimensional aircraft configurations

NASA Technical Reports Server (NTRS)

Craidon, C. B.; Smith, R. E., Jr.

1975-01-01

A computer program developed to fit smooth surfaces to the component parts of three-dimensional aircraft configurations was described. The resulting equation definition of an aircraft numerical model is useful in obtaining continuous two-dimensional cross section plots in arbitrarily defined planes, local tangents, enriched surface plots and other pertinent geometric information; the geometry organization used as input to the program has become known as the Harris Wave Drag Geometry.

Transonic small disturbances equation applied to the solution of two-dimensional nonsteady flows

NASA Technical Reports Server (NTRS)

Couston, M.; Angelini, J. J.; Mulak, P.

1980-01-01

Transonic nonsteady flows are of large practical interest. Aeroelastic instability prediction, control figured vehicle techniques or rotary wings in forward flight are some examples justifying the effort undertaken to improve knowledge of these problems is described. The numerical solution of these problems under the potential flow hypothesis is described. The use of an alternating direction implicit scheme allows the efficient resolution of the two dimensional transonic small perturbations equation.

Steady state magnetic field configurations for the earth's magnetotail

NASA Technical Reports Server (NTRS)

Hau, L.-N.; Wolf, R. A.; Voigt, G.-H.; Wu, C. C.

1989-01-01

A two-dimensional, force-balance magnetic field model is presented. The theoretical existence of a steady state magnetic field configuration that is force-balanced and consistent with slow, lossless, adiabatic, earthward convection within the limit of the ideal MHD is demonstrated. A numerical solution is obtained for a two-dimensional magnetosphere with a rectangular magnetopause and nonflaring tail. The results are consistent with the convection time sequences reported by Erickson (1985).

Three-dimensional turbulent boundary layers; Proceedings of the Symposium, Berlin, West Germany, March 29-April 1, 1982

NASA Astrophysics Data System (ADS)

Fernholz, H. H.; Krause, E.

Papers are presented on recent research concerning three-dimensional turbulent boundary layers. Topics examined include experimental techniques in three-dimensional turbulent boundary layers, turbulence measurements in ship-model flow, measurements of Reynolds-stress profiles in the stern region of a ship model, the effects of crossflow on the vortex-layer-type three-dimensional flow separation, and wind tunnel investigations of some three-dimensional separated turbulent boundary layers. Also examined are three-dimensional boundary layers in turbomachines, the boundary layers on bodies of revolution spinning in axial flows, the effect on a developed turbulent boundary layer of a sudden local wall motion, three-dimensional turbulent boundary layer along a concave wall, the numerical computation of three-dimensional boundary layers, a numerical study of corner flows, three-dimensional boundary calculations in design aerodynamics, and turbulent boundary-layer calculations in design aerodynamics. For individual items see A83-47012 to A83-47036

Pore water pressure variations in Subpermafrost groundwater : Numerical modeling compared with experimental modeling

NASA Astrophysics Data System (ADS)

Rivière, Agnès.; Goncalves, Julio; Jost, Anne; Font, Marianne

2010-05-01

Development and degradation of permafrost directly affect numerous hydrogeological processes such as thermal regime, exchange between river and groundwater, groundwater flows patterns and groundwater recharge (Michel, 1994). Groundwater in permafrost area is subdivided into two zones: suprapermafrost and subpermafrost which are separated by permafrost. As a result of the volumetric expansion of water upon freezing and assuming ice lenses and frost heave do not form freezing in a saturated aquifer, the progressive formation of permafrost leads to the pressurization of the subpermafrost groundwater (Wang, 2006). Therefore disappearance or aggradation of permafrost modifies the confined or unconfined state of subpermafrost groundwater. Our study focuses on modifications of pore water pressure of subpermafrost groundwater which could appear during thawing and freezing of soil. Numerical simulation allows elucidation of some of these processes. Our numerical model accounts for phase changes for coupled heat transport and variably saturated flow involving cycles of freezing and thawing. The flow model is a combination of a one-dimensional channel flow model which uses Manning-Strickler equation and a two-dimensional vertically groundwater flow model using Richards equation. Numerical simulation of heat transport consisted in a two dimensional model accounting for the effects of latent heat of phase change of water associated with melting/freezing cycles which incorporated the advection-diffusion equation describing heat-transfer in porous media. The change of hydraulic conductivity and thermal conductivity are considered by our numerical model. The model was evaluated by comparing predictions with data from laboratory freezing experiments. Experimental design was undertaken at the Laboratory M2C (Univesité de Caen-Basse Normandie, CNRS, France). The device consisted of a Plexiglas box insulated on all sides except on the top. Precipitation and ambient temperature are imposed. The Plexiglas box is filled with glass beads of which hydraulics and thermal parameters are known. All parameters required for our numerical model are controlled and continuous monitoring of soil temperatures and pore water pressure are reported. Our results of experimental model allow us to test the relevance of processes described by our numerical simulation and to quantify the impact of permafrost on pore water pressure of subpermafrost groundwater during a cycle of freezing and thawing. Michel, Frederick A. and Van Everdingen, Robert O. 1994. Changes in hydrogeologic regimes in permafrost regions due to climatic change. Permafrost and Periglacial Processes, 5: 191-195. Wang, Chi-yuen and Manga, Michael and Hanna, Jeffrey C. 2006. Can freezing cause floods on Mars? Geophysical Research Letters, 33

Experimental and numerical simulation of three-dimensional gravity currents on smooth and rough bottom

NASA Astrophysics Data System (ADS)

La Rocca, Michele; Adduce, Claudia; Sciortino, Giampiero; Pinzon, Allen Bateman

2008-10-01

The dynamics of a three-dimensional gravity current is investigated by both laboratory experiments and numerical simulations. The experiments take place in a rectangular tank, which is divided into two square reservoirs with a wall containing a sliding gate of width b. The two reservoirs are filled to the same height H, one with salt water and the other with fresh water. The gravity current starts its evolution as soon as the sliding gate is manually opened. Experiments are conducted with either smooth or rough surface on the bottom of the tank. The bottom roughness is created by gluing sediment material of different diameters to the surface. Five diameter values for the surface roughness and two salinity conditions for the fluid are investigated. The mathematical model is based on shallow-water theory together with the single-layer approximation, so that the model is strictly hyperbolic and can be put into conservative form. Consequently, a finite-volume-based numerical algorithm can be applied. The Godunov formulation is used together with Roe's approximate Riemann solver. Comparisons between the numerical and experimental results show satisfactory agreement. The behavior of the gravity current is quite unusual and cannot be interpreted using the usual model framework adopted for two-dimensional and axisymmetric gravity currents. Two main phases are apparent in the gravity current evolution; during the first phase the front velocity increases, and during the second phase the front velocity decreases and the dimensionless results, relative to the different densities, collapse onto the same curve. A systematic discrepancy is seen between the numerical and experimental results, mainly during the first phase of the gravity current evolution. This discrepancy is attributed to the limits of the mathematical formulation, in particular, the neglect of entrainment in the mathematical model. An interesting result arises from the influence of the bottom surface roughness; it both reduces the front velocity during the second phase of motion and attenuates the differences between the experimental and numerical front velocities during the first phase of motion.

Formation of Spiral-Arm Spurs and Bound Clouds in Vertically Stratified Galactic Gas Disks

NASA Astrophysics Data System (ADS)

Kim, Woong-Tae; Ostriker, Eve C.

2006-07-01

We investigate the growth of spiral-arm substructure in vertically stratified, self-gravitating, galactic gas disks, using local numerical MHD simulations. Our new models extend our previous two-dimensional studies, which showed that a magnetized spiral shock in a thin disk can undergo magneto-Jeans instability (MJI), resulting in regularly spaced interarm spur structures and massive gravitationally bound fragments. Similar spur (or ``feather'') features have recently been seen in high-resolution observations of several galaxies. Here we consider two sets of numerical models: two-dimensional simulations that use a ``thick-disk'' gravitational kernel, and three-dimensional simulations with explicit vertical stratification. Both models adopt an isothermal equation of state with cs=7 km s-1. When disks are sufficiently magnetized and self-gravitating, the result in both sorts of models is the growth of spiral-arm substructure similar to that in our previous razor-thin models. Reduced self-gravity due to nonzero disk thickness increases the spur spacing to ~10 times the Jeans length at the arm peak. Bound clouds that form from spur fragmentation have masses ~(1-3)×107 Msolar each, similar to the largest observed GMCs. The mass-to-flux ratios and specific angular momenta of the bound condensations are lower than large-scale galactic values, as is true for observed GMCs. We find that unmagnetized or weakly magnetized two-dimensional models are unstable to the ``wiggle instability'' previously identified by Wada & Koda. However, our fully three-dimensional models do not show this effect. Nonsteady motions and strong vertical shear prevent coherent vortical structures from forming, evidently suppressing the wiggle instability. We also find no clear traces of Parker instability in the nonlinear spiral arm substructures that emerge, although conceivably Parker modes may help seed the MJI at early stages since azimuthal wavelengths are similar.

Two-dimensional numerical simulation of chimney fluidization in a granular medium using a combination of discrete element and lattice Boltzmann methods

NASA Astrophysics Data System (ADS)

Ngoma, Jeff; Philippe, Pierre; Bonelli, Stéphane; Radjaï, Farhang; Delenne, Jean-Yves

2018-05-01

We present here a numerical study dedicated to the fluidization of a submerged granular medium induced by a localized fluid injection. To this end, a two-dimensional (2D) model is used, coupling the lattice Boltzmann method (LBM) with the discrete element method (DEM) for a relevant description of fluid-grains interaction. An extensive investigation has been carried out to analyze the respective influences of the different parameters of our configuration, both geometrical (bed height, grain diameter, injection width) and physical (fluid viscosity, buoyancy). Compared to previous experimental works, the same qualitative features are recovered as regards the general phenomenology including transitory phase, stationary states, and hysteretic behavior. We also present quantitative findings about transient fluidization, for which several dimensionless quantities and scaling laws are proposed, and about the influence of the injection width, from localized to homogeneous fluidization. Finally, the impact of the present 2D geometry is discussed, by comparison to the real three-dimensional (3D) experiments, as well as the crucial role of the prevailing hydrodynamic regime within the expanding cavity, quantified through a cavity Reynolds number, that can presumably explain some substantial differences observed regarding upward expansion process of the fluidized zone when the fluid viscosity is changed.

Three-dimensional volume containing multiple two-dimensional information patterns

NASA Astrophysics Data System (ADS)

Nakayama, Hirotaka; Shiraki, Atsushi; Hirayama, Ryuji; Masuda, Nobuyuki; Shimobaba, Tomoyoshi; Ito, Tomoyoshi

2013-06-01

We have developed an algorithm for recording multiple gradated two-dimensional projection patterns in a single three-dimensional object. When a single pattern is observed, information from the other patterns can be treated as background noise. The proposed algorithm has two important features: the number of patterns that can be recorded is theoretically infinite and no meaningful information can be seen outside of the projection directions. We confirmed the effectiveness of the proposed algorithm by performing numerical simulations of two laser crystals: an octagonal prism that contained four patterns in four projection directions and a dodecahedron that contained six patterns in six directions. We also fabricated and demonstrated an actual prototype laser crystal from a glass cube engraved by a laser beam. This algorithm has applications in various fields, including media art, digital signage, and encryption technology.

Numerical investigations of passive scalar transport in Taylor-Couette flows: Counter-rotation effect

NASA Astrophysics Data System (ADS)

Ouazib, Nabila; Salhi, Yacine; Si-Ahmed, El-Khider; Legrand, Jack; Degrez, G.

2017-07-01

Numerical methods for solving convection-diffusion-reaction (CDR) scalar transport equation in three-dimensional flow are used in the present investigation. The flow is confined between two concentric cylinders both the inner cylinder and the outer one are allowed to rotate. Direct numerical simulations (DNS) have been achieved to study the effects of the gravitational and the centrifugal potentials on the stability of incompressible Taylor-Couette flow. The Navier-Stokes equations and the uncoupled convection-diffusion-reaction equation are solved using a spectral development in one direction combined together with a finite element discretization in the two remaining directions. The complexity of the patterns is highlighted. Since, it increases as the rotation rates of the cylinders increase. In addition, the effect of the counter-rotation of the cylinders on the mass transfer is pointed out.

Exploring load, velocity, and surface disorder dependence of friction with one-dimensional and two-dimensional models.

PubMed

Dagdeviren, Omur E

2018-08-03

The effect of surface disorder, load, and velocity on friction between a single asperity contact and a model surface is explored with one-dimensional and two-dimensional Prandtl-Tomlinson (PT) models. We show that there are fundamental physical differences between the predictions of one-dimensional and two-dimensional models. The one-dimensional model estimates a monotonic increase in friction and energy dissipation with load, velocity, and surface disorder. However, a two-dimensional PT model, which is expected to approximate a tip-sample system more realistically, reveals a non-monotonic trend, i.e. friction is inert to surface disorder and roughness in wearless friction regime. The two-dimensional model discloses that the surface disorder starts to dominate the friction and energy dissipation when the tip and the sample interact predominantly deep into the repulsive regime. Our numerical calculations address that tracking the minimum energy path and the slip-stick motion are two competing effects that determine the load, velocity, and surface disorder dependence of friction. In the two-dimensional model, the single asperity can follow the minimum energy path in wearless regime; however, with increasing load and sliding velocity, the slip-stick movement dominates the dynamic motion and results in an increase in friction by impeding tracing the minimum energy path. Contrary to the two-dimensional model, when the one-dimensional PT model is employed, the single asperity cannot escape to the minimum energy minimum due to constraint motion and reveals only a trivial dependence of friction on load, velocity, and surface disorder. Our computational analyses clarify the physical differences between the predictions of the one-dimensional and two-dimensional models and open new avenues for disordered surfaces for low energy dissipation applications in wearless friction regime.

Deformable cells in confined geometries: From hemolysis to hydrodynamic interactions

NASA Astrophysics Data System (ADS)

Abkarian, Manouk; Faivre, Magalie; Stone, Howard A.

2004-11-01

Recent developments in microfluidics allow a wide range of possibilities for studying cellular-scale hydrodynamics. Here we use microfluidic technology to address several open questions in the blood flow literature where cell deformation and hydrodynamic interactions are significant. In particular, we investigate the pressure-driven flow of a dilute suspension in a channel and characterize the transition from steady axisymmetric cell shapes (for which numerical calculations exist) to asymmetric, highly extended shapes, which are precursors to hemolysis (i.e. destruction of the cell). In addition, we examine the influence of geometry on hydrodynamic interactions of deformable cells by contrasting one-dimensional motion of a train of particles in a channel with two-dimensional motions in a Hele-Shaw cell. This study can help to understand flow of cells in microcirculation from the unidirectional flow in capillaries to the two-dimensional flow in the lung alveoli and provides the basic steps to understand certain aspects of microcirculatory deseases like sickle cell anemia for example.

Development of a three dimensional numerical water quality model for continental shelf applications

NASA Technical Reports Server (NTRS)

Spaulding, M.; Hunter, D.

1975-01-01

A model to predict the distribution of water quality parameters in three dimensions was developed. The mass transport equation was solved using a non-dimensional vertical axis and an alternating-direction-implicit finite difference technique. The reaction kinetics of the constituents were incorporated into a matrix method which permits computation of the interactions of multiple constituents. Methods for the computation of dispersion coefficients and coliform bacteria decay rates were determined. Numerical investigations of dispersive and dissipative effects showed that the three-dimensional model performs as predicted by analysis of simpler cases. The model was then applied to a two dimensional vertically averaged tidal dynamics model for the Providence River. It was also extended to a steady state application by replacing the time step with an iteration sequence. This modification was verified by comparison to analytical solutions and applied to a river confluence situation.

Modeling and numerical simulations of growth and morphologies of three dimensional aggregated silver films

NASA Astrophysics Data System (ADS)

Davis, L. J.; Boggess, M.; Kodpuak, E.; Deutsch, M.

2012-11-01

We report on a model for the deposition of three dimensional, aggregated nanocrystalline silver films, and an efficient numerical simulation method developed for visualizing such structures. We compare our results to a model system comprising chemically deposited silver films with morphologies ranging from dilute, uniform distributions of nanoparticles to highly porous aggregated networks. Disordered silver films grown in solution on silica substrates are characterized using digital image analysis of high resolution scanning electron micrographs. While the latter technique provides little volume information, plane-projected (two dimensional) island structure and surface coverage may be reliably determined. Three parameters governing film growth are evaluated using these data and used as inputs for the deposition model, greatly reducing computing requirements while still providing direct access to the complete (bulk) structure of the films throughout the growth process. We also show how valuable three dimensional characteristics of the deposited materials can be extracted using the simulated structures.

A two-state hysteresis model from high-dimensional friction

PubMed Central

Biswas, Saurabh; Chatterjee, Anindya

2015-01-01

In prior work (Biswas & Chatterjee 2014 Proc. R. Soc. A 470, 20130817 (doi:10.1098/rspa.2013.0817)), we developed a six-state hysteresis model from a high-dimensional frictional system. Here, we use a more intuitively appealing frictional system that resembles one studied earlier by Iwan. The basis functions now have simple analytical description. The number of states required decreases further, from six to the theoretical minimum of two. The number of fitted parameters is reduced by an order of magnitude, to just six. An explicit and faster numerical solution method is developed. Parameter fitting to match different specified hysteresis loops is demonstrated. In summary, a new two-state model of hysteresis is presented that is ready for practical implementation. Essential Matlab code is provided. PMID:26587279

Entropic Barriers for Two-Dimensional Quantum Memories

NASA Astrophysics Data System (ADS)

Brown, Benjamin J.; Al-Shimary, Abbas; Pachos, Jiannis K.

2014-03-01

Comprehensive no-go theorems show that information encoded over local two-dimensional topologically ordered systems cannot support macroscopic energy barriers, and hence will not maintain stable quantum information at finite temperatures for macroscopic time scales. However, it is still well motivated to study low-dimensional quantum memories due to their experimental amenability. Here we introduce a grid of defect lines to Kitaev's quantum double model where different anyonic excitations carry different masses. This setting produces a complex energy landscape which entropically suppresses the diffusion of excitations that cause logical errors. We show numerically that entropically suppressed errors give rise to superexponential inverse temperature scaling and polynomial system size scaling for small system sizes over a low-temperature regime. Curiously, these entropic effects are not present below a certain low temperature. We show that we can vary the system to modify this bound and potentially extend the described effects to zero temperature.

Numerical simulation of detonation reignition in H 2-O 2 mixtures in area expansions

NASA Astrophysics Data System (ADS)

Jones, D. A.; Kemister, G.; Tonello, N. A.; Oran, E. S.; Sichel, M.

Time-dependent, two-dimensional, numerical simulations of a transmitted detonation show reignition occuring by one of two mechanisms. The first mechanism involves the collision of triple points as they expand along a decaying shock front. In the second mechanism ignition results from the coalescence of a number of small, relatively high pressure regions left over from the decay of weakened transverse waves. The simulations were performed using an improved chemical kinetic model for stoichiometric H 2-O 2 mixtures. The initial conditions were a propagating, two-dimensional detonation resolved enough to show transverse wave structure. The calculations provide clarification of the reignition mechanism seen in previous H 2-O 2-Ar simulations, and again demonstrate that the transverse wave structure of the detonation front is critical to the reignition process.

Direct Simulation of Evolution and Control of Three-Dimensional Instabilities in Attachment-Line Boundary Layers

NASA Technical Reports Server (NTRS)

Joslin, Ronald D.

1995-01-01

The spatial evolution of three-dimensional disturbances in an attachment-line boundary layer is computed by direct numerical simulation of the unsteady, incompressible Navier-Stokes equations. Disturbances are introduced into the boundary layer by harmonic sources that involve unsteady suction and blowing through the wall. Various harmonic- source generators are implemented on or near the attachment line, and the disturbance evolutions are compared. Previous two-dimensional simulation results and nonparallel theory are compared with the present results. The three-dimensional simulation results for disturbances with quasi-two-dimensional features indicate growth rates of only a few percent larger than pure two-dimensional results; however, the results are close enough to enable the use of the more computationally efficient, two-dimensional approach. However, true three-dimensional disturbances are more likely in practice and are more stable than two-dimensional disturbances. Disturbances generated off (but near) the attachment line spread both away from and toward the attachment line as they evolve. The evolution pattern is comparable to wave packets in at-plate boundary-layer flows. Suction stabilizes the quasi-two-dimensional attachment-line instabilities, and blowing destabilizes these instabilities; these results qualitatively agree with the theory. Furthermore, suction stabilizes the disturbances that develop off the attachment line. Clearly, disturbances that are generated near the attachment line can supply energy to attachment-line instabilities, but suction can be used to stabilize these instabilities.

Entanglement Area Law in Disordered Free Fermion Anderson Model in One, Two, and Three Dimensions

DOE PAGES

Pouranvari, Mohammad; Zhang, Yuhui; Yang, Kun

2015-01-01

We calculate numerically the entanglement entropy of free fermion ground states in one-, two-, and three-dimensional Anderson models and find that it obeys the area law as long as the linear size of the subsystem is sufficiently larger than the mean free path. This result holds in the metallic phase of the three-dimensional Anderson model, where the mean free path is finite although the localization length is infinite. Relation between the present results and earlier ones on area law violation in special one-dimensional models that support metallic phases is discussed.

Resonant scattering from a two-dimensional honeycomb PT dipole structure

NASA Astrophysics Data System (ADS)

Markoš, P.; Kuzmiak, V.

2018-05-01

We studied numerically the electromagnetic response of the finite periodic structure consisting of the PT dipoles represented by two infinitely long, parallel cylinders with the opposite sign of the imaginary part of a refractive index, which are centered at the positions of a two-dimensional honeycomb lattice. We observed that the total scattered energy reveals a series of sharp resonances at which the energy increases by two orders of magnitude and an incident wave is scattered only in a few directions given by spatial symmetry of the periodic structure. We explain this behavior by analysis of the complex frequency spectra associated with an infinite honeycomb array of the PT dipoles and identify the lowest resonance with the broken PT -symmetry mode formed by a doubly degenerate pair with complex conjugate eigenfrequencies corresponding to the K point of the reciprocal lattice.

Stochastic solution to quantum dynamics

NASA Technical Reports Server (NTRS)

John, Sarah; Wilson, John W.

1994-01-01

The quantum Liouville equation in the Wigner representation is solved numerically by using Monte Carlo methods. For incremental time steps, the propagation is implemented as a classical evolution in phase space modified by a quantum correction. The correction, which is a momentum jump function, is simulated in the quasi-classical approximation via a stochastic process. The technique, which is developed and validated in two- and three- dimensional momentum space, extends an earlier one-dimensional work. Also, by developing a new algorithm, the application to bound state motion in an anharmonic quartic potential shows better agreement with exact solutions in two-dimensional phase space.

Entanglement Area Law in Disordered Free Fermion Anderson Model in One, Two, and Three Dimensions

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

Pouranvari, Mohammad; Zhang, Yuhui; Yang, Kun

We calculate numerically the entanglement entropy of free fermion ground states in one-, two-, and three-dimensional Anderson models and find that it obeys the area law as long as the linear size of the subsystem is sufficiently larger than the mean free path. This result holds in the metallic phase of the three-dimensional Anderson model, where the mean free path is finite although the localization length is infinite. Relation between the present results and earlier ones on area law violation in special one-dimensional models that support metallic phases is discussed.

A discontinuous Galerkin method for two-dimensional PDE models of Asian options

NASA Astrophysics Data System (ADS)

Hozman, J.; Tichý, T.; Cvejnová, D.

2016-06-01

In our previous research we have focused on the problem of plain vanilla option valuation using discontinuous Galerkin method for numerical PDE solution. Here we extend a simple one-dimensional problem into two-dimensional one and design a scheme for valuation of Asian options, i.e. options with payoff depending on the average of prices collected over prespecified horizon. The algorithm is based on the approach combining the advantages of the finite element methods together with the piecewise polynomial generally discontinuous approximations. Finally, an illustrative example using DAX option market data is provided.

Application of numerical simulation on optimum design of two-dimensional sedimentation tanks in the wastewater treatment plant.

PubMed

Zeng, Guang-Ming; Zhang, Shuo-Fu; Qin, Xiao-Sheng; Huang, Guo-He; Li, Jian-Bing

2003-05-01

The paper establishes the relationship between the settling efficiency and the sizes of the sedimentation tank through the process of numerical simulation, which is taken as one of the constraints to set up a simple optimum designing model of sedimentation tank. The feasibility and advantages of this model based on numerical calculation are verified through the application of practical case.

Approximate and exact numerical integration of the gas dynamic equations

NASA Technical Reports Server (NTRS)

Lewis, T. S.; Sirovich, L.

1979-01-01

A highly accurate approximation and a rapidly convergent numerical procedure are developed for two dimensional steady supersonic flow over an airfoil. Examples are given for a symmetric airfoil over a range of Mach numbers. Several interesting features are found in the calculation of the tail shock and the flow behind the airfoil.

Simulation of Supersonic Base Flows: Numerical Investigations Using DNS, LES, and URANS

DTIC Science & Technology

2006-10-01

global instabilities were found for a two-dimensional bluff body with a blunt base by Hannemann & Oertel (1989). Oertel (1990) found that the... Hannemann , K. & Oertel, H. 1989 Numerical simulation of the absolutely and convectively unstable wake. J. Fluid Mech. 199, 55–88. Harris, P. J. 1997

Numerical simulation of small-scale thermal convection in the atmosphere

NASA Technical Reports Server (NTRS)

Somerville, R. C. J.

1973-01-01

A Boussinesq system is integrated numerically in three dimensions and time in a study of nonhydrostatic convection in the atmosphere. Simulation of cloud convection is achieved by the inclusion of parametrized effects of latent heat and small-scale turbulence. The results are compared with the cell structure observed in Rayleigh-Benard laboratory conversion experiments in air. At a Rayleigh number of 4000, the numerical model adequately simulates the experimentally observed evolution, including some prominent transients of a flow from a randomly perturbed initial conductive state into the final state of steady large-amplitude two-dimensional rolls. At Rayleigh number 9000, the model reproduces the experimentally observed unsteady equilibrium of vertically coherent oscillatory waves superimposed on rolls.

Three-Dimensional Numerical Simulation on Triaxial Failure Mechanical Behavior of Rock-Like Specimen Containing Two Unparallel Fissures

NASA Astrophysics Data System (ADS)

Huang, Yan-Hua; Yang, Sheng-Qi; Zhao, Jian

2016-12-01

A three-dimensional particle flow code (PFC3D) was used for a systematic numerical simulation of the strength failure and cracking behavior of rock-like material specimens containing two unparallel fissures under conventional triaxial compression. The micro-parameters of the parallel bond model were first calibrated using the laboratory results of intact specimens and then validated from the experimental results of pre-fissured specimens under triaxial compression. Numerically simulated stress-strain curves, strength and deformation parameters and macro-failure modes of pre-fissured specimens were all in good agreement with the experimental results. The relationship between stress and the micro-crack numbers was summarized. Crack initiation, propagation and coalescence process of pre-fissured specimens were analyzed in detail. Finally, horizontal and vertical cross sections of numerical specimens were derived from PFC3D. A detailed analysis to reveal the internal damage behavior of rock under triaxial compression was carried out. The experimental and simulated results are expected to improve the understanding of the strength failure and cracking behavior of fractured rock under triaxial compression.

An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry

NASA Astrophysics Data System (ADS)

Wintermeyer, Niklas; Winters, Andrew R.; Gassner, Gregor J.; Kopriva, David A.

2017-07-01

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.

Dynamics of a differential-difference integrable (2+1)-dimensional system.

PubMed

Yu, Guo-Fu; Xu, Zong-Wei

2015-06-01

A Kadomtsev-Petviashvili- (KP-) type equation appears in fluid mechanics, plasma physics, and gas dynamics. In this paper, we propose an integrable semidiscrete analog of a coupled (2+1)-dimensional system which is related to the KP equation and the Zakharov equation. N-soliton solutions of the discrete equation are presented. Some interesting examples of soliton resonance related to the two-soliton and three-soliton solutions are investigated. Numerical computations using the integrable semidiscrete equation are performed. It is shown that the integrable semidiscrete equation gives very accurate numerical results in the cases of one-soliton evolution and soliton interactions.

Optimal swimming of a sheet.

PubMed

Montenegro-Johnson, Thomas D; Lauga, Eric

2014-06-01

Propulsion at microscopic scales is often achieved through propagating traveling waves along hairlike organelles called flagella. Taylor's two-dimensional swimming sheet model is frequently used to provide insight into problems of flagellar propulsion. We derive numerically the large-amplitude wave form of the two-dimensional swimming sheet that yields optimum hydrodynamic efficiency: the ratio of the squared swimming speed to the rate-of-working of the sheet against the fluid. Using the boundary element method, we show that the optimal wave form is a front-back symmetric regularized cusp that is 25% more efficient than the optimal sine wave. This optimal two-dimensional shape is smooth, qualitatively different from the kinked form of Lighthill's optimal three-dimensional flagellum, not predicted by small-amplitude theory, and different from the smooth circular-arc-like shape of active elastic filaments.

Distributed Two-Dimensional Fourier Transforms on DSPs with an Application for Phase Retrieval

NASA Technical Reports Server (NTRS)

Smith, Jeffrey Scott

2006-01-01

Many applications of two-dimensional Fourier Transforms require fixed timing as defined by system specifications. One example is image-based wavefront sensing. The image-based approach has many benefits, yet it is a computational intensive solution for adaptive optic correction, where optical adjustments are made in real-time to correct for external (atmospheric turbulence) and internal (stability) aberrations, which cause image degradation. For phase retrieval, a type of image-based wavefront sensing, numerous two-dimensional Fast Fourier Transforms (FFTs) are used. To meet the required real-time specifications, a distributed system is needed, and thus, the 2-D FFT necessitates an all-to-all communication among the computational nodes. The 1-D floating point FFT is very efficient on a digital signal processor (DSP). For this study, several architectures and analysis of such are presented which address the all-to-all communication with DSPs. Emphasis of this research is on a 64-node cluster of Analog Devices TigerSharc TS-101 DSPs.

Creep crack-growth: A new path-independent T sub o and computational studies

NASA Technical Reports Server (NTRS)

Stonesifer, R. B.; Atluri, S. N.

1981-01-01

Two path independent integral parameters which show some degree of promise as fracture criteria are the C* and delta T sub c integrals. The mathematical aspects of these parameters are reviewed. This is accomplished by deriving generalized vector forms of the parameters using conservation laws which are valid for arbitrary, three dimensional, cracked bodies with crack surface tractions (or applied displacements), body forces, inertial effects and large deformations. Two principal conclusions are that delta T sub c is a valid crack tip parameter during nonsteady as well as steady state creep and that delta T sub c has an energy rate interpretation whereas C* does not. An efficient, small displacement, infinitestimal strain, displacement based finite element model is developed for general elastic/plastic material behavior. For the numerical studies, this model is specialized to two dimensional plane stress and plane strain and to power law creep constitutive relations.

Application of High-resolution Aerial LiDAR Data in Calibration of a Two-dimensional Urban Flood Simulation

NASA Astrophysics Data System (ADS)

Piotrowski, J.; Goska, R.; Chen, B.; Krajewski, W. F.; Young, N.; Weber, L.

2009-12-01

In June 2008, the state of Iowa experienced an unprecedented flood event which resulted in an economic loss of approximately $2.88 billion. Flooding in the Iowa River corridor, which exceeded the previous flood of record by 3 feet, devastated several communities, including Coralville and Iowa City, home to the University of Iowa. Recognizing an opportunity to capture a unique dataset detailing the impacts of the historic flood, the investigators contacted the National Center for Airborne Laser Mapping (NCALM), which performed an aerial Light Detection and Ranging (LiDAR) survey along the Iowa River. The survey, conducted immediately following the flood peak, provided coverage of a 60-mile reach. The goal of the present research is to develop a process by which flood extents and water surface elevations can be accurately extracted from the LiDAR data set and to evaluate the benefit of such data in calibrating one- and two-dimensional hydraulic models. Whereas data typically available for model calibration include sparsely distributed point observations and high water marks, the LiDAR data used in the present study provide broad-scale, detailed, and continuous information describing the spatial extent and depth of flooding. Initial efforts were focused on a 10-mile, primarily urban reach of the Iowa River extending from Coralville Reservoir, a United States Army Corps of Engineers flood control project, downstream through the Coralville and Iowa City. Spatial extent and depth of flooding were estimated from the LiDAR data. At a given cross-sectional location, river channel and floodplain measurements were compared. When differences between floodplain and river channel measurements were less than a standard deviation of the vertical uncertainty in the LiDAR survey, floodplain measurements were classified as flooded. A flood water surface DEM was created using measurements classified as flooded. A two-dimensional, depth-averaged numerical model of a 10-mile reach of the Iowa River corridor was developed using the United States Bureau of Reclamation SRH-2D hydraulic modeling software. The numerical model uses an unstructured numerical mesh and variable surface roughness, assigned according to observed land use and cover. The numerical model was calibrated using inundation extents and water surface elevations derived from the LiDAR data. It was also calibrated using high water marks and land survey data collected daily during the 2008 flood. The investigators compared the two calibrations to evaluate the benefit of high-resolution LiDAR data in improving the accuracy of a two-dimensional urban flood simulation.

Two dimensional simulation of patternable conducting polymer electrode based organic thin film transistor

NASA Astrophysics Data System (ADS)

Nair, Shiny; Kathiresan, M.; Mukundan, T.

2018-02-01

Device characteristics of organic thin film transistor (OTFT) fabricated with conducting polyaniline:polystyrene sulphonic acid (PANi-PSS) electrodes, patterned by the Parylene lift-off method are systematically analyzed by way of two dimensional numerical simulation. The device simulation was performed taking into account field-dependent mobility, low mobility layer at the electrode-semiconductor interface, trap distribution in pentacene film and trapped charge at the organic/insulator interface. The electrical characteristics of bottom contact thin film transistor with PANi-PSS electrodes and pentacene active material is superior to those with palladium electrodes due to a lower charge injection barrier. Contact resistance was extracted in both cases by the transfer line method (TLM). The extracted charge concentration and potential profile from the two dimensional numerical simulation was used to explain the observed electrical characteristics. The simulated device characteristics not only matched the experimental electrical characteristics, but also gave an insight on the charge injection, transport and trap properties of the OTFTs as a function of different electrode materials from the perspectives of transistor operation.

Numerical solution of the two-dimensional time-dependent incompressible Euler equations

NASA Technical Reports Server (NTRS)

Whitfield, David L.; Taylor, Lafayette K.

1994-01-01

A numerical method is presented for solving the artificial compressibility form of the 2D time-dependent incompressible Euler equations. The approach is based on using an approximate Riemann solver for the cell face numerical flux of a finite volume discretization. Characteristic variable boundary conditions are developed and presented for all boundaries and in-flow out-flow situations. The system of algebraic equations is solved using the discretized Newton-relaxation (DNR) implicit method. Numerical results are presented for both steady and unsteady flow.

A SEMI-LAGRANGIAN TWO-LEVEL PRECONDITIONED NEWTON-KRYLOV SOLVER FOR CONSTRAINED DIFFEOMORPHIC IMAGE REGISTRATION.

PubMed

Mang, Andreas; Biros, George

2017-01-01

We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport equation. We use a pseudospectral discretization in space and second-order accurate semi-Lagrangian time stepping scheme for the transport equations. We solve for a stationary velocity field using a preconditioned, globalized, matrix-free Newton-Krylov scheme. We propose and test a two-level Hessian preconditioner. We consider two strategies for inverting the preconditioner on the coarse grid: a nested preconditioned conjugate gradient method (exact solve) and a nested Chebyshev iterative method (inexact solve) with a fixed number of iterations. We test the performance of our solver in different synthetic and real-world two-dimensional application scenarios. We study grid convergence and computational efficiency of our new scheme. We compare the performance of our solver against our initial implementation that uses the same spatial discretization but a standard, explicit, second-order Runge-Kutta scheme for the numerical time integration of the transport equations and a single-level preconditioner. Our improved scheme delivers significant speedups over our original implementation. As a highlight, we observe a 20 × speedup for a two dimensional, real world multi-subject medical image registration problem.

Surface critical behavior of thin Ising films at the ‘special point’

NASA Astrophysics Data System (ADS)

Moussa, Najem; Bekhechi, Smaine

2003-03-01

The critical surface phenomena of a magnetic thin Ising film is studied using numerical Monte-Carlo method based on Wolff cluster algorithm. With varying the surface coupling, js= Js/ J, the phase diagram exhibits a special surface coupling jsp at which all the films have a unique critical temperature Tc for an arbitrary thickness n. In spite of this, the critical exponent of the surface magnetization at the special point is found to increase with n. Moreover, non-universal features as well as dimensionality crossover from two- to three-dimensional behavior are found at this point.

Generalized Kubo formulas for the transport properties of incommensurate 2D atomic heterostructures

NASA Astrophysics Data System (ADS)

Cancès, Eric; Cazeaux, Paul; Luskin, Mitchell

2017-06-01

We give an exact formulation for the transport coefficients of incommensurate two-dimensional atomic multilayer systems in the tight-binding approximation. This formulation is based upon the C* algebra framework introduced by Bellissard and collaborators [Coherent and Dissipative Transport in Aperiodic Solids, Lecture Notes in Physics (Springer, 2003), Vol. 597, pp. 413-486 and J. Math. Phys. 35(10), 5373-5451 (1994)] to study aperiodic solids (disordered crystals, quasicrystals, and amorphous materials), notably in the presence of magnetic fields (quantum Hall effect). We also present numerical approximations and test our methods on a one-dimensional incommensurate bilayer system.

Approximate analysis of thermal convection in a crystal-growth cell for Spacelab 3

NASA Technical Reports Server (NTRS)

Dressler, R. F.

1982-01-01

The transient and steady thermal convection in microgravity is described. The approach is applicable to many three dimensional flows in containers of various shapes with various thermal gradients imposed. The method employs known analytical solutions to two dimensional thermal flows in simpler geometries, and does not require recourse to numerical calculations by computer.

Inverse energy cascades in three-dimensional turbulence

NASA Technical Reports Server (NTRS)

Hossain, Murshed

1991-01-01

Fully three-dimensional magnetohydrodynamic (MHD) turbulence at large kinetic and low magnetic Reynolds numbers is considered in the presence of a strong uniform magnetic field. It is shown by numerical simulation of a model of MHD that the energy inverse cascades to longer length scales when the interaction parameter is large. While the steady-state dynamics of the driven problem is three-dimensional in character, the behavior has resemblance to two-dimensional hydrodynamics. These results have implications in turbulence theory, MHD power generator, planetary dynamos, and fusion reactor blanket design.

Dynamic colloidal assembly pathways via low dimensional models

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

Yang, Yuguang; Bevan, Michael A., E-mail: mabevan@jhu.edu; Thyagarajan, Raghuram

2016-05-28

Here we construct a low-dimensional Smoluchowski model for electric field mediated colloidal crystallization using Brownian dynamic simulations, which were previously matched to experiments. Diffusion mapping is used to infer dimensionality and confirm the use of two order parameters, one for degree of condensation and one for global crystallinity. Free energy and diffusivity landscapes are obtained as the coefficients of a low-dimensional Smoluchowski equation to capture the thermodynamics and kinetics of microstructure evolution. The resulting low-dimensional model quantitatively captures the dynamics of different assembly pathways between fluid, polycrystal, and single crystals states, in agreement with the full N-dimensional data as characterizedmore » by first passage time distributions. Numerical solution of the low-dimensional Smoluchowski equation reveals statistical properties of the dynamic evolution of states vs. applied field amplitude and system size. The low-dimensional Smoluchowski equation and associated landscapes calculated here can serve as models for predictive control of electric field mediated assembly of colloidal ensembles into two-dimensional crystalline objects.« less

Dynamo transition in low-dimensional models.

PubMed

Verma, Mahendra K; Lessinnes, Thomas; Carati, Daniele; Sarris, Ioannis; Kumar, Krishna; Singh, Meenakshi

2008-09-01

Two low-dimensional magnetohydrodynamic models containing three velocity and three magnetic modes are described. One of them (nonhelical model) has zero kinetic and current helicity, while the other model (helical) has nonzero kinetic and current helicity. The velocity modes are forced in both these models. These low-dimensional models exhibit a dynamo transition at a critical forcing amplitude that depends on the Prandtl number. In the nonhelical model, dynamo exists only for magnetic Prandtl number beyond 1, while the helical model exhibits dynamo for all magnetic Prandtl number. Although the model is far from reproducing all the possible features of dynamo mechanisms, its simplicity allows a very detailed study and the observed dynamo transition is shown to bear similarities with recent numerical and experimental results.

Lee wave breaking region: the map of instability development scenarios

NASA Astrophysics Data System (ADS)

Yakovenko, S. N.

2017-10-01

Numerical study of a stably stratified flow above the two-dimensional cosine-shaped obstacle has been performed by DNS and LES. These methods were implemented to solve the three-dimensional Navier-Stokes equations in the Boussinesq approximation, together with by the scalar diffusion equation. The results of scanning in the wide ranges of physical parameters (Reynolds and Prandtl/Schmidt numbers relating to laboratory experiment cases and atmospheric or oceanic situations) are presented for instability and turbulence development scenarios in the overturning internal lee waves. The latter is generated by the obstacle in a flow with the constant inflow values of velocity and stable density gradient. Evolution of lee-wave breaking is explored by visualization of velocity and scalar (density) fields, and the analysis of spectra. Based on the numerical simulation results, the power-law dependence on Reynolds number is demonstrated for the wavelength of the most unstable perturbation.

Study on Damage Evaluation and Machinability of UD-CFRP for the Orthogonal Cutting Operation Using Scanning Acoustic Microscopy and the Finite Element Method.

PubMed

Wang, Dongyao; He, Xiaodong; Xu, Zhonghai; Jiao, Weicheng; Yang, Fan; Jiang, Long; Li, Linlin; Liu, Wenbo; Wang, Rongguo

2017-02-20

Owing to high specific strength and designability, unidirectional carbon fiber reinforced polymer (UD-CFRP) has been utilized in numerous fields to replace conventional metal materials. Post machining processes are always required for UD-CFRP to achieve dimensional tolerance and assembly specifications. Due to inhomogeneity and anisotropy, UD-CFRP differs greatly from metal materials in machining and failure mechanism. To improve the efficiency and avoid machining-induced damage, this paper undertook to study the correlations between cutting parameters, fiber orientation angle, cutting forces, and cutting-induced damage for UD-CFRP laminate. Scanning acoustic microscopy (SAM) was employed and one-/two-dimensional damage factors were then created to quantitatively characterize the damage of the laminate workpieces. According to the 3D Hashin's criteria a numerical model was further proposed in terms of the finite element method (FEM). A good agreement between simulation and experimental results was validated for the prediction and structural optimization of the UD-CFRP.

Study on Damage Evaluation and Machinability of UD-CFRP for the Orthogonal Cutting Operation Using Scanning Acoustic Microscopy and the Finite Element Method

PubMed Central

Wang, Dongyao; He, Xiaodong; Xu, Zhonghai; Jiao, Weicheng; Yang, Fan; Jiang, Long; Li, Linlin; Liu, Wenbo; Wang, Rongguo

2017-01-01

Owing to high specific strength and designability, unidirectional carbon fiber reinforced polymer (UD-CFRP) has been utilized in numerous fields to replace conventional metal materials. Post machining processes are always required for UD-CFRP to achieve dimensional tolerance and assembly specifications. Due to inhomogeneity and anisotropy, UD-CFRP differs greatly from metal materials in machining and failure mechanism. To improve the efficiency and avoid machining-induced damage, this paper undertook to study the correlations between cutting parameters, fiber orientation angle, cutting forces, and cutting-induced damage for UD-CFRP laminate. Scanning acoustic microscopy (SAM) was employed and one-/two-dimensional damage factors were then created to quantitatively characterize the damage of the laminate workpieces. According to the 3D Hashin’s criteria a numerical model was further proposed in terms of the finite element method (FEM). A good agreement between simulation and experimental results was validated for the prediction and structural optimization of the UD-CFRP. PMID:28772565

Shock probes in a one-dimensional Katz-Lebowitz-Spohn model

NASA Astrophysics Data System (ADS)

Chatterjee, Sakuntala; Barma, Mustansir

2008-06-01

We consider shock probes in a one-dimensional driven diffusive medium with nearest-neighbor Ising interaction (KLS model). Earlier studies based on an approximate mapping of the present system to an effective zero-range process concluded that the exponents characterizing the decays of several static and dynamical correlation functions of the probes depend continuously on the strength of the Ising interaction. On the contrary, our numerical simulations indicate that over a substantial range of the interaction strength, these exponents remain constant and their values are the same as in the case of no interaction (when the medium executes an ASEP). We demonstrate this by numerical studies of several dynamical correlation functions for two probes and also for a macroscopic number of probes. Our results are consistent with the expectation that the short-ranged correlations induced by the Ising interaction should not affect the large time and large distance properties of the system, implying that scaling forms remain the same as in the medium with no interactions present.

Numerical simulation of premixed flame propagation in a closed tube

NASA Astrophysics Data System (ADS)

Kuzuu, Kazuto; Ishii, Katsuya; Kuwahara, Kunio

1996-08-01

Premixed flame propagation of methane-air mixture in a closed tube is estimated through a direct numerical simulation of the three-dimensional unsteady Navier-Stokes equations coupled with chemical reaction. In order to deal with a combusting flow, an extended version of the MAC method, which can be applied to a compressible flow with strong density variation, is employed as a numerical method. The chemical reaction is assumed to be an irreversible single step reaction between methane and oxygen. The chemical species are CH 4, O 2, N 2, CO 2, and H 2O. In this simulation, we reproduce a formation of a tulip flame in a closed tube during the flame propagation. Furthermore we estimate not only a two-dimensional shape but also a three-dimensional structure of the flame and flame-induced vortices, which cannot be observed in the experiments. The agreement between the calculated results and the experimental data is satisfactory, and we compare the phenomenon near the side wall with the one in the corner of the tube.

On the Navier Stokes equations simulation of the head-on collision between two surface solitary waves

NASA Astrophysics Data System (ADS)

Lubin, Pierre; Vincent, Stéphane; Caltagirone, Jean-Paul

2005-04-01

The scope of this Note is to show the results obtained for simulating the two-dimensional head-on collision of two solitary waves by solving the Navier-Stokes equations in air and water. The work is dedicated to the numerical investigation of the hydrodynamics associated to this highly nonlinear flow configuration, the first numerical results being analyzed. The original numerical model is proved to be efficient and accurate in predicting the main features described in experiments found in the literature. This Note also outlines the interest of this configuration to be considered as a test-case for numerical models dedicated to computational fluid mechanics. To cite this article: P. Lubin et al., C. R. Mecanique 333 (2005).

Two-Dimensional Versus Three-Dimensional Conceptualization in Astronomy Education

NASA Astrophysics Data System (ADS)

Reynolds, Michael David

Numerous science conceptual issues are naturally three-dimensional. Classroom presentations are often two -dimensional or at best multidimensional. Several astronomy topics are of this nature, e. g. mechanics of the phases of the moon. Textbooks present this three-dimensional topic in two-dimensions; such is often the case in the classroom. This study was conducted to examine conceptions exhibited by pairs of like-sex 11th grade standard physics students as they modeled the lunar phases. Student pairs, 13 male and 13 female, were randomly selected and assigned. Pairing comes closer to classroom emulation, minimizes needs for direct probes, and pair discussion is more likely to display variety and depth. Four hypotheses were addressed: (1) Participants who model three-dimensionally will more likely achieve a higher explanation score. (2) Students who experienced more earth or physical science exposure will more likely model three-dimensionally. (3) Pairs that exhibit a strong science or mathematics preference will more likely model three-dimensionally. (4) Males will model in three dimensions more than females. Students provided background information, including science course exposure and subject preference. Each pair laid out a 16-card set representing two complete lunar phase changes. The pair was asked to explain why the phases occur. Materials were provided for use, including disks, spheres, paper and pen, and flashlight. Activities were videotaped for later evaluation. Statistics of choice was a correlation determination between course preference and model type and ANOVA for the other hypotheses. It was determined that pairs who modeled three -dimensionally achieved a higher score on their phases mechanics explanation at p <.05 level. Pairs with earth science or physical science exposure, those who prefer science or mathematics, and male participants were not more likely to model three-dimensionally. Possible reasons for lack of significance was small sample size and in the case of course preferences, small differences in course preference means. Based on this study, instructors should be aware of dimensionality and student misconceptions. Whenever possible, three-dimensional concepts should be modeled as such. Authors and publishers should consider modeling suggestions and three-dimensional ancillaries.

Numeric stratigraphic modeling: Testing sequence Numeric stratigraphic modeling: Testing sequence stratigraphic concepts using high resolution geologic examples

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

Armentrout, J.M.; Smith-Rouch, L.S.; Bowman, S.A.

1996-08-01

Numeric simulations based on integrated data sets enhance our understanding of depositional geometry and facilitate quantification of depositional processes. Numeric values tested against well-constrained geologic data sets can then be used in iterations testing each variable, and in predicting lithofacies distributions under various depositional scenarios using the principles of sequence stratigraphic analysis. The stratigraphic modeling software provides a broad spectrum of techniques for modeling and testing elements of the petroleum system. Using well-constrained geologic examples, variations in depositional geometry and lithofacies distributions between different tectonic settings (passive vs. active margin) and climate regimes (hothouse vs. icehouse) can provide insight tomore » potential source rock and reservoir rock distribution, maturation timing, migration pathways, and trap formation. Two data sets are used to illustrate such variations: both include a seismic reflection profile calibrated by multiple wells. The first is a Pennsylvanian mixed carbonate-siliciclastic system in the Paradox basin, and the second a Pliocene-Pleistocene siliciclastic system in the Gulf of Mexico. Numeric simulations result in geometry and facies distributions consistent with those interpreted using the integrated stratigraphic analysis of the calibrated seismic profiles. An exception occurs in the Gulf of Mexico study where the simulated sediment thickness from 3.8 to 1.6 Ma within an upper slope minibasin was less than that mapped using a regional seismic grid. Regional depositional patterns demonstrate that this extra thickness was probably sourced from out of the plane of the modeled transect, illustrating the necessity for three-dimensional constraints on two-dimensional modeling.« less

Some issues in the simulation of two-phase flows: The relative velocity

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

Gräbel, J.; Hensel, S.; Ueberholz, P.

In this paper we compare numerical approximations for solving the Riemann problem for a hyperbolic two-phase flow model in two-dimensional space. The model is based on mixture parameters of state where the relative velocity between the two-phase systems is taken into account. This relative velocity appears as a main discontinuous flow variable through the complete wave structure and cannot be recovered correctly by some numerical techniques when simulating the associated Riemann problem. Simulations are validated by comparing the results of the numerical calculation qualitatively with OpenFOAM software. Simulations also indicate that OpenFOAM is unable to resolve the relative velocity associatedmore » with the Riemann problem.« less