Frequency and Time Domain Modeling of Acoustic Liner Boundary Conditions
NASA Technical Reports Server (NTRS)
Bliss, Donald B.
1982-01-01
As part of a research program directed at the acoustics of advanced subsonic propulsion systems undertaken at NASA Langley, Duke University was funded to develop a boundary condition model for bulk-reacting nacelle liners. The overall objective of the Langley program was to understand and predict noise from advanced subsonic transport engines and to develop related noise control technology. The overall technical areas included: fan and propeller source noise, acoustics of ducts and duct liners, interior noise, subjective acoustics, and systems noise prediction. The Duke effort was directed toward duct liner acoustics for the development of analytical methods to characterize liner behavior in both frequency domain and time domain. A review of duct acoustics and liner technology can be found in Reference [1]. At that time, NASA Langley was investigating the propulsion concept of an advanced ducted fan, with a large diameter housed inside a relatively short duct. Fan diameters in excess of ten feet were proposed. The lengths of both the inlet and exhaust portions of the duct were to be short, probably less than half the fan diameter. The nacelle itself would be relatively thin-walled for reasons of aerodynamic efficiency. The blade-passage frequency was expected to be less than I kHz, and very likely in the 200 to 300 Hz range. Because of the design constraints of a short duct, a thin nacelle, and long acoustic wavelengths, the application of effective liner technology would be especially challenging. One of the needs of the NASA Langley program was the capability to accurately and efficiently predict the behavior of the acoustic liner. The traditional point impedance method was not an adequate model for proposed liner designs. The method was too restrictive to represent bulk reacting liners and to allow for the characterization of many possible innovative liner concepts. In the research effort at Duke, an alternative method, initially developed to handle bulk
Periodic Time-Domain Nonlocal Nonreflecting Boundary Conditions for Duct Acoustics
NASA Technical Reports Server (NTRS)
Watson, Willie R.; Zorumski, William E.
1996-01-01
Periodic time-domain boundary conditions are formulated for direct numerical simulation of acoustic waves in ducts without flow. Well-developed frequency-domain boundary conditions are transformed into the time domain. The formulation is presented here in one space dimension and time; however, this formulation has an advantage in that its extension to variable-area, higher dimensional, and acoustically treated ducts is rigorous and straightforward. The boundary condition simulates a nonreflecting wave field in an infinite uniform duct and is implemented by impulse-response operators that are applied at the boundary of the computational domain. These operators are generated by convolution integrals of the corresponding frequency-domain operators. The acoustic solution is obtained by advancing the Euler equations to a periodic state with the MacCormack scheme. The MacCormack scheme utilizes the boundary condition to limit the computational space and preserve the radiation boundary condition. The success of the boundary condition is attributed to the fact that it is nonreflecting to periodic acoustic waves. In addition, transient waves can pass rapidly out of the solution domain. The boundary condition is tested for a pure tone and a multitone source in a linear setting. The effects of various initial conditions are assessed. Computational solutions with the boundary condition are consistent with the known solutions for nonreflecting wave fields in an infinite uniform duct.
Time dependent inflow-outflow boundary conditions for 2D acoustic systems
NASA Technical Reports Server (NTRS)
Watson, Willie R.; Myers, Michael K.
1989-01-01
An analysis of the number and form of the required inflow-outflow boundary conditions for the full two-dimensional time-dependent nonlinear acoustic system in subsonic mean flow is performed. The explicit predictor-corrector method of MacCormack (1969) is used. The methodology is tested on both uniform and sheared mean flows with plane and nonplanar sources. Results show that the acoustic system requires three physical boundary conditions on the inflow and one on the outflow boundary. The most natural choice for the inflow boundary conditions is judged to be a specification of the vorticity, the normal acoustic impedance, and a pressure gradient-density gradient relationship normal to the boundary. Specification of the acoustic pressure at the outflow boundary along with these inflow boundary conditions is found to give consistent reliable results. A set of boundary conditions developed earlier, which were intended to be nonreflecting is tested using the current method and is shown to yield unstable results for nonplanar acoustic waves.
Jing, Yun; Xiang, Ning
2008-01-01
This paper proposes a modified boundary condition to improve the room-acoustic prediction accuracy of a diffusion equation model. Previous boundary conditions for the diffusion equation model have certain limitations which restrict its application to a certain number of room types. The boundary condition employing the Sabine absorption coefficient [V. Valeau et al., J. Acoust. Soc. Am. 119, 1504-1513 (2006)] cannot predict the sound field well when the absorption coefficient is high, while the boundary condition employing the Eyring absorption coefficient [Y. Jing and N. Xiang, J. Acoust. Soc. Am. 121, 3284-3287 (2007); A. Billon et al., Appl. Acoust. 69, (2008)] has a singularity whenever any surface material has an absorption coefficient of 1.0. The modified boundary condition is derived based on an analogy between sound propagation and light propagation. Simulated and experimental data are compared to verify the modified boundary condition in terms of room-acoustic parameter prediction. The results of this comparison suggest that the modified boundary condition is valid for a range of absorption coefficient values and successfully eliminates the singularity problem. PMID:18177146
Structural acoustic control of plates with variable boundary conditions: design methodology.
Sprofera, Joseph D; Cabell, Randolph H; Gibbs, Gary P; Clark, Robert L
2007-07-01
A method for optimizing a structural acoustic control system subject to variations in plate boundary conditions is provided. The assumed modes method is used to build a plate model with varying levels of rotational boundary stiffness to simulate the dynamics of a plate with uncertain edge conditions. A transducer placement scoring process, involving Hankel singular values, is combined with a genetic optimization routine to find spatial locations robust to boundary condition variation. Predicted frequency response characteristics are examined, and theoretically optimized results are discussed in relation to the range of boundary conditions investigated. Modeled results indicate that it is possible to minimize the impact of uncertain boundary conditions in active structural acoustic control by optimizing the placement of transducers with respect to those uncertainties. PMID:17614487
A comparison of time domain boundary conditions for acoustic waves in wave guides
NASA Technical Reports Server (NTRS)
Banks, H. T.; Propst, G.; Silcox, R. J.
1991-01-01
Researchers consider several types of boundary conditions in the context of time domain models for acoustic waves. Experiments with four different duct terminations (hard wall, free radiation, foam, and wedge) were carried out in a wave duct from which reflection coefficients over a wide frequency range were measured. These reflection coefficients were used to estimate parameters in the time domain boundary conditions. A comparison of the relative merits of the models in describing the data is presented. Boundary conditions which yield a good fit of the model to the experimental data were found for all duct terminations except the wedge.
Active control of the acoustic boundary conditions of combustion test rigs
NASA Astrophysics Data System (ADS)
Bothien, Mirko R.; Moeck, Jonas P.; Oliver Paschereit, Christian
2008-12-01
In the design process of burners for gas turbines, new burner generations are generally tested in single or multi burner combustion test rigs. With these experiments, computational fluid dynamics, and finite element calculations, the burners' performance in the full-scale engine is sought to be predicted. Especially, information about the thermoacoustic behaviour and the emission characteristics is very important. As the thermoacoustics strongly depend on the acoustic boundary conditions of the system, it is obvious that test rig conditions should match, or be close to those of the full-scale engine. This is, however, generally not the case. Hence, if the combustion process in the test rig is stable at certain operating conditions, it may show unfavourable dynamics at the same conditions in the engine. In this work, a method is proposed which uses an active control scheme to manipulate the acoustic boundary conditions of the test rig. Using this method, the boundary conditions can be continuously modified, ranging from anechoic to fully reflecting in a broad frequency range. The concept is applied to an atmospheric combustion test rig with a swirl-stabilized burner. It is shown that the test rig's properties can be tuned to correspond to those of the full-scale engine. For example, the test rig length can be virtually extended, thereby introducing different resonance frequencies, without having to implement any hardware changes. Furthermore, the acoustic boundary condition can be changed to that of a choked flow without actually needing the flow to be choked.
Evaluation of several non-reflecting computational boundary conditions for duct acoustics
NASA Technical Reports Server (NTRS)
Watson, Willie R.; Zorumski, William E.; Hodge, Steve L.
1994-01-01
Several non-reflecting computational boundary conditions that meet certain criteria and have potential applications to duct acoustics are evaluated for their effectiveness. The same interior solution scheme, grid, and order of approximation are used to evaluate each condition. Sparse matrix solution techniques are applied to solve the matrix equation resulting from the discretization. Modal series solutions for the sound attenuation in an infinite duct are used to evaluate the accuracy of each non-reflecting boundary conditions. The evaluations are performed for sound propagation in a softwall duct, for several sources, sound frequencies, and duct lengths. It is shown that a recently developed nonlocal boundary condition leads to sound attenuation predictions considerably more accurate for short ducts. This leads to a substantial reduction in the number of grid points when compared to other non-reflecting conditions.
Li, Chenxi; Cazzolato, Ben; Zander, Anthony
2016-01-01
The classic analytical model for the sound absorption of micro perforated materials is well developed and is based on a boundary condition where the velocity of the material is assumed to be zero, which is accurate when the material vibration is negligible. This paper develops an analytical model for finite-sized circular micro perforated membranes (MPMs) by applying a boundary condition such that the velocity of air particles on the hole wall boundary is equal to the membrane vibration velocity (a zero-slip condition). The acoustic impedance of the perforation, which varies with its position, is investigated. A prediction method for the overall impedance of the holes and the combined impedance of the MPM is also provided. The experimental results for four different MPM configurations are used to validate the model and good agreement between the experimental and predicted results is achieved. PMID:26827008
Ultrasound-induced lung hemorrhage: Role of acoustic boundary conditions at the pleural surface
NASA Astrophysics Data System (ADS)
O'Brien, William D.; Kramer, Jeffrey M.; Waldrop, Tony G.; Frizzell, Leon A.; Miller, Rita J.; Blue, James P.; Zachary, James F.
2002-02-01
In a previous study [J. Acoust. Soc. Am. 108, 1290 (2000)] the acoustic impedance difference between intercostal tissue and lung was evaluated as a possible explanation for the enhanced lung damage with increased hydrostatic pressure, but the hydrostatic-pressure-dependent impedance difference alone could not explain the enhanced occurrence of hemorrhage. In that study, it was hypothesized that the animal's breathing pattern might be altered as a function of hydrostatic pressure, which in turn might affect the volume of air inspired and expired. The acoustic impedance difference between intercostal tissue and lung would be affected with altered lung inflation, thus altering the acoustic boundary conditions. In this study, 12 rats were exposed to 3 volumes of lung inflation (inflated: approximately tidal volume; half-deflated: half-tidal volume; deflated: lung volume at functional residual capacity), 6 rats at 8.6-MPa in situ peak rarefactional pressure (MI of 3.1) and 6 rats at 16-MPa in situ peak rarefactional pressure (MI of 5.8). Respiration was chemically inhibited and a ventilator was used to control lung volume and respiratory frequency. Superthreshold ultrasound exposures of the lungs were used (3.1-MHz, 1000-Hz PRF, 1.3-μs pulse duration, 10-s exposure duration) to produce lesions. Deflated lungs were more easily damaged than half-deflated lungs, and half-deflated lungs were more easily damaged than inflated lungs. In fact, there were no lesions observed in inflated lungs in any of the rats. The acoustic impedance difference between intercostal tissue and lung is much less for the deflated lung condition, suggesting that the extent of lung damage is related to the amount of acoustic energy that is propagated across the pleural surface boundary.
NASA Technical Reports Server (NTRS)
Tam, Christopher K. W.; Fang, Jun; Kurbatskii, Konstantin A.
1996-01-01
A set of nonhomogeneous radiation and outflow conditions which automatically generate prescribed incoming acoustic or vorticity waves and, at the same time, are transparent to outgoing sound waves produced internally in a finite computation domain is proposed. This type of boundary condition is needed for the numerical solution of many exterior aeroacoustics problems. In computational aeroacoustics, the computation scheme must be as nondispersive ans nondissipative as possible. It must also support waves with wave speeds which are nearly the same as those of the original linearized Euler equations. To meet these requirements, a high-order/large-stencil scheme is necessary The proposed nonhomogeneous radiation and outflow boundary conditions are designed primarily for use in conjunction with such high-order/large-stencil finite difference schemes.
Feng, Xue; Ben Tahar, Mabrouk; Baccouche, Ryan
2016-01-01
This paper presents a solution for aero-acoustic problems using the Galbrun equation in the time domain with a non-uniform steady mean flow in a two-dimensional coordinate system and the perfectly matched layer technique as the boundary conditions corresponding to an unbounded domain. This approach is based on an Eulerian-Lagrangian description corresponding to a wave equation written only in terms of the Lagrangian perturbation of the displacement. It is an alternative to the Linearized Euler Equations for solving aero-acoustic problems. The Galbrun equation is solved using a mixed pressure-displacement Finite Element Method. A complex Laplace transform scheme is used to study the time dependent variables. Several numerical examples are presented to validate and illustrate the efficiency of the proposed approach. PMID:26827028
NASA Technical Reports Server (NTRS)
Hariharan, S. I.
1985-01-01
Elliptic and hyperbolic problems in unbounded regions are considered. These problems, when one wants to solve them numerically, have the difficulty of prescribing boundary conditions at infinity. Computationally, one needs a finite region in which to solve these problems. The corresponding conditions at infinity imposed on the finite distance boundaries should dictate the boundary conditions at infinity and be accurate with respect to the interior numerical scheme. The treatment of these boundary conditions for wave-like equations is discussed.
NASA Astrophysics Data System (ADS)
King, J. R. C.; Ziolkowski, A. M.; Ruffert, M.
2015-03-01
We have developed a new boundary condition for finite volume simulations of oscillating bubbles. Our method uses an approximation to the motion outside the domain, based on the solution at the domain boundary. We then use this approximation to apply boundary conditions by defining incoming characteristic waves at the domain boundary. Our boundary condition is applicable in regions where the motion is close to spherically symmetric. We have tested our method on a range of one- and two-dimensional test cases. Results show good agreement with previous studies. The method allows simulations of oscillating bubbles for long run times (5 ×105 time steps with a CFL number of 0.8) on highly truncated domains, in which the boundary condition may be applied within 0.1% of the maximum bubble radius. Conservation errors due to the boundary conditions are found to be of the order of 0.1% after 105 time steps. The method significantly reduces the computational cost of fixed grid finite volume simulations of oscillating bubbles. Two-dimensional results demonstrate that highly asymmetric bubble features, such as surface instabilities and the formation of jets, may be captured on a small domain using this boundary condition.
Asymptotic behavior to a von Kármán equations of memory type with acoustic boundary conditions
NASA Astrophysics Data System (ADS)
Kang, Jum-Ran
2016-06-01
We study the stability of solutions to a von Kármán plate model of memory type with acoustic boundary conditions. We establish the general decay rate result, using some properties of the convex functions. Our result is obtained without imposing any restrictive assumptions on the behavior of the relaxation function at infinity. These general decay estimates extend and improve on some earlier results-exponential or polynomial decay rates.
NASA Technical Reports Server (NTRS)
Darling, Douglas; Radhakrishnan, Krishnan; Oyediran, Ayo
1995-01-01
Premixed combustors, which are being considered for low NOx engines, are susceptible to instabilities due to feedback between pressure perturbations and combustion. This feedback can cause damaging mechanical vibrations of the system as well as degrade the emissions characteristics and combustion efficiency. In a lean combustor instabilities can also lead to blowout. A model was developed to perform linear combustion-acoustic stability analysis using detailed chemical kinetic mechanisms. The Lewis Kinetics and Sensitivity Analysis Code, LSENS, was used to calculate the sensitivities of the heat release rate to perturbations in density and temperature. In the present work, an assumption was made that the mean flow velocity was small relative to the speed of sound. Results of this model showed the regions of growth of perturbations to be most sensitive to the reflectivity of the boundary when reflectivities were close to unity.
Wright, Louise; Robinson, Stephen P; Humphrey, Victor F
2009-03-01
This paper presents a computational technique using the boundary element method for prediction of radiated acoustic waves from axisymmetric surfaces with nonaxisymmetric boundary conditions. The aim is to predict the far-field behavior of underwater acoustic transducers based on their measured behavior in the near-field. The technique is valid for all wavenumbers and uses a volume integral method to calculate the singular integrals required by the boundary element formulation. The technique has been implemented on a distributed computing system to take advantage of its parallel nature, which has led to significant reductions in the time required to generate results. Measurement data generated by a pair of free-flooding underwater acoustic transducers encapsulated in a polyurethane polymer have been used to validate the technique against experiment. The dimensions of the outer surface of the transducers (including the polymer coating) were an outer diameter of 98 mm with an 18 mm wall thickness and a length of 92 mm. The transducers were mounted coaxially, giving an overall length of 185 mm. The cylinders had resonance frequencies at 13.9 and 27.5 kHz, and the data were gathered at these frequencies. PMID:19275294
NASA Astrophysics Data System (ADS)
Song, Peng; Liu, Zhaolun; Zhang, Xiaobo; Tan, Jun; Xia, Dongming; Li, Jing; Zhu, Bo
2015-12-01
This paper introduces the fourth-order absorbing boundary condition (ABC) into staggered-grid finite difference forward modeling of the first-order stress-velocity acoustic equation, and develops a new method to optimize coefficients of the fourth-order ABC to further improve its overall absorbing effect. Theoretical analysis and the results of numerical tests demonstrate that the fourth-order ABC with optimized coefficients has much higher absorbing efficiency than both the conventional second-order and fourth-order ABCs without optimized coefficients, for waves with large incident angles. Compared with the perfectly matched layer (PML) with 40 layers, the fourth-order ABC not only has a much better absorbing effect, but also uses far less computer memory for calculation. We present the fourth-order ABC with optimized coefficients as an ideal artificial boundary for the simulation of the acoustic equation based on extensive and complex structure models. Supported by the Fundamental Research Funds for the Central Universities (201513005).
Dynamic Acoustic Detection of Boundary Layer transition
NASA Technical Reports Server (NTRS)
Grohs, Jonathan R.
1995-01-01
The wind tunnel investigation into the acoustic nature of boundary layer transition using miniature microphones. This research is the groundwork for entry into the National Transonic Facility (NTF) at the NASA Langley Research Center (LaRC). Due to the extreme environmental conditions of NTF testing, low temperatures and high pressures, traditional boundary layer detection methods are not available. The emphasis of this project and further studies is acoustical sampling of a typical boundary layer and environmental durability of the miniature microphones. The research was conducted with the 14 by 22 Foot Subsonic Tunnel, concurrent with another wind tunnel test. Using the resources of LaRC, a full inquiry into the feasibility of using Knowles Electronics, Inc. EM-3086 microphones to detect the surface boundary layer, under differing conditions, was completed. This report shall discuss the difficulties encountered, product performance and observations, and future research adaptability of this method.
Solitons induced by boundary conditions
Zhou, R.L.
1987-01-01
Although soliton phenomena have attracted wide attention since 1965, there are still not enough efforts paid to mixed-boundary - initial-value problems that are important in real physical cases. The main purpose of this thesis is to study carefully the various boundary-induced soliton under different initial conditions. The author states with three sets of nonlinear equations: KdV equations and Boussinesq equations (for water); two-fluid equations for cold-ion plasma. He was interested in four types of problems involved with water solitons: excitation by different time-dependent boundary conditions under different initial conditions; head-on and over-taking collisions; reflection at a wall and the excitation by pure initial conditions. For KdV equations, only cases one and four are conducted. The results from two fully nonlinear KdV and Boussinesq equations are compared, and agree extremely well. The Boussinesq equations permit solition head-on collisions and reflections, studied the first time. The results from take-over collision agree with KdV results. For the ion-acoustic plasma, a set of Boussinesq-type equations was derived from the standard two-fluid equations for the ion-acoustic plasma. It theoretically proves the essential nature of the solitary wave solutions of the cold-ion plasma. The ion acoustic solitons are also obtained by prescribing a potential phi/sub 0/ at one grid point.
Evaluation of Boundary Conditions for Computational Aeroacoustics
NASA Technical Reports Server (NTRS)
Hixon, R.; Shih, S.-H.; Mankbadi, Reda R.
1995-01-01
The performance of three boundary conditions for aeroacoustics were investigated, namely, (1) Giles-1990; (2) Tam and Webb-1993, and (3) Thompson-1987. For each boundary condition, various implementations were tested to study the sensitivity of their performance to the implementation procedure. Details of all implementations are given. Results are shown for the acoustic field of a monopole in a uniform freestream.
Acoustic radar investigations of boundary layer phenomena
NASA Technical Reports Server (NTRS)
Marks, J. R.
1974-01-01
A comparison is made between acoustic radar echoes and conventional meteorological data obtained from the WKY tower, for the purpose of better understanding the relationships between acoustic radar echoes and boundary layer processes. Two thunderstorm outflow cases are presented and compared to both acoustic radar data and Charba's gust front model. The acoustic radar echoes reveal the boundary between warm and cold air and other areas of mixing and strong thermal gradient quite well. The thunderstorm outflow of 27 June 1972 is found to compare with in most respects to Charba's gust front model. The major difference is the complete separation of the head from the main body of cold air, probably caused by erosion of the area behind the head by mixing with the ambient air. Two cases of nocturnal inversions caused by advection of warmer air aloft are presented. It is found that areas of turbulent mixing or strong thermal gradient can be identified quite easily in the acoustic radar record.
NASA Astrophysics Data System (ADS)
Liu, Yang; Sen, Mrinal K.
2011-09-01
Most conventional finite-difference methods adopt second-order temporal and (2M)th-order spatial finite-difference stencils to solve the 3D acoustic wave equation. When spatial finite-difference stencils devised from the time-space domain dispersion relation are used to replace these conventional spatial finite-difference stencils devised from the space domain dispersion relation, the accuracy of modelling can be increased from second-order along any directions to (2M)th-order along 48 directions. In addition, the conventional high-order spatial finite-difference modelling accuracy can be improved by using a truncated finite-difference scheme. In this paper, we combine the time-space domain dispersion-relation-based finite difference scheme and the truncated finite-difference scheme to obtain optimised spatial finite-difference coefficients and thus to significantly improve the modelling accuracy without increasing computational cost, compared with the conventional space domain dispersion-relation-based finite difference scheme. We developed absorbing boundary conditions for the 3D acoustic wave equation, based on predicting wavefield values in a transition area by weighing wavefield values from wave equations and one-way wave equations. Dispersion analyses demonstrate that high-order spatial finite-difference stencils have greater accuracy than low-order spatial finite-difference stencils for high frequency components of wavefields, and spatial finite-difference stencils devised in the time-space domain have greater precision than those devised in the space domain under the same discretisation. The modelling accuracy can be improved further by using the truncated spatial finite-difference stencils. Stability analyses show that spatial finite-difference stencils devised in the time-space domain have better stability condition. Numerical modelling experiments for homogeneous, horizontally layered and Society of Exploration Geophysicists/European Association of
Numerical Boundary Condition Procedures
NASA Technical Reports Server (NTRS)
1981-01-01
Topics include numerical procedures for treating inflow and outflow boundaries, steady and unsteady discontinuous surfaces, far field boundaries, and multiblock grids. In addition, the effects of numerical boundary approximations on stability, accuracy, and convergence rate of the numerical solution are discussed.
Advances in Numerical Boundary Conditions for Computational Aeroacoustics
NASA Technical Reports Server (NTRS)
Tam, Christopher K. W.
1997-01-01
Advances in Computational Aeroacoustics (CAA) depend critically on the availability of accurate, nondispersive, least dissipative computation algorithm as well as high quality numerical boundary treatments. This paper focuses on the recent developments of numerical boundary conditions. In a typical CAA problem, one often encounters two types of boundaries. Because a finite computation domain is used, there are external boundaries. On the external boundaries, boundary conditions simulating the solution outside the computation domain are to be imposed. Inside the computation domain, there may be internal boundaries. On these internal boundaries, boundary conditions simulating the presence of an object or surface with specific acoustic characteristics are to be applied. Numerical boundary conditions, both external or internal, developed for simple model problems are reviewed and examined. Numerical boundary conditions for real aeroacoustic problems are also discussed through specific examples. The paper concludes with a description of some much needed research in numerical boundary conditions for CAA.
Acoustic sounding in the planetary boundary layer
NASA Technical Reports Server (NTRS)
Kelly, E. H.
1974-01-01
Three case studies are presented involving data from an acoustic radar. The first two cases examine data collected during the passage of a mesoscale cold-air intrusion, probably thunderstorm outflow, and a synoptic-scale cold front. In these studies the radar data are compared to conventional meteorological data obtained from the WKY tower facility for the purpose of radar data interpretation. It is shown that the acoustic radar echoes reveal the boundary between warm and cold air and other areas of turbulent mixing, regions of strong vertical temperature gradients, and areas of weak or no wind shear. The third case study examines the relationship between the nocturnal radiation inversion and the low-level wind maximum or jet in the light of conclusions presented by Blackadar (1957). The low-level jet is seen forming well above the top of the inversion. Sudden rapid growth of the inversion occurs which brings the top of the inversion to a height equal that of the jet. Coincident with the rapid growth of the inversion is a sudden decrease in the intensity of the acoustic radar echoes in the inversion layer. It is suggested that the decrease in echo intensity reveals a decrease in turbulent mixing in the inversion layer as predicted by Blackadar. It is concluded that the acoustic radar can be a valuable tool for study in the lower atmosphere.
Solution of Exterior Acoustic Problems by the Boundary Element Method.
NASA Astrophysics Data System (ADS)
Kirkup, Stephen Martin
Available from UMI in association with The British Library. The boundary element method is described and investigated, especially in respect of its application to exterior two -dimensional Laplace problems. Both empirical and algebraic analyses (including the effects of approximation of the boundary and boundary functions and the precision of the evaluation of the discrete forms) are developed. Methods for the automatic evaluation of the discrete forms of the Laplace and Helmholtz integral operators are reviewed and extended. Boundary element methods for the solution of exterior Helmholtz problems with general (but most importantly Neumann) boundary conditions are reviewed and some are explicitly stated using a new notation. Boundary element methods based on the boundary integral equations introduced by Brakhage & Werner/ Leis/ Panich/ Kussmaul (indirect) and Burton & Miller (direct) are given prime consideration and implemented for three -dimensional problems. The influence of the choice of weighting parameter on the performance of the methods is explored and further guidance is given. The application of boundary element methods and methods based on the Rayleigh integral to acoustic radiation problems are considered. Methods for speeding up their solution via the boundary element method are developed. Library subroutines for the solution of acoustic radiation problems are described and demonstrated. Computational techniques for the problem of predicting the noise produced by a running engine are reviewed and appraised. The application of the boundary element method to low-noise engine design and in the design of noise shields is considered. The boundary element method is applied to the Ricardo crankcase simulation rig, which is an engine -like structure. A comparison of predicted and measured sound power spectra is given.
Solution of exterior acoustic problems by the boundary element method
NASA Astrophysics Data System (ADS)
Kirkup, Stephen Martin
The boundary element method is described and investigated, especially in respect of its application to exterior two-dimensional Laplace problems. Both empirical and algebraic analyses (including the effects of approximation of the boundary and boundary functions and the precision of the evaluation of the discrete forms) are developed. Methods for the automatic evaluation of the discrete forms of the Laplace and Helmholtz integral operators are reviewed and extended. Boundary element methods for the solution of exterior Helmholtz problems with general (but most importantly Neumann) boundary conditions are reviewed and some are explicitly stated using a new notation. Boundary element methods based on the boundary integral equations introduced by Brakhage and Werner/Leis/Panich/Kussmaul (indirect) and Burton and Miller (direct) are given prime consideration and implemented for three-dimensional problems. The influence of the choice of weighting parameter on the performance of the methods is explored and further guidance is given. The application of boundary element methods and methods based on the Rayleigh integral to acoustic radiation problems are considered. Methods for speeding up their solution via the boundary element method are developed. Library subroutines for the solution of acoustic radiation problems are described and demonstrated. Computational techniques for the problem of predicting the noise produced by a running engine are reviewed and appraised. The application of the boundary element method to low-noise engine design and in the design of noise shields is considered. The boundary element method is applied to the Ricardo crankcase simulation rig, which is an engine-like structure. A comparison of predicted and measured sound power spectra is given.
Acoustics of laminar boundary layers breakdown
NASA Technical Reports Server (NTRS)
Wang, Meng
1994-01-01
Boundary layer flow transition has long been suggested as a potential noise source in both marine (sonar-dome self noise) and aeronautical (aircraft cabin noise) applications, owing to the highly transient nature of process. The design of effective noise control strategies relies upon a clear understanding of the source mechanisms associated with the unsteady flow dynamics during transition. Due to formidable mathematical difficulties, theoretical predictions either are limited to early linear and weakly nonlinear stages of transition, or employ acoustic analogy theories based on approximate source field data, often in the form of empirical correlation. In the present work, an approach which combines direct numerical simulation of the source field with the Lighthill acoustic analogy is utilized. This approach takes advantage of the recent advancement in computational capabilities to obtain detailed information about the flow-induced acoustic sources. The transitional boundary layer flow is computed by solving the incompressible Navier-Stokes equations without model assumptions, thus allowing a direct evaluation of the pseudosound as well as source functions, including the Lighthill stress tensor and the wall shear stress. The latter are used for calculating the radiated pressure field based on the Curle-Powell solution of the Lighthill equation. This procedure allows a quantitative assessment of noise source mechanisms and the associated radiation characteristics during transition from primary instability up to the laminar breakdown stage. In particular, one is interested in comparing the roles played by the fluctuating volume Reynolds stress and the wall-shear-stresses, and in identifying specific flow processes and structures that are effective noise generators.
Time-Domain Impedance Boundary Conditions for Computational Aeroacoustics
NASA Technical Reports Server (NTRS)
Tam, Christopher K. W.; Auriault, Laurent
1996-01-01
It is an accepted practice in aeroacoustics to characterize the properties of an acoustically treated surface by a quantity known as impedance. Impedance is a complex quantity. As such, it is designed primarily for frequency-domain analysis. Time-domain boundary conditions that are the equivalent of the frequency-domain impedance boundary condition are proposed. Both single frequency and model broadband time-domain impedance boundary conditions are provided. It is shown that the proposed boundary conditions, together with the linearized Euler equations, form well-posed initial boundary value problems. Unlike ill-posed problems, they are free from spurious instabilities that would render time-marching computational solutions impossible.
Prediction of sound fields in acoustical cavities using the boundary element method. M.S. Thesis
NASA Technical Reports Server (NTRS)
Kipp, C. R.; Bernhard, R. J.
1985-01-01
A method was developed to predict sound fields in acoustical cavities. The method is based on the indirect boundary element method. An isoparametric quadratic boundary element is incorporated. Pressure, velocity and/or impedance boundary conditions may be applied to a cavity by using this method. The capability to include acoustic point sources within the cavity is implemented. The method is applied to the prediction of sound fields in spherical and rectangular cavities. All three boundary condition types are verified. Cases with a point source within the cavity domain are also studied. Numerically determined cavity pressure distributions and responses are presented. The numerical results correlate well with available analytical results.
Xu, Y.; Xia, J.; Miller, R.D.
2007-01-01
The need for incorporating the traction-free condition at the air-earth boundary for finite-difference modeling of seismic wave propagation has been discussed widely. A new implementation has been developed for simulating elastic wave propagation in which the free-surface condition is replaced by an explicit acoustic-elastic boundary. Detailed comparisons of seismograms with different implementations for the air-earth boundary were undertaken using the (2,2) (the finite-difference operators are second order in time and space) and the (2,6) (second order in time and sixth order in space) standard staggered-grid (SSG) schemes. Methods used in these comparisons to define the air-earth boundary included the stress image method (SIM), the heterogeneous approach, the scheme of modifying material properties based on transversely isotropic medium approach, the acoustic-elastic boundary approach, and an analytical approach. The method proposed achieves the same or higher accuracy of modeled body waves relative to the SIM. Rayleigh waves calculated using the explicit acoustic-elastic boundary approach differ slightly from those calculated using the SIM. Numerical results indicate that when using the (2,2) SSG scheme for SIM and our new method, a spatial step of 16 points per minimum wavelength is sufficient to achieve 90% accuracy; 32 points per minimum wavelength achieves 95% accuracy in modeled Rayleigh waves. When using the (2,6) SSG scheme for the two methods, a spatial step of eight points per minimum wavelength achieves 95% accuracy in modeled Rayleigh waves. Our proposed method is physically reasonable and, based on dispersive analysis of simulated seismographs from a layered half-space model, is highly accurate. As a bonus, our proposed method is easy to program and slightly faster than the SIM. ?? 2007 Society of Exploration Geophysicists.
Boundary Condition for Modeling Semiconductor Nanostructures
NASA Technical Reports Server (NTRS)
Lee, Seungwon; Oyafuso, Fabiano; von Allmen, Paul; Klimeck, Gerhard
2006-01-01
A recently proposed boundary condition for atomistic computational modeling of semiconductor nanostructures (particularly, quantum dots) is an improved alternative to two prior such boundary conditions. As explained, this boundary condition helps to reduce the amount of computation while maintaining accuracy.
Acoustic streaming field structure. Part II. Examples that include boundary-driven flow.
Bradley, Charles
2012-01-01
In this paper three simple acoustic streaming problems are presented and solved. The purpose of the paper is to demonstrate the use of a previously published streaming model by Bradley [J. Acoust. Soc. Am. 100(3), 1399-1408 (1996)] and illustrate, with concrete examples, some of the features of streaming flows that were predicted by the general model. In particular, the problems are intended to demonstrate cases in which the streaming field boundary condition at the face of the radiator has a nontrivial lateral dc velocity component. Such a boundary condition drives a steady solenoidal flow just like a laterally translating boundary drives Couette flow. PMID:22280567
Acoustic Emissions Reveal Combustion Conditions
NASA Technical Reports Server (NTRS)
Ramohalli, D. N. R.; Seshan, P. K.
1983-01-01
Turbulent-flame acoustic emissions change with air/fuel ratio variations. Acoustic emissions sensed and processed to detect inefficient operation; control system responds by adjusting fuel/air mixture for greater efficiency. Useful for diagnosis of combustion processes and fuel/air control.
Tidal Boundary Conditions in SEAWAT
Mulligan, Ann E.; Langevin, Christian; Post, Vincent E.A.
2011-01-01
SEAWAT, a U.S. Geological Survey groundwater flow and transport code, is increasingly used to model the effects of tidal motion on coastal aquifers. Different options are available to simulate tidal boundaries but no guidelines exist nor have comparisons been made to identify the most effective approach. We test seven methods to simulate a sloping beach and a tidal flat. The ocean is represented in one of the three ways: directly using a high hydraulic conductivity (high-K) zone and indirect simulation via specified head boundaries using either the General Head Boundary (GHB) or the new Periodic Boundary Condition (PBC) package. All beach models simulate similar water fluxes across the upland boundary and across the sediment-water interface although the ratio of intertidal to subtidal flow is different at low tide. Simulating a seepage face results in larger intertidal fluxes and influences near-shore heads and salinity. Major differences in flow occur in the tidal flat simulations. Because SEAWAT does not simulate unsaturated flow the water table only rises via flow through the saturated zone. This results in delayed propagation of the rising tidal signal inland. Inundation of the tidal flat is delayed as is flow into the aquifer across the flat. This is severe in the high-K and PBC models but mild in the GHB models. Results indicate that any of the tidal boundary options are fine if the ocean-aquifer interface is steep. However, as the slope of that interface decreases, the high-K and PBC approaches perform poorly and the GHB boundary is preferable.
NASA Technical Reports Server (NTRS)
Stakolich, E. G.
1978-01-01
An air ejector was designed and built to remove the boundary-layer air from the inlet a turbofan engine during an acoustic ground test program. This report describes; (1) how the ejector was sized; (2) how the ejector performed; and (3) the performance of a scale model ejector built and tested to verify the design. With proper acoustic insulation, the ejector was effective in reducing boundary layer thickness in the inlet of the turbofan engine while obtaining the desired acoustic test conditions.
Acoustic transmission enhancement through a soft interlayer with a reactance boundary.
Quan, Li; Qian, Feng; Liu, Xiaozhou; Gong, Xiufen
2015-08-01
Research has shown that acoustic transmission enhancement (ATE) can occur in stiff materials with high acoustic impedance that include a soft interlayer with low acoustic impedance inserted between them without any opening (i.e., without any links between the two stiff materials). Previously, ATE was induced either by coupling acoustic surface waves or Love waves with the Fabry-Perot resonant modes inside the apertures or by the locally resonant modes of the structure. However, in this article ATE is achieved using wave-vector redistribution induced by a reactance boundary. An optimal boundary was designed to adjust the wave vector in the propagation direction, decreasing reflection caused by impedance differences. The role of boundary conditions on ATE was also clarified. PMID:26328694
NASA Technical Reports Server (NTRS)
Kompenhans, J.
1977-01-01
The reflection factor at a tube which ends at a plate over which a flow is forming was determined as a function of the Strouhal number, formed from the flow velocity, the aperture radius, and the acoustic frequency. Several adjacent openings were investigated to determine the interactions between several openings.
Acoustic Radiation From a Mach 14 Turbulent Boundary Layer
NASA Technical Reports Server (NTRS)
Zhang, Chao; Duan, Lian; Choudhari, Meelan M.
2016-01-01
Direct numerical simulations (DNS) are used to examine the turbulence statistics and the radiation field generated by a high-speed turbulent boundary layer with a nominal freestream Mach number of 14 and wall temperature of 0:18 times the recovery temperature. The flow conditions fall within the range of nozzle exit conditions of the Arnold Engineering Development Center (AEDC) Hypervelocity Tunnel No. 9 facility. The streamwise domain size is approximately 200 times the boundary-layer thickness at the inlet, with a useful range of Reynolds number corresponding to Re 450 ?? 650. Consistent with previous studies of turbulent boundary layer at high Mach numbers, the weak compressibility hypothesis for turbulent boundary layers remains applicable under this flow condition and the computational results confirm the validity of both the van Driest transformation and Morkovin's scaling. The Reynolds analogy is valid at the surface; the RMS of fluctuations in the surface pressure, wall shear stress, and heat flux is 24%, 53%, and 67% of the surface mean, respectively. The magnitude and dominant frequency of pressure fluctuations are found to vary dramatically within the inner layer (z/delta 0.< or approx. 0.08 or z+ < or approx. 50). The peak of the pre-multiplied frequency spectrum of the pressure fluctuation is f(delta)/U(sub infinity) approx. 2.1 at the surface and shifts to a lower frequency of f(delta)/U(sub infinity) approx. 0.7 in the free stream where the pressure signal is predominantly acoustic. The dominant frequency of the pressure spectrum shows a significant dependence on the freestream Mach number both at the wall and in the free stream.
Mean Flow Boundary Conditions for Computational Aeroacoustics
NASA Technical Reports Server (NTRS)
Hixon, R.; Nallasamy, M.; Sawyer, S.; Dyson, R.
2003-01-01
In this work, a new type of boundary condition for time-accurate Computational Aeroacoustics solvers is described. This boundary condition is designed to complement the existing nonreflective boundary conditions while ensuring that the correct mean flow conditions are maintained throughout the flow calculation. Results are shown for a loaded 2D cascade, started with various initial conditions.
Evaluation of Boundary Conditions for the Gust-Cascade Problem
NASA Technical Reports Server (NTRS)
Hixon, R.; Shih, S.-H.; Mankbadi, R. R.
1998-01-01
Using a high-order accuracy finite-difference time-domain algorithm, the acoustic scattering from a flat-plate cascade is computed. Keeping the grid and time step fixed, the effect of four different boundary conditions on the accuracy and stability of the computed solution is compared.
Increasing Accuracy in Computed Inviscid Boundary Conditions
NASA Technical Reports Server (NTRS)
Dyson, Roger
2004-01-01
A technique has been devised to increase the accuracy of computational simulations of flows of inviscid fluids by increasing the accuracy with which surface boundary conditions are represented. This technique is expected to be especially beneficial for computational aeroacoustics, wherein it enables proper accounting, not only for acoustic waves, but also for vorticity and entropy waves, at surfaces. Heretofore, inviscid nonlinear surface boundary conditions have been limited to third-order accuracy in time for stationary surfaces and to first-order accuracy in time for moving surfaces. For steady-state calculations, it may be possible to achieve higher accuracy in space, but high accuracy in time is needed for efficient simulation of multiscale unsteady flow phenomena. The present technique is the first surface treatment that provides the needed high accuracy through proper accounting of higher-order time derivatives. The present technique is founded on a method known in art as the Hermitian modified solution approximation (MESA) scheme. This is because high time accuracy at a surface depends upon, among other things, correction of the spatial cross-derivatives of flow variables, and many of these cross-derivatives are included explicitly on the computational grid in the MESA scheme. (Alternatively, a related method other than the MESA scheme could be used, as long as the method involves consistent application of the effects of the cross-derivatives.) While the mathematical derivation of the present technique is too lengthy and complex to fit within the space available for this article, the technique itself can be characterized in relatively simple terms: The technique involves correction of surface-normal spatial pressure derivatives at a boundary surface to satisfy the governing equations and the boundary conditions and thereby achieve arbitrarily high orders of time accuracy in special cases. The boundary conditions can now include a potentially infinite number
Acoustic Radiation from High-Speed Turbulent Boundary Layers in a Tunnel-Like Environment
NASA Technical Reports Server (NTRS)
Duan, Lian; Choudhari, Meelan M.; Zhang, Chao
2015-01-01
Direct numerical simulation of acoustic radiation from a turbulent boundary layer in a cylindrical domain will be conducted under the flow conditions corresponding to those at the nozzle exit of the Boeing/AFOSR Mach-6 Quiet Tunnel (BAM6QT) operated under noisy-flow conditions with a total pressure p(sub t) of 225 kPa and a total temperature of T(sub t) equal to 430 K. Simulations of acoustic radiation from a turbulent boundary layer over a flat surface are used as a reference configuration to illustrate the effects of the cylindrical enclosure. A detailed analysis of acoustic freestream disturbances in the cylindrical domain will be reported in the final paper along with a discussion pertaining to the significance of the flat-plate acoustic simulations and guidelines concerning the modeling of the effects of an axisymmetric tunnel wall on the noise field.
Application of the double absorbing boundary condition in seismic modeling
NASA Astrophysics Data System (ADS)
Liu, Yang; Li, Xiang-Yang; Chen, Shuang-Quan
2015-03-01
We apply the newly proposed double absorbing boundary condition (DABC) (Hagstrom et al., 2014) to solve the boundary reflection problem in seismic finite-difference (FD) modeling. In the DABC scheme, the local high-order absorbing boundary condition is used on two parallel artificial boundaries, and thus double absorption is achieved. Using the general 2D acoustic wave propagation equations as an example, we use the DABC in seismic FD modeling, and discuss the derivation and implementation steps in detail. Compared with the perfectly matched layer (PML), the complexity decreases, and the stability and flexibility improve. A homogeneous model and the SEG salt model are selected for numerical experiments. The results show that absorption using the DABC is considerably improved relative to the Clayton-Engquist boundary condition and nearly the same as that in the PML.
Receptivity of Hypersonic Boundary Layers to Acoustic and Vortical Disturbances
NASA Technical Reports Server (NTRS)
Balakamar, P.; Kegerise, Michael A.
2011-01-01
Boundary layer receptivity to two-dimensional acoustic disturbances at different incidence angles and to vortical disturbances is investigated by solving the Navier-Stokes equations for Mach 6 flow over a 7deg half-angle sharp-tipped wedge and a cone. Higher order spatial and temporal schemes are employed to obtain the solution. The results show that the instability waves are generated in the leading edge region and that the boundary layer is much more receptive to slow acoustic waves as compared to the fast waves. It is found that the receptivity of the boundary layer on the windward side (with respect to the acoustic forcing) decreases when the incidence angle is increased from 0 to 30 degrees. However, the receptivity coefficient for the leeward side is found to vary relatively weakly with the incidence angle. The maximum receptivity is obtained when the wave incident angle is about 20 degrees. Vortical disturbances also generate unstable second modes, however the receptivity coefficients are smaller than that for the acoustic waves. Vortical disturbances first generate the fast acoustic modes and they switch to the slow mode near the continuous spectrum.
Acoustic Markers of Prosodic Boundaries in Spanish Spontaneous Alaryngeal Speech
ERIC Educational Resources Information Center
Cuenca, M. H.; Barrio, M. M.
2010-01-01
Prosodic information aids segmentation of the continuous speech signal and thereby facilitates auditory speech processing. Durational and pitch variations are prosodic cues especially necessary to convey prosodic boundaries, but alaryngeal speakers have inconsistent control over acoustic parameters such as F0 and duration, being as a result noisy…
Dependence of Boundary Layer Mixing On Lateral Boundary Conditions
NASA Astrophysics Data System (ADS)
Straub, D.
Ocean circulation models often show strong mixing in association with lateral bound- ary layers. Such mixing is generally considered to be artifactual rather than real. Fur- thermore, the severity of the problem is boundary condition dependent. For example, an inconsistency between geostrophy and insulating boundary conditions on tempera- ture and salinity cause many modelers to opt for the no slip, rather than slip boundary condtion on the tangential component of momentum. As modellers increasingly move into the eddy revealing regime, biharmonic, rather than harmonic dissipative operators are likely to become more common. Biharmonic operators, however, require specifi- cation of additional boundary conditions. For example, there are several `natural ex- tensions' to each of the slip and no slip conditions. Here, these various possiblities are considered in the context of a simple model. Particular attention is payed to how mixing (and the associated overturning cell) is affected by the choice of boundary condition.
Acoustic boundary control method for interior sound suppression
NASA Astrophysics Data System (ADS)
Sun, Jian Q.; Hirsch, S. M.
1997-06-01
Suppressing interior sound radiation in helicopters, fixed- wing aircraft and land vehicles is a very important problem. It has been studied quite extensively in the past few decades. There are two mainstream methods for this problem: active noise cancellation (ANC) using loudspeakers and sound radiation reduction via structural controls (often called active structural acoustic control or ASAC). An ANC system often requires an impractically high dimensionality to achieve the level of global noise reduction in a three dimensional volume that ASAC systems with a relatively low dimensionality are capable of, while actuators for structural control systems are power intensive and less reliable. This paper presents an acoustic boundary control method that may reserve the advantages of both ANC and ASAC. Numerical simulation results of interior noise control are presented to demonstrate the ability of the acoustic boundary control to cancel sound fields due to different primary sources. A discussion is also presented on the spatial characteristics of the acoustic boundary control as a function of frequency. An interesting phenomenon is discovered that may have significant implications to the actuator grouping studies.
Logarithmic minimal models with Robin boundary conditions
NASA Astrophysics Data System (ADS)
Bourgine, Jean-Emile; Pearce, Paul A.; Tartaglia, Elena
2016-06-01
We consider general logarithmic minimal models LM≤ft( p,{{p}\\prime}\\right) , with p,{{p}\\prime} coprime, on a strip of N columns with the (r, s) Robin boundary conditions introduced by Pearce, Rasmussen and Tipunin. On the lattice, these models are Yang–Baxter integrable loop models that are described algebraically by the one-boundary Temperley–Lieb algebra. The (r, s) Robin boundary conditions are a class of integrable boundary conditions satisfying the boundary Yang–Baxter equations which allow loop segments to either reflect or terminate on the boundary. The associated conformal boundary conditions are organized into infinitely extended Kac tables labelled by the Kac labels r\\in {Z} and s\\in {N} . The Robin vacuum boundary condition, labelled by ≤ft(r,s-\\frac{1}{2}\\right)=≤ft(0,\\frac{1}{2}\\right) , is given as a linear combination of Neumann and Dirichlet boundary conditions. The general (r, s) Robin boundary conditions are constructed, using fusion, by acting on the Robin vacuum boundary with an (r, s)-type seam consisting of an r-type seam of width w columns and an s-type seam of width d = s ‑ 1 columns. The r-type seam admits an arbitrary boundary field which we fix to the special value ξ =-\\fracλ{2} where λ =\\frac≤ft( {{p}\\prime}-p\\right)π{{{p}\\prime}} is the crossing parameter. The s-type boundary introduces d defects into the bulk. We consider the commuting double-row transfer matrices and their associated quantum Hamiltonians and calculate analytically the boundary free energies of the (r, s) Robin boundary conditions. Using finite-size corrections and sequence extrapolation out to system sizes N+w+d≤slant 26 , the conformal spectrum of boundary operators is accessible by numerical diagonalization of the Hamiltonians. Fixing the parity of N for r\
Acoustic Radiation from a Mach 14 Turbulent Boundary layer
NASA Astrophysics Data System (ADS)
Zhang, Chao; Duan, Lian; Choudhari, Meelan
2015-11-01
Direct numerical simulations (DNS) are used to examine the pressure fluctuations generated by a high-speed turbulent boundary layer with a nominal freestream Mach number of 14 and wall temperature of 0.18 times the recovery temperature. The emphasis is on characterizing the acoustic radiation from the turbulent boundary layer and comparing it with previous simulations at Mach 2.5 and Mach 6 to assess the Mach-number dependence of the freestream pressure fluctuations. In particular, the numerical database is used to provide insights into the pressure disturbance spectrum and amplitude scaling with respect to the freestream Mach number as well as to understand the acoustic source mechanisms at very high Mach numbers. Such information is important for characterizing the freestream disturbance environment in conventional (i.e., noisy) hypersonic wind tunnels. Spectral characteristics of pressure fluctuations at the surface are also investigated. Sponsored by Air Force Office of Scientific Research.
Traction boundary conditions for molecular static simulations
NASA Astrophysics Data System (ADS)
Li, Xiantao; Lu, Jianfeng
2016-08-01
This paper presents a consistent approach to prescribe traction boundary conditions in atomistic models. Due to the typical multiple-neighbor interactions, finding an appropriate boundary condition that models a desired traction is a non-trivial task. We first present a one-dimensional example, which demonstrates how such boundary conditions can be formulated. We further analyze the stability, and derive its continuum limit. We also show how the boundary conditions can be extended to higher dimensions with an application to a dislocation dipole problem under shear stress.
Tunable acoustic radiation pattern assisted by effective impedance boundary
NASA Astrophysics Data System (ADS)
Qian, Feng; Quan, Li; Wang, Li-Wei; Liu, Xiao-Zhou; Gong, Xiu-Fen
2016-02-01
The acoustic wave propagation from a two-dimensional subwavelength slit surrounded by metal plates decorated with Helmholtz resonators (HRs) is investigated both numerically and experimentally in this work. Owing to the presence of HRs, the effective impedance of metal surface boundary can be manipulated. By optimizing the distribution of HRs, the asymmetric effective impedance boundary will be obtained, which contributes to generating tunable acoustic radiation pattern such as directional acoustic beaming. These dipole-like radiation patterns have high radiation efficiency, no fingerprint of sidelobes, and a wide tunable range of the radiation pattern directivity angle which can be steered by the spatial displacements of HRs. Project supported by the National Basic Research Program of China (Grant Nos. 2012CB921504 and 2011CB707902), the National Natural Science Foundation of China (Grant No.11474160), the Fundamental Research Funds for Central Universities, China (Grant No. 020414380001), the State Key Laboratory of Acoustics, Chinese Academy of Sciences (Grant No. SKLOA201401), the Priority Academic Program Development of Jiangsu Higher Education Institutions, and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.
Numerical Boundary Conditions for Computational Aeroacoustics Benchmark Problems
NASA Technical Reports Server (NTRS)
Tam, Chritsopher K. W.; Kurbatskii, Konstantin A.; Fang, Jun
1997-01-01
Category 1, Problems 1 and 2, Category 2, Problem 2, and Category 3, Problem 2 are solved computationally using the Dispersion-Relation-Preserving (DRP) scheme. All these problems are governed by the linearized Euler equations. The resolution requirements of the DRP scheme for maintaining low numerical dispersion and dissipation as well as accurate wave speeds in solving the linearized Euler equations are now well understood. As long as 8 or more mesh points per wavelength is employed in the numerical computation, high quality results are assured. For the first three categories of benchmark problems, therefore, the real challenge is to develop high quality numerical boundary conditions. For Category 1, Problems 1 and 2, it is the curved wall boundary conditions. For Category 2, Problem 2, it is the internal radiation boundary conditions inside the duct. For Category 3, Problem 2, they are the inflow and outflow boundary conditions upstream and downstream of the blade row. These are the foci of the present investigation. Special nonhomogeneous radiation boundary conditions that generate the incoming disturbances and at the same time allow the outgoing reflected or scattered acoustic disturbances to leave the computation domain without significant reflection are developed. Numerical results based on these boundary conditions are provided.
Boundary conditions for viscous vortex methods
Koumoutsakos, P.; Leonard, A.; Pepin, F. )
1994-07-01
This paper presents a Neumann-type vorticity boundary condition for the vorticity formulation of the Navier-Stokes equations. The vorticity creation process at the boundary, due to the no-slip condition, is expressed in terms of a vorticity flux. The scheme is incorporated then into a Lagrangian vortex blob method that uses a particle strength exchange algorithm for viscous diffusion. The no-slip condition is not enforced by the generation of new vortices at the boundary but instead by modifying the strength of the vortices in the vicinity of the boundary. 19 refs., 5 figs.
Boundary conditions for the subdiffusion equation
Shkilev, V. P.
2013-04-15
The boundary conditions for the subdiffusion equations are formulated using the continuous-time random walk model, as well as several versions of the random walk model on an irregular lattice. It is shown that the boundary conditions for the same equation in different models have different forms, and this difference considerably affects the solutions of this equation.
Unified slip boundary condition for fluid flows.
Thalakkottor, Joseph John; Mohseni, Kamran
2016-08-01
Determining the correct matching boundary condition is fundamental to our understanding of several everyday problems. Despite over a century of scientific work, existing velocity boundary conditions are unable to consistently explain and capture the complete physics associated with certain common but complex problems, such as moving contact lines and corner flows. The widely used Maxwell and Navier slip boundary conditions make an implicit assumption that velocity varies only in the wall normal direction. This makes their boundary condition inapplicable in the vicinity of contact lines and corner points, where velocity gradient exists both in the wall normal and wall tangential directions. In this paper, by identifying this implicit assumption we are able to extend Maxwell's slip model. Here, we present a generalized velocity boundary condition that shows that slip velocity is a function of not only the shear rate but also the linear strain rate. In addition, we present a universal relation for slip length, which shows that, for a general flow, slip length is a function of the principal strain rate. The universal relation for slip length along with the generalized velocity boundary condition provides a unified slip boundary condition to model a wide range of steady Newtonian fluid flows. We validate the unified slip boundary for simple Newtonian liquids by using molecular dynamics simulations and studying both the moving contact line and corner flow problems. PMID:27627398
Boundary Conditions of the Heliosphere
NASA Technical Reports Server (NTRS)
Slavin, Jonathan D.; Frisch, Priscilla C .
2001-01-01
We present new calculations of the ionization of the Local Interstellar Cloud (LIC) by directly observed sources including nearby stellar extreme ultraviolet (EUV) sources and the diffuse emission of the Soft X-ray Background (SXRB). In addition, we model the important, unobserved EUV emission both from the hot gas responsible for the SXRB and from a possible evaporative boundary between the LIC and the hot gas. We show that these ionization sources can provide the necessary ionization and heating of the cloud to match observations. Including the radiation from the conductive boundary, while not required, does improve the agreement with observations of the temperature of the LIC. The ionization predicted in our models shows good agreement with pickup ion results, interstellar absorption line data towards epsilon CMa, and EUV opacity measurements of nearby white dwarf stars. The areas of disagreement point to a possible underabundance (relative to solar abundance) of neon in the LIC. The presence of dust in the cloud, or at least depleted abundances, is necessary to maintain the heating/cooling balance and reach the observed temperature.
Downstream boundary conditions for viscous flow problems
NASA Technical Reports Server (NTRS)
Fix, G.; Gunzburger, M.
1977-01-01
The problem of the specification of artificial outflow conditions in flow problems is studied. It is shown that for transport type equations incorrect outflow conditions will adversely affect the solution only in a small region near the outflow boundary, while for elliptic equations, e.g. those governing the streamfunction or pressure, a correct boundary specification is essential. In addition, integral outflow boundary conditions for fluid dynamical problems are considered. It is shown that such conditions are well posed, and their effect on the solutions of the Navier-Stokes equations is also considered.
Acoustic explorations of the upper ocean boundary layer
NASA Astrophysics Data System (ADS)
Vagle, Svein
2005-04-01
The upper ocean boundary layer is an important but difficult to probe part of the ocean. A better understanding of small scale processes at the air-sea interface, including the vertical transfer of gases, heat, mass and momentum, are crucial to improving our understanding of the coupling between atmosphere and ocean. Also, this part of the ocean contains a significant part of the total biomass at all trophic levels and is therefore of great interest to researchers in a range of different fields. Innovative measurement plays a critical role in developing our understanding of the processes involved in the boundary layer, and the availability of low-cost, compact, digital signal processors and sonar technology in self-contained and cabled configurations has led to a number of exciting developments. This talk summarizes some recent explorations of this dynamic boundary layer using both active and passive acoustics. The resonant behavior of upper ocean bubbles combined with single and multi-frequency broad band active and passive devices are now giving us invaluable information on air-sea gas transfer, estimation of biological production, marine mammal behavior, wind speed and precipitation, surface and internal waves, turbulence, and acoustic communication in the surf zone.
The Pauli equation with complex boundary conditions
NASA Astrophysics Data System (ADS)
Kochan, D.; Krejčiřík, D.; Novák, R.; Siegl, P.
2012-11-01
We consider one-dimensional Pauli Hamiltonians in a bounded interval with possibly non-self-adjoint Robin-type boundary conditions. We study the influence of the spin-magnetic interaction on the interplay between the type of boundary conditions and the spectrum. Special attention is paid to {PT}-symmetric boundary conditions with the physical choice of the time-reversal operator {T}. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.
From Neuman to Dirichlet boundary conditions
Nikolic, B.; Sazdovic, B.
2007-04-23
The Dirichlet boundary conditions for the end-point of the open string define Dp-brane. It is parameterized by the rest of coordinates, with Neuman boundary conditions. The relations between background fields can produce the local gauge symmetries of the world-sheet action. After gauge fixing, some Neuman boundary conditions turn into the Dirichlet ones, decreasing the number of Dp-brane dimensions. The physical Dp-brane is gauge invariant part of the initial one. The gauge invariant coordinates are expressed as linear combinations of the effective coordinates and momenta. This fact explains the origin of non-commutativity and the existence of commutative Dp-brane coordinates.
An Evaluation of Boundary Conditions for Modeling Urban Boundary Layers
Calhoun, R.J.; Chan, S.T.; Lee, R.L.
2000-05-18
Numerical modeling of the urban boundary layer is complicated by the need to describe airflow patterns outside of the computational domain. These patterns have an impact on how successfully the simulation is able to model the turbulence associated with the urban boundary layer. This talk presents experiments with the model boundary conditions for simulations that were done to support two Department of Energy observational programs involving the Salt Lake City basin. The Chemical/Biological Non-proliferation Program (CBNP) is concerned with the effects of buildings on influencing dispersion patterns in urban environments. The Vertical Transport and Mixing Program (VTMX) investigating mixing mechanisms in the stable boundary layer and how they are influenced by the channeling caused by drainage flows or by obstacles such as building complexes. Both of these programs are investigating the turbulent mixing caused by building complexes and other urban obstacles.
Stable boundary conditions for Cartesian grid calculations
NASA Technical Reports Server (NTRS)
Berger, M. J.; Leveque, R. J.
1990-01-01
The inviscid Euler equations in complicated geometries are solved using a Cartesian grid. This requires solid wall boundary conditions in the irregular grid cells near the boundary. Since these cells may be orders of magnitude smaller than the regular grid cells, stability is a primary concern. An approach to this problem is presented and its use is illustrated.
Implementation of a Compressor Face Boundary Condition Based on Small Disturbances
NASA Technical Reports Server (NTRS)
Slater, John W.; Paynter, Gerald C.
2000-01-01
A compressor-face boundary condition that models the unsteady interactions of acoustic and convective velocity disturbances with a compressor has been implemented into a three-dimensional computational fluid dynamics code. Locally one-dimensional characteristics along with a small-disturbance model are used to compute the acoustic response as a function of the local stagger angle and the strength and direction of the disturbance. Simulations of the inviscid flow in a straight duct, a duct coupled to a compressor, and a supersonic inlet demonstrate the behavior of the boundary condition in relation to existing boundary conditions. Comparisons with experimental data show a large improvement in accuracy over existing boundary conditions in the ability to predict the reflected disturbance from the interaction of an acoustic disturbance with a compressor.
Boundary Conditions for Jet Flow Computations
NASA Technical Reports Server (NTRS)
Hayder, M. E.; Turkel, E.
1994-01-01
Ongoing activities are focused on capturing the sound source in a supersonic jet through careful large eddy simulation (LES). One issue that is addressed is the effect of the boundary conditions, both inflow and outflow, on the predicted flow fluctuations, which represent the sound source. In this study, we examine the accuracy of several boundary conditions to determine their suitability for computations of time-dependent flows. Various boundary conditions are used to compute the flow field of a laminar axisymmetric jet excited at the inflow by a disturbance given by the corresponding eigenfunction of the linearized stability equations. We solve the full time dependent Navier-Stokes equations by a high order numerical scheme. For very small excitations, the computed growth of the modes closely corresponds to that predicted by the linear theory. We then vary the excitation level to see the effect of the boundary conditions in the nonlinear flow regime.
Experiments on initial and boundary conditions
NASA Technical Reports Server (NTRS)
Moretti, G.
1980-01-01
Effects of three different models for the treatment of subsonic boundary conditions, applied to the problem of flow in a channel with a bump, are discussed. A preliminary discussion of the numerical treatment of the corners is presented.
Multireflection boundary conditions for lattice Boltzmann models.
Ginzburg, Irina; d'Humières, Dominique
2003-12-01
We present a general framework for several previously introduced boundary conditions for lattice Boltzmann models, such as the bounce-back rule and the linear and quadratic interpolations. The objectives are twofold: first to give theoretical tools to study the existing link-type boundary conditions and their corresponding accuracy; second to design boundary conditions for general flows which are third-order kinetic accurate. Using these new boundary conditions, Couette and Poiseuille flows are exact solutions of the lattice Boltzmann models for a Reynolds number Re=0 (Stokes limit) for arbitrary inclination with the lattice directions. Numerical comparisons are given for Stokes flows in periodic arrays of spheres and cylinders, linear periodic array of cylinders between moving plates, and for Navier-Stokes flows in periodic arrays of cylinders for Re<200. These results show a significant improvement of the overall accuracy when using the linear interpolations instead of the bounce-back reflection (up to an order of magnitude on the hydrodynamics fields). Further improvement is achieved with the new multireflection boundary conditions, reaching a level of accuracy close to the quasianalytical reference solutions, even for rather modest grid resolutions and few points in the narrowest channels. More important, the pressure and velocity fields in the vicinity of the obstacles are much smoother with multireflection than with the other boundary conditions. Finally the good stability of these schemes is highlighted by some simulations of moving obstacles: a cylinder between flat walls and a sphere in a cylinder. PMID:14754343
On High-Order Radiation Boundary Conditions
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas
1995-01-01
In this paper we develop the theory of high-order radiation boundary conditions for wave propagation problems. In particular, we study the convergence of sequences of time-local approximate conditions to the exact boundary condition, and subsequently estimate the error in the solutions obtained using these approximations. We show that for finite times the Pade approximants proposed by Engquist and Majda lead to exponential convergence if the solution is smooth, but that good long-time error estimates cannot hold for spatially local conditions. Applications in fluid dynamics are also discussed.
Influence of Spanwise Boundary Conditions on Slat Noise Simulations
NASA Technical Reports Server (NTRS)
Lockard, David P.; Choudhari, Meelan M.; Buning, Pieter G.
2015-01-01
The slat noise from the 30P/30N high-lift system is being investigated through computational fluid dynamics simulations with the OVERFLOW code in conjunction with a Ffowcs Williams-Hawkings acoustics solver. In the present study, two different spanwise grids are being used to investigate the effect of the spanwise extent and periodicity on the near-field unsteady structures and radiated noise. The baseline grid with periodic boundary conditions has a short span equal to 1/9th of the stowed chord, whereas the other, longer span grid adds stretched grids on both sides of the core, baseline grid to allow inviscid surface boundary conditions at both ends. The results indicate that the near-field mean statistics obtained using the two grids are similar to each other, as are the directivity and spectral shapes of the radiated noise. However, periodicity forces all acoustic waves with less than one wavelength across the span to be two-dimensional, without any variation in the span. The spanwise coherence of the acoustic waves is what is needed to make estimates of the noise that would be radiated from realistic span lengths. Simulations with periodic conditions need spans of at least six slat chords to allow spanwise variation in the low-frequencies associated with the peak of broadband slat noise. Even then, the full influence of the periodicity is unclear, so employing grids with a fine, central region and highly stretched meshes that go to slip walls may be a more efficient means of capturing the spanwise decorrelation of low-frequency acoustic phenomena.
Boundary conditions for the gravitational field
NASA Astrophysics Data System (ADS)
Winicour, Jeffrey
2012-06-01
A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the harmonic formulation of Einstein's equations and a tetrad formulation of the Einstein-Bianchi system. However, a universal approach valid for other formulations is not in hand. In particular, there is no satisfactory boundary theory for the 3+1 formulations which have been highly successful in binary black hole simulation. I discuss the underlying problems that make the initial-boundary-value problem much more complicated than the Cauchy problem. I review the progress that has been made and the important open questions that remain. Science is a differential equation. Religion is a boundary condition. (Alan Turing, quoted in J D Barrow, ‘Theories of Everything’)
MBTS Boundary Conditions in Continuous Systems
NASA Astrophysics Data System (ADS)
Benesh, G. A.; Haydock, Roger
2015-03-01
Boundary conditions imposed on a local system that is joined to a larger substrate system often introduce unphysical reflections that affect eigenstate energies, densities of states, and charge densities. These problems are common in both atomic cluster and surface slab calculations. Solutions of the Schrodinger equation for the physical system do not possess such reflections; these wave functions carry current smoothly across the (artificial) boundary between the local system and the underlying medium. Previously, Haydock and Nex derived a non-reflecting boundary condition for discrete systems [Phys. Rev. B 75, 205121 (2006)]. Solutions satisfying this maximal breaking of time-reversal symmetry (MBTS) boundary condition carry current away from the boundary at a maximal rate--in much the same way as the exact wave functions for the physical system. The MBTS boundary condition has proved useful in discrete systems for constructing densities of states and other distributions from moments or continued fractions. The MBTS approach has now been extended to studies employing continuous spatial wave functions, including surface slab calculations and model systems. Results are compared with free slab calculations, embedding calculations, and experiment.
Improving Boundary Conditions for Electronic Structure Calculations
NASA Astrophysics Data System (ADS)
Benesh, G. A.; Haydock, Roger
Boundary conditions imposed on a local system joined to a much larger substrate system routinely introduce unphysical reflections that affect the calculation of electronic properties such as energies, charge densities, and densities of states. These problems persist in atomic cluster, slab, and supercell calculations alike. However, wave functions in real, physical systems do not reflect at artificial boundaries. Instead, they carry current smoothly across the surface separating the local system from the underlying medium. Haydock and Nex have derived a non-reflecting boundary condition that works well for discrete systems [Phys. Rev. B 75, 205121 (2006)]. Solutions satisfying their maximal breaking of time-reversal symmetry (MBTS) boundary condition carry current away from the boundary at a maximal rate--in much the same way as exact wave functions in physical systems. The MBTS approach has now been extended to studies employing continuous basis functions. In model systems, MBTS boundary conditions work well for calculating wave functions, eigenenergies, and densities of states. Results are reported for an Al(001) surface. Comparisons are made with slab calculations, embedding calculations, and experiment.
Velocity boundary conditions at a tokamak resistive wall
Strauss, H. R.
2014-03-15
Velocity boundary conditions appropriate for magnetohydrodynamic simulations have been controversial recently. A comparison of numerical simulations of sideways wall force in disruptions is presented for Dirichlet, Neumann, Robin, and DEBS boundary conditions. It is shown that all the boundary conditions give qualitatively similar results. It is shown that Dirichlet boundary conditions are valid in the small Larmor radius limit of electromagnetic sheath boundary conditions.
Transition in a Supersonic Boundary-Layer Due to Roughness and Acoustic Disturbances
NASA Technical Reports Server (NTRS)
Balakumar, P.
2003-01-01
The transition process induced by the interaction of an isolated roughness with acoustic disturbances in the free stream is numerically investigated for a boundary layer over a flat plate with a blunted leading edge at a free stream Mach number of 3.5. The roughness is assumed to be of Gaussian shape and the acoustic disturbances are introduced as boundary condition at the outer field. The governing equations are solved using the 5'h-rder accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third- order total-variation-diminishing (TVD) Runge- Kutta scheme for time integration. The steady field induced by the two and three-dimensional roughness is also computed. The flow field induced by two-dimensional roughness exhibits different characteristics depending on the roughness heights. At small roughness heights the flow passes smoothly over the roughness, at moderate heights the flow separates downstream of the roughness and at larger roughness heights the flow separates upstream and downstream of the roughness. Computations also show that disturbances inside the boundary layer is due to the direct interaction of the acoustic waves and isolated roughness plays a minor role in generating instability waves.
Anchored boundary conditions for locally isostatic networks
NASA Astrophysics Data System (ADS)
Theran, Louis; Nixon, Anthony; Ross, Elissa; Sadjadi, Mahdi; Servatius, Brigitte; Thorpe, M. F.
2015-11-01
Finite pieces of locally isostatic networks have a large number of floppy modes because of missing constraints at the surface. Here we show that by imposing suitable boundary conditions at the surface the network can be rendered effectively isostatic. We refer to these as anchored boundary conditions. An important example is formed by a two-dimensional network of corner sharing triangles, which is the focus of this paper. Another way of rendering such networks isostatic is by adding an external wire along which all unpinned vertices can slide (sliding boundary conditions). This approach also allows for the incorporation of boundaries associated with internal holes and complex sample geometries, which are illustrated with examples. The recent synthesis of bilayers of vitreous silica has provided impetus for this work. Experimental results from the imaging of finite pieces at the atomic level need such boundary conditions, if the observed structure is to be computer refined so that the interior atoms have the perception of being in an infinite isostatic environment.
Time-domain implementation of an impedance boundary condition with boundary layer correction
NASA Astrophysics Data System (ADS)
Brambley, E. J.; Gabard, G.
2016-09-01
A time-domain boundary condition is derived that accounts for the acoustic impedance of a thin boundary layer over an impedance boundary, based on the asymptotic frequency-domain boundary condition of Brambley (2011) [25]. A finite-difference reference implementation of this condition is presented and carefully validated against both an analytic solution and a discrete dispersion analysis for a simple test case. The discrete dispersion analysis enables the distinction between real physical instabilities and artificial numerical instabilities. The cause of the latter is suggested to be a combination of the real physical instabilities present and the aliasing and artificial zero group velocity of finite-difference schemes. It is suggested that these are general properties of any numerical discretization of an unstable system. Existing numerical filters are found to be inadequate to remove these artificial instabilities as they have a too wide pass band. The properties of numerical filters required to address this issue are discussed and a number of selective filters are presented that may prove useful in general. These filters are capable of removing only the artificial numerical instabilities, allowing the reference implementation to correctly reproduce the stability properties of the analytic solution.
NASA Astrophysics Data System (ADS)
Jena, D. P.; Panigrahi, S. N.
2016-03-01
Requirement of designing a sophisticated digital band-pass filter in acoustic based condition monitoring has been eliminated by introducing a passive acoustic filter in the present work. So far, no one has attempted to explore the possibility of implementing passive acoustic filters in acoustic based condition monitoring as a pre-conditioner. In order to enhance the acoustic based condition monitoring, a passive acoustic band-pass filter has been designed and deployed. Towards achieving an efficient band-pass acoustic filter, a generalized design methodology has been proposed to design and optimize the desired acoustic filter using multiple filter components in series. An appropriate objective function has been identified for genetic algorithm (GA) based optimization technique with multiple design constraints. In addition, the sturdiness of the proposed method has been demonstrated in designing a band-pass filter by using an n-branch Quincke tube, a high pass filter and multiple Helmholtz resonators. The performance of the designed acoustic band-pass filter has been shown by investigating the piston-bore defect of a motor-bike using engine noise signature. On the introducing a passive acoustic filter in acoustic based condition monitoring reveals the enhancement in machine learning based fault identification practice significantly. This is also a first attempt of its own kind.
Boundary conditions in tunneling via quantum hydrodynamics
NASA Technical Reports Server (NTRS)
Nassar, Antonio B.
1993-01-01
Via the hydrodynamical formulation of quantum mechanics, an approach to the problem of tunneling through sharp-edged potential barriers is developed. Above all, it is shown how more general boundary conditions follow from the continuity of mass, momentum, and energy.
How good is the impedance boundary condition?
NASA Technical Reports Server (NTRS)
Lee, Shung-Wu; Gee, W.
1987-01-01
The impedance boundary condition (IBC) is often used in scattering problems involving material-coated conducting bodies. It is shown that for some commonly encountered coating configurations, the value of the impedance varies significantly as functions of the incident angle and polarization. Hence, the use of IBC in a rigorously formulated problem may affect the accuracy of the final solution.
Boundary conditions in Chebyshev and Legendre methods
NASA Technical Reports Server (NTRS)
Canuto, C.
1984-01-01
Two different ways of treating non-Dirichlet boundary conditions in Chebyshev and Legendre collocation methods are discussed for second order differential problems. An error analysis is provided. The effect of preconditioning the corresponding spectral operators by finite difference matrices is also investigated.
Transition in a Supersonic Boundary Layer due to Acoustic Disturbances
NASA Technical Reports Server (NTRS)
Balakumar, Ponnampalam
2004-01-01
The boundary layer receptivity process due to the interaction of three-dimensional slow and fast acoustic disturbances with a blunted flat plate is numerically investigated at a free stream Mach number of 3.5 and at a high Reynolds number of 106/inch. The computations are performed with and without two-dimensional isolated roughness element located near the leading edge. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using the 5th-order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. The simulations showed that the linear instability waves are generated very close to the leading edge. The wavelength of the disturbances inside the boundary layer first increases gradually and becomes longer than the wavelength for the instability waves within a short distance from the leading edge. The wavelength then decreases gradually and merges with the wavelength for the Tollmien_Schlichting wave. The initial amplitudes of the instability waves near the neutral points, the receptivity coefficients, are about 1.20 and 0.07 times the amplitude of the free-stream disturbances for the slow and the fast waves respectively. It was also revealed that small isolated roughness element does not enhance the receptivity process for the given nose bluntness.
Transition in a Supersonic Boundary Layer Due to Acoustic Disturbances
NASA Technical Reports Server (NTRS)
Balakumar, P.
2005-01-01
The boundary layer receptivity process due to the interaction of three-dimensional slow and fast acoustic disturbances with a blunted flat plate is numerically investigated at a free stream Mach number of 3.5 and at a high Reynolds number of 10(exp 6)/inch. The computations are performed with and without two-dimensional isolated roughness element located near the leading edge. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using the fifth-order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. The simulations showed that the linear instability waves are generated very close to the leading edge. The wavelength of the disturbances inside the boundary layer first increases gradually and becomes longer than the wavelength for the instability waves within a short distance from the leading edge. The wavelength then decreases gradually and merges with the wavelength for the Tollmien-Schlichting wave. The initial amplitudes of the instability waves near the neutral points, the receptivity coefficients, are about 1.20 and 0.07 times the amplitude of the free-stream disturbances for the slow and the fast waves respectively. It was also revealed that small isolated roughness element does not enhance the receptivity process for the given nose bluntness.
Low density gas dynamic wall boundary conditions
NASA Technical Reports Server (NTRS)
Collins, F. G.
1986-01-01
Low density nozzles or large expansion ratio nozzles used in space experience rarefaction effects near their exit in the form of velocity slip and temperature jump at the walls. In addition, the boundary layers become very thick and there is a very strong viscous/inviscid interaction. For these reasons no existing design technique has been found to accurately predict the nozzle flow properties up to the nozzle exit. The objective of this investigation was to examine the slip boundary conditions and formulate them in a form appropriate for use with a full Navier-Stokes numerical code. The viscous/inviscid interaction would automatically be accounted for by using a compressible Navier-Stokes code. Through examination of the interaction of molecules with solid surfaces, a model for the distribution function of the reflected molecules has been determined and this distribution function has been used to develop a new slip boundary condition that can be shown to yield more realistic surface boundary conditions.
The effect of boundaries on the ion acoustic beam-plasma instability in experiment and simulation
Rapson, Christopher; Grulke, Olaf; Matyash, Konstantin; Klinger, Thomas
2014-05-15
The ion acoustic beam-plasma instability is known to excite strong solitary waves near the Earth's bow shock. Using a double plasma experiment, tightly coupled with a 1-dimensional particle-in-cell simulation, the results presented here show that this instability is critically sensitive to the experimental conditions. Boundary effects, which do not have any counterpart in space or in most simulations, unavoidably excite parasitic instabilities. Potential fluctuations from these instabilities lead to an increase of the beam temperature which reduces the growth rate such that non-linear effects leading to solitary waves are less likely to be observed. Furthermore, the increased temperature modifies the range of beam velocities for which an ion acoustic beam plasma instability is observed.
Spatial periodic boundary condition for MODFLOW.
Laattoe, Tariq; Post, Vincent E A; Werner, Adrian D
2014-01-01
Small-scale hyporheic zone (HZ) models often use a spatial periodic boundary (SPB) pair to simulate an infinite repetition of bedforms. SPB's are common features of commercially available multiphysics modeling packages. MODFLOW's lack of this boundary type has precluded it from being effectively utilized in this area of HZ research. We present a method to implement the SPB in MODFLOW by development of the appropriate block-centered finite-difference expressions. The implementation is analogous to MODFLOW's general head boundary package. The difference is that the terms on the right hand side of the solution equations must be updated with each iteration. Consequently, models that implement the SPB converge best with solvers that perform both inner and outer iterations. The correct functioning of the SPB condition in MODFLOW is verified by two examples. This boundary condition allows users to build HZ-bedform models in MODFLOW, facilitating further research using related codes such as MT3DMS and PHT3D. PMID:23808416
Symmetry boundary condition in dissipative particle dynamics
NASA Astrophysics Data System (ADS)
Pal, Souvik; Lan, Chuanjin; Li, Zhen; Hirleman, E. Daniel; Ma, Yanbao
2015-07-01
Dissipative particle dynamics (DPD) is a coarse-grained particle method for modeling mesoscopic hydrodynamics. Most of the DPD simulations are carried out in 3D requiring remarkable computation time. For symmetric systems, this time can be reduced significantly by simulating only one half or one quarter of the systems. However, such simulations are not yet possible due to a lack of schemes to treat symmetric boundaries in DPD. In this study, we propose a numerical scheme for the implementation of the symmetric boundary condition (SBC) in both dissipative particle dynamics (DPD) and multibody dissipative particle dynamics (MDPD) using a combined ghost particles and specular reflection (CGPSR) method. We validate our scheme in four different configurations. The results demonstrate that our scheme can accurately reproduce the system properties, such as velocity, density and meniscus shapes of a full system with numerical simulations of a subsystem. Using a symmetric boundary condition for one half of the system, we demonstrate about 50% computation time saving in both DPD and MDPD. This approach for symmetric boundary treatment can be also applied to other coarse-grained particle methods such as Brownian and Langevin Dynamics to significantly reduce computation time.
Schiffter, Heiko; Lee, Geoffrey
2007-09-01
The suitability of a single droplet drying acoustic levitator as a model for the spray drying of aqueous, pharmaceutically-relevant solutes used to produce protein-loaded particles has been examined. The acoustic levitator was initially evaluated by measuring the drying rates of droplets of pure water in dependence of drying-air temperature and flow rate. The measured drying rates were higher than those predicted by boundary layer theory because of the effects of primary acoustic streaming. Sherwood numbers of 2.6, 3.6, and 4.4 at drying-air temperatures of 25 degrees C, 40 degrees C, and 60 degrees C were determined, respectively. Acoustic levitation theory could predict the measured drying rates and Sherwood numbers only when a forced-convection drying-air stream was used to neuralize the retarding effect of secondary acoustic streaming on evaporation rate. At still higher drying-air flow rates, the Ranz-Marshall correlation accurately predicts Sherwood number, provided a stable droplet position in the standing acoustic wave is maintained. The measured Sherwood numbers and droplet Reynolds numbers show that experiments performed in the levitator in still air are taking place effectively under conditions of substantial forced convection. The similitude of these values to those occurring in spray dryers is fortuitous for the suitability of the acoustic levitator as a droplet evaporation model for spray drying. PMID:17582811
NASA Astrophysics Data System (ADS)
Erhard, Klaus; Potthast, Roland
2003-10-01
We employ the point source method (PSM) for the reconstruction of some field u on parts of a domain Omega from the Cauchy data for the field on the boundary partialOmega of the domain. Then, the boundary condition for a perfectly conducting inclusion or a sound-soft object in Omega can be used to find the location and shape of the inhomogeneity. The results show that we can detect perfectly conducting inclusions in impedance tomography from the voltages for one injected current. For acoustic scattering a sound-soft object is found from the knowledge of one (total) field and its normal derivative on partialOmega. The work redesigns the PSM, which was first proposed in the framework of inverse scattering, to solve inverse boundary value problems. Numerical examples are provided for impedance tomography and the sound-soft acoustic boundary value problem.
An immersed boundary computational model for acoustic scattering problems with complex geometries.
Sun, Xiaofeng; Jiang, Yongsong; Liang, An; Jing, Xiaodong
2012-11-01
An immersed boundary computational model is presented in order to deal with the acoustic scattering problem by complex geometries, in which the wall boundary condition is treated as a direct body force determined by satisfying the non-penetrating boundary condition. Two distinct discretized grids are used to discrete the fluid domain and immersed boundary, respectively. The immersed boundaries are represented by Lagrangian points and the direct body force determined on these points is applied on the neighboring Eulerian points. The coupling between the Lagrangian points and Euler points is linked by a discrete delta function. The linearized Euler equations are spatially discretized with a fourth-order dispersion-relation-preserving scheme and temporal integrated with a low-dissipation and low-dispersion Runge-Kutta scheme. A perfectly matched layer technique is applied to absorb out-going waves and in-going waves in the immersed bodies. Several benchmark problems for computational aeroacoustic solvers are performed to validate the present method. PMID:23145603
Integrable open boundary conditions for XXC models
NASA Astrophysics Data System (ADS)
Arnaudon, Daniel; Maassarani, Ziad
1998-10-01
The XXC models are multistate generalizations of the well known spin-½ XXZ model. These integrable models share a common underlying su(2) structure. We derive integrable open boundary conditions for the hierarchy of conserved quantities of the XXC models . Due to lack of crossing unitarity of the R-matrix, we develop specific methods to prove integrability. The symmetry of the spectrum is determined.
Magnetohydrodynamic boundary conditions for global models
NASA Technical Reports Server (NTRS)
Forbes, T. G.
1988-01-01
Boundary conditions in the ionosphere and the upstream solar wind are important in determining the dynamics of global magnetohydrodynamic models of the magnetosphere. It is generally recognized that the orientation of the magnetic field in the upstream solar wind strongly modulates the rate of energy input into the magnetosphere by magnetic reconnection. However, other aspects of the upstream boundary conditions may determine whether the reconnection occurs in a patchy manner, as in flux transfer events, or in a global manner, as in the Paschmann et al. (1979) events. Ionospheric boundary conditions should also affect the reconnection process. For example, ionospheric line-tying can cause x-line motion in the outer magnetosphere. If it is assumed that auroras occur on field lines mapping to x-lines, then auroral motions are different than the local convective motion of the plasma in which they occur. Global magnetohydrodynamic models which incorporate both magnetospheric reconnection and ionospheric convection could be used to investigate the effect of reconnection and convection upon dayside and nightside auroral motions during the course of a magnetic substorm.
Receptivity of Hypersonic Boundary Layers to Acoustic and Vortical Disturbances (Invited)
NASA Technical Reports Server (NTRS)
Balakumar, P.
2015-01-01
Boundary-layer receptivity to two-dimensional acoustic and vortical disturbances for hypersonic flows over two-dimensional and axi-symmetric geometries were numerically investigated. The role of bluntness, wall cooling, and pressure gradients on the receptivity and stability were analyzed and compared with the sharp nose cases. It was found that for flows over sharp nose geometries in adiabatic wall conditions the instability waves are generated in the leading-edge region and that the boundary layer is much more receptive to slow acoustic waves as compared to the fast waves. The computations confirmed the stabilizing effect of nose bluntness and the role of the entropy layer in the delay of boundary layer transition. The receptivity coefficients in flows over blunt bodies are orders of magnitude smaller than that for the sharp cone cases. Wall cooling stabilizes the first mode strongly and destabilizes the second mode. However, the receptivity coefficients are also much smaller compared to the adiabatic case. The adverse pressure gradients increased the unstable second mode regions.
Beyond the no-slip boundary condition.
Brenner, Howard
2011-10-01
This paper offers a simple macroscopic approach to the question of the slip boundary condition to be imposed upon the tangential component of the fluid velocity at a solid boundary. Plausible reasons are advanced for believing that it is the energy equation rather than the momentum equation that determines the correct fluid-mechanical boundary condition. The scheme resulting therefrom furnishes the following general, near-equilibrium linear constitutive relation for the slip velocity of mass along a relatively flat wall bounding a single-component gas or liquid: (v(m))(slip)=-α∂lnρ/∂s|(wall), where α and ρ are, respectively, the fluid's thermometric diffusivity and mass density, while the length δs refers to distance measured along the wall in the direction in which the slip or creep occurs. This constitutive relation is shown to agree with experimental data for gases and liquids undergoing thermal creep or pressure-driven viscous creep at solid surfaces. PMID:22181263
Failure of the Ingard-Myers boundary condition for a lined duct: an experimental investigation.
Renou, Ygaäl; Aurégan, Yves
2011-07-01
This paper deals with experimental investigation of the lined wall boundary condition in flow duct applications such as aircraft engine systems or automobile mufflers. A first experiment, based on a microphone array located in the liner test section, is carried out in order to extract the axial wavenumbers with the help of an "high-accurate" singular value decomposition Prony-like algorithm. The experimental axial wavenumbers are then used to provide the lined wall impedance for both downstream and upstream acoustic propagation by means of a straightforward impedance education method involving the classical Ingard-Myers boundary condition. The results show that the Ingard-Myers boundary condition fails to predict with accuracy the acoustic behavior in a lined duct with flow. An effective lined wall impedance, valid whatever the direction of acoustic propagation, can be suitably found from experimental axial wavenumbers and a modified version of the Ingard-Myers condition with the form inspired from a previous theoretical study [Aurégan et al., J. Acoust. Soc. Am. 109, 59-64 (2001)]. In a second experiment, the scattering matrix of the liner test section is measured and is then compared to the predicted scattering matrix using the multimodal approach and the lined wall impedances previously deduced. A large discrepancy is observed between the measured and the predicted scattering coefficients that confirms the poor accuracy provided from the Ingard-Myers boundary condition widely used in lined duct applications. PMID:21786877
Open Boundary Conditions for Dissipative MHD
Meier, E T
2011-11-10
In modeling magnetic confinement, astrophysics, and plasma propulsion, representing the entire physical domain is often difficult or impossible, and artificial, or 'open' boundaries are appropriate. A novel open boundary condition (BC) for dissipative MHD, called Lacuna-based open BC (LOBC), is presented. LOBC, based on the idea of lacuna-based truncation originally presented by V.S. Ryaben'kii and S.V. Tsynkov, provide truncation with low numerical noise and minimal reflections. For hyperbolic systems, characteristic-based BC (CBC) exist for separating the solution into outgoing and incoming parts. In the hyperbolic-parabolic dissipative MHD system, such separation is not possible, and CBC are numerically unstable. LOBC are applied in dissipative MHD test problems including a translating FRC, and coaxial-electrode plasma acceleration. Solution quality is compared to solutions using CBC and zero-normal derivative BC. LOBC are a promising new open BC option for dissipative MHD.
Some observations on boundary conditions for numerical conservation laws
NASA Technical Reports Server (NTRS)
Kamowitz, David
1988-01-01
Four choices of outflow boundary conditions are considered for numerical conservation laws. All four methods are stable for linear problems, for which examples are presented where either a boundary layer forms or the numerical scheme, together with the boundary condition, is unstable due to the formation of a reflected shock. A simple heuristic argument is presented for determining the suitability of the boundary condition.
Compressible turbulent channel flow with impedance boundary conditions
NASA Astrophysics Data System (ADS)
Scalo, Carlo; Bodart, Julien; Lele, Sanjiva
2014-11-01
We have performed large-eddy simulations of compressible turbulent channel flow at one bulk Reynolds number, Reb = 6900, for bulk Mach numbers Mb = 0.05, 0.2, 0.5, with linear acoustic impedance boundary conditions (IBCs). The IBCs are formulated in the time domain following Fung and Ju (2004) and coupled with a Navier-Stokes solver. The impedance model adopted is a three-parameter Helmholtz oscillator with resonant frequency tuned to the outer layer eddies. The IBC's resistance, R, has been varied in the range, R = 0.01, 0.10, 1.00. Tuned IBCs result in a noticeable drag increase for sufficiently high Mb and/or low R, exceeding 300% for Mb = 0.5 and R = 0.01, and thus represents a promising passive control technique for delaying boundary layer separation and/or enhancing wall heat transfer. Alterations to the turbulent flow structure are confined to the first 15% of the boundary layer thickness where the classical buffer-layer coherent vortical structures are replaced by an array of Kelvin-Helmholtz-like rollers. The non-zero asymptotic value of the Reynolds shear stress gradient at the wall results in the disappearance of the viscous sublayer and very early departure of the mean velocity profiles from the law of the wall.
Boundary conditions and consistency of effective theories
Polonyi, Janos; Siwek, Alicja
2010-04-15
Effective theories are nonlocal at the scale of the eliminated heavy particles modes. The gradient expansion, which represents such nonlocality, must be truncated to have treatable models. This step leads to the proliferation of the degrees of freedom, which renders the identification of the states of the effective theory nontrivial. Furthermore, it generates nondefinite metric in the Fock space, which in turn endangers the unitarity of the effective theory. It is shown that imposing a generalized Kubo-Martin-Schwinger boundary conditions for the new degrees of freedom leads to reflection positivity for a wide class of Euclidean effective theories, thereby these lead to acceptable theories when extended to real-time.
Compressible turbulent channel flow with impedance boundary conditions
NASA Astrophysics Data System (ADS)
Scalo, Carlo; Bodart, Julien; Lele, Sanjiva K.
2015-03-01
We have performed large-eddy simulations of isothermal-wall compressible turbulent channel flow with linear acoustic impedance boundary conditions (IBCs) for the wall-normal velocity component and no-slip conditions for the tangential velocity components. Three bulk Mach numbers, Mb = 0.05, 0.2, 0.5, with a fixed bulk Reynolds number, Reb = 6900, have been investigated. For each Mb, nine different combinations of IBC settings were tested, in addition to a reference case with impermeable walls, resulting in a total of 30 simulations. The adopted numerical coupling strategy allows for a spatially and temporally consistent imposition of physically realizable IBCs in a fully explicit compressible Navier-Stokes solver. The IBCs are formulated in the time domain according to Fung and Ju ["Time-domain impedance boundary conditions for computational acoustics and aeroacoustics," Int. J. Comput. Fluid Dyn. 18(6), 503-511 (2004)]. The impedance adopted is a three-parameter damped Helmholtz oscillator with resonant angular frequency, ωr, tuned to the characteristic time scale of the large energy-containing eddies. The tuning condition, which reads ωr = 2πMb (normalized with the speed of sound and channel half-width), reduces the IBCs' free parameters to two: the damping ratio, ζ, and the resistance, R, which have been varied independently with values, ζ = 0.5, 0.7, 0.9, and R = 0.01, 0.10, 1.00, for each Mb. The application of the tuned IBCs results in a drag increase up to 300% for Mb = 0.5 and R = 0.01. It is shown that for tuned IBCs, the resistance, R, acts as the inverse of the wall-permeability and that varying the damping ratio, ζ, has a secondary effect on the flow response. Typical buffer-layer turbulent structures are completely suppressed by the application of tuned IBCs. A new resonance buffer layer is established characterized by large spanwise-coherent Kelvin-Helmholtz rollers, with a well-defined streamwise wavelength λx, traveling downstream with
A New Boundary Condition for Computer Simulations of Interfacial Systems
Wong, Ka-Yiu; Pettitt, Bernard M.; Montgomery, B.
2000-08-18
A new boundary condition for computer simulations of interfacial systems is presented. The simulation box used in this boundary condition is the asymmetric unit of space group Pb, and it contains only one interface. Compared to the simulation box using common periodic boundary conditions which contains two interfaces, the number of particles in the simulation is reduced by half. This boundary condition was tested against common periodic boundary conditions in molecular dynamic simulations of liquid water interacting with hydroxylated silica surfaces. It yielded results essentially identical to periodic boundary condition and consumed less CPU time for comparable statistics.
A new boundary condition for computer simulations of interfacial systems
NASA Astrophysics Data System (ADS)
Wong, Ka-Yiu; Pettitt, B. Montgomery
2000-08-01
A new boundary condition for computer simulations of interfacial systems is presented. The simulation box used in this boundary condition is the asymmetric unit of space group Pb, and it contains only one interface. Compared to the simulation box using common periodic boundary conditions which contains two interfaces, the number of particles in the simulation is reduced by half. This boundary condition was tested against common periodic boundary conditions in molecular dynamic simulations of liquid water interacting with hydroxylated silica surfaces. It yielded results essentially identical to periodic boundary condition and consumed less CPU time for comparable statistics.
Interpreting Underwater Acoustic Images of the Upper Ocean Boundary Layer
ERIC Educational Resources Information Center
Ulloa, Marco J.
2007-01-01
A challenging task in physical studies of the upper ocean using underwater sound is the interpretation of high-resolution acoustic images. This paper covers a number of basic concepts necessary for undergraduate and postgraduate students to identify the most distinctive features of the images, providing a link with the acoustic signatures of…
NASA Astrophysics Data System (ADS)
Wada, Yuji; Koyama, Daisuke; Nakamura, Kentaro
2012-05-01
Direct finite difference fluid simulation of acoustic streaming on the fine-meshed three-dimensiona model by graphics processing unit (GPU)-oriented calculation array is discussed. Airflows due to the acoustic traveling wave are induced when an intense sound field is generated in a gap between a bending transducer and a reflector. Calculation results showed good agreement with the measurements in the pressure distribution. In addition to that, several flow-vortices were observed near the boundary of the reflector and the transducer, which have been often discussed in acoustic tube near the boundary, and have never been observed in the calculation in the ultrasonic air pump of this type.
Slip boundary conditions over curved surfaces.
Guo, Lin; Chen, Shiyi; Robbins, Mark O
2016-01-01
Molecular dynamics simulations are used to investigate the influence of surface curvature on the slip boundary condition for a simple fluid. The slip length is measured for flows in planar and cylindrical geometries with a range of wall-fluid interactions. As wall curvature increases, the slip length decreases dramatically for closely packed surfaces and increases for sparse ones. The magnitude of the changes depends on the crystallographic orientation and differs for flow along and perpendicular to the direction of curvature. These different patterns of behavior are related to the curvature-induced variation in the ratio of the spacing between fluid atoms to the spacing between minima in the potential from the solid surface. The results are consistent with a microscopic theory for the viscous friction between fluid and wall that expresses the slip length in terms of the lateral response of the fluid to the wall potential and the characteristic decay time of this response. PMID:26871153
Slip boundary conditions over curved surfaces
NASA Astrophysics Data System (ADS)
Guo, Lin; Chen, Shiyi; Robbins, Mark O.
2016-01-01
Molecular dynamics simulations are used to investigate the influence of surface curvature on the slip boundary condition for a simple fluid. The slip length is measured for flows in planar and cylindrical geometries with a range of wall-fluid interactions. As wall curvature increases, the slip length decreases dramatically for closely packed surfaces and increases for sparse ones. The magnitude of the changes depends on the crystallographic orientation and differs for flow along and perpendicular to the direction of curvature. These different patterns of behavior are related to the curvature-induced variation in the ratio of the spacing between fluid atoms to the spacing between minima in the potential from the solid surface. The results are consistent with a microscopic theory for the viscous friction between fluid and wall that expresses the slip length in terms of the lateral response of the fluid to the wall potential and the characteristic decay time of this response.
Towards Arbitrary Accuracy Inviscid Surface Boundary Conditions
NASA Technical Reports Server (NTRS)
Dyson, Rodger W.; Hixon, Ray
2002-01-01
Inviscid nonlinear surface boundary conditions are currently limited to third order accuracy in time for non-moving surfaces and actually reduce to first order in time when the surfaces move. For steady-state calculations it may be possible to achieve higher accuracy in space, but high accuracy in time is required for efficient simulation of multiscale unsteady phenomena. A surprisingly simple technique is shown here that can be used to correct the normal pressure derivatives of the flow at a surface on a Cartesian grid so that arbitrarily high order time accuracy is achieved in idealized cases. This work demonstrates that nonlinear high order time accuracy at a solid surface is possible and desirable, but it also shows that the current practice of only correcting the pressure is inadequate.
Strength function under the absorbing boundary condition
NASA Astrophysics Data System (ADS)
Iwasaki, M.; Otani, R.; Ito, M.
2014-12-01
The strength function of the linear response by the external field is calculated in the formalism of the absorbing boundary condition (ABC). The dipole excitation of a schematic two-body system is treated in the present study. The extended completeness relation, which is assumed on the analogy of the formulation in the complex scaling method (CSM), is applied to the calculation of the strength function. The calculation of the strength function is successful in the present formalism and hence, the extended completeness relation seems to work well in the ABC formalism. The contributions from the resonance and the non-resonant continuum is also analyzed according to the decomposition of the energy levels in the extended completeness relation.
Diffraction for a Neumann boundary condition
Lafitte, O.
1997-11-01
Let 0 be a bounded open set in R{sup n} and P be a constant coefficient operator of order 2 in R{sup n} x R{sub t} such that (P, {Omega}{sup c}) admits a strictly diffractive point. We calculate in this paper the principal symbol of the operator K transforming {partial_derivative}{sub n}u into u/{sub {partial_derivative}{Omega}} for a solution u of Pu = 0 in the neighborhood of a strictly diffractive point {rho}{sub 0} for (P, {Omega}{sup c}). We deduce from this calculation the principal symbol of the wave diffracted by a strictly convex analytic obstacle with a Neumann boundary condition. This result is used to calculate the electromagnetic wave diffracted by a perfectly conducting body. 7 refs., 2 figs.
Boundary regularized integral equation formulation of the Helmholtz equation in acoustics.
Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y C
2015-01-01
A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals. PMID:26064591
Conformal counterterms and boundary conditions for open strings
de Beer, W.
1988-03-15
It is explained how Neumann boundary conditions still lead to the mixed boundary conditions required to calculate the functional determinants in the Polyakov model. Neumann boundary conditions on the conformal factor are obtained, thereby negating the need for a finite counterterm in the quantum bare action.
NASA Technical Reports Server (NTRS)
Mei, Chuh; Pates, Carl S., III
1994-01-01
A coupled boundary element (BEM)-finite element (FEM) approach is presented to accurately model structure-acoustic interaction systems. The boundary element method is first applied to interior, two and three-dimensional acoustic domains with complex geometry configurations. Boundary element results are very accurate when compared with limited exact solutions. Structure-interaction problems are then analyzed with the coupled FEM-BEM method, where the finite element method models the structure and the boundary element method models the interior acoustic domain. The coupled analysis is compared with exact and experimental results for a simplistic model. Composite panels are analyzed and compared with isotropic results. The coupled method is then extended for random excitation. Random excitation results are compared with uncoupled results for isotropic and composite panels.
On the nonlinear Schrodinger equation with nonzero boundary conditions
NASA Astrophysics Data System (ADS)
Fagerstrom, Emily
This thesis is concerned with the study of the nonlinear Schrodinger (NLS) equation, which is important both from a physical and a mathematical point of view. In physics, it is a universal model for the evolutions of weakly nonlinear dispersive wave trains. As such it appears in many physical contexts, such as optics, acoustics, plasmas, biology, etc. Mathematically, it is a completely integrable, infinite-dimensional Hamiltonian system, and possesses a surprisingly rich structure. This equation has been extensively studied in the last 50 years, but many important questions are still open. In particular, this thesis contains the following original contributions: NLS with real spectral singularities. First, the focusing NLS equation is considered with decaying initial conditions. This situation has been studied extensively before, but the assumption is almost always made that the scattering coefficients have no real zeros, and thus the scattering data had no poles on the real axis. However, it is easy to produce example potentials with this behavior. For example, by modifying parameters in Satsuma-Yajima's sech potential, or by choosing a "box" potential with a particular area, one can obtain corresponding scattering entries with real zeros. The inverse scattering transform can be implemented by formulating the modified Jost eigenfunctions and the scattering data as a Riemann Hilbert problem. But it can also be formulated by using integral kernels. Doing so produces the Gelf'and-Levitan-Marchenko (GLM) equations. Solving these integral equations requires integrating an expression containing the reflection coefficient over the real axis. Under the usual assumption, the reflection coefficient has no poles on the real axis. In general, the integration contour cannot be deformed to avoid poles, because the reflection coefficient may not admit analytic extension off the real axis. Here it is shown that the GLM equations may be (uniquely) solved using a principal value
Homogenized boundary conditions and resonance effects in Faraday cages
Hewitt, I. J.
2016-01-01
We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called ‘Faraday cage effect’). Taking the limit as the number of wires in the cage tends to infinity, we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. We show how the resulting models depend on key cage parameters such as the size and shape of the wires, and, in the electromagnetic case, on the frequency and polarization of the incident field. In the electromagnetic case, there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying the continuum model, we calculate the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated shells. PMID:27279775
Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions
NASA Technical Reports Server (NTRS)
Hodge, Steve L.; Zorumski, William E.; Watson, Willie R.
1995-01-01
The Helmholtz equation is solved within a three-dimensional rectangular duct with a nonlocal radiation boundary condition at the duct exit plane. This condition accurately models the acoustic admittance at an arbitrarily-located computational boundary plane. A linear system of equations is constructed with second-order central differences for the Helmholtz operator and second-order backward differences for both local admittance conditions and the gradient term in the nonlocal radiation boundary condition. The resulting matrix equation is large, sparse, and non-Hermitian. The size and structure of the matrix makes direct solution techniques impractical; as a result, a nonstationary iterative technique is used for its solution. The theory behind the nonstationary technique is reviewed, and numerical results are presented for radiation from both a point source and a planar acoustic source. The solutions with the nonlocal boundary conditions are invariant to the location of the computational boundary, and the same nonlocal conditions are valid for all solutions. The nonlocal conditions thus provide a means of minimizing the size of three-dimensional computational domains.
NASA Astrophysics Data System (ADS)
Wang, Y.; Shu, C.; Yang, L. M.
2016-02-01
A boundary condition-enforced-immersed boundary-lattice Boltzmann flux solver is proposed in this work for effective simulation of thermal flows with Neumann boundary conditions. In this method, two auxiliary layers of Lagrangian points are introduced and respectively placed inside and outside of the solid body, on which the temperature corrections (related to the heat source) are set as unknowns. To effectively consider the fluid-boundary interaction, these unknowns are expressed as algebraic summations of the temperature correction on Eulerian points, which are in turn obtained from biased distributions of unknown temperature corrections on the immersed boundary. By enforcing the temperature gradient at the solid boundary being equal to that approximated by the corrected temperature field, a set of algebraic equations are formed and solved to obtain all the unknowns simultaneously. They are then distributed biasedly to the inner region of the auxiliary layer so that the diffusion from the smooth delta function can be reduced substantially. In addition, the solutions of the flow and temperature fields are obtained by the thermal lattice Boltzmann flux solver with the second order of accuracy. The proposed method is well validated through its applications to simulate several benchmarks of natural, forced and mixed convection problems. It has been demonstrated that the present solver has about 1.724 order of accuracy and the error between the present result and theoretical value for the temperature gradient on the solid surface is in the order of 10-13, which indicates that the proposed method is able to satisfy the Neumann boundary condition accurately.
Improvement in separation characteristics of protein precipitates by acoustic conditioning.
Hoare, M; Titchener, N J; Foster, P R
1987-01-01
The effect of acoustic conditioning on the particle size distribution of isoelectric and calcium-ion-precipitated soya protein has been examined in low-residence-time chambers. In a previous study a beat frequency of 5 Hz obtained using a dual-source system of opposing vibrators was determined as giving optimal improvement in particle-settling characteristics for isoelectric soya protein precipitate. In this study the effect of amplitude of vibration, a measure of acoustic power input, and residence time of acoustic conditioning has been examined. Acoustic power input changed the flow pattern in the conditioning chamber from laminar streamline flow to a well-mixed, turbulent pattern. Such a mixing effect promoted the rapid aggregation of fine particles, a process that was modeled on the basis of orthokinetically controlled collisions. The rate of removal of fine particles due to acoustic conditioning was shown to be proportional to a mixing effect that was related to the acoustic power dissipated per unit volume. The consequences of fine-particle aggregation on the centrifugal recovery of the precipitate are discussed. PMID:18561125
Room Acoustic Conditions of Performers in AN Old Opera House
NASA Astrophysics Data System (ADS)
IANNACE, GINO; IANNIELLO, CARMINE; MAFFEI, LUIGI; ROMANO, ROSARIO
2000-04-01
Proposed objective criteria related to the acoustic conditions for instrumentalists and singers have not received a sufficiently wide consent yet. In spite of this situation, it is the opinion of the authors that the measurement of existing criteria is useful for analysis and comparison. This paper reports the results of various acoustic measurements carried out in the Teatro di San Carlo, Naples-Italy, with the aim of obtaining objective information about its acoustics for performers. A first set of measurements was carried out when the theater was fitted for a symphonic concert and a second one when it was fitted for an opera performance.
Artificial Boundary Conditions Based on the Difference Potentials Method
NASA Technical Reports Server (NTRS)
Tsynkov, Semyon V.
1996-01-01
While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears to be most significant in many areas of scientific computing, for example, in problems originating from acoustics, electrodynamics, solid mechanics, and fluid dynamics. In particular, in computational fluid dynamics (where external problems present a wide class of practically important formulations) the proper treatment of external boundaries may have a profound impact on the overall quality and performance of numerical algorithms. Most of the currently used techniques for setting the ABC's can basically be classified into two groups. The methods from the first group (global ABC's) usually provide high accuracy and robustness of the numerical procedure but often appear to be fairly cumbersome and (computationally) expensive. The methods from the second group (local ABC's) are, as a rule, algorithmically simple, numerically cheap, and geometrically universal; however, they usually lack accuracy of computations. In this paper we first present a survey and provide a comparative assessment of different existing methods for constructing the ABC's. Then, we describe a relatively new ABC's technique of ours and review the corresponding results. This new technique, in our opinion, is currently one of the most promising in the field. It enables one to construct such ABC's that combine the advantages relevant to the two aforementioned classes of existing methods. Our approach is based on application of the difference potentials method attributable to V. S. Ryaben'kii. This approach allows us to obtain highly accurate ABC's in the form of certain (nonlocal) boundary operator equations. The operators involved are analogous to the pseudodifferential boundary projections first introduced by A. P. Calderon and then
Generalized Flows Satisfying Spatial Boundary Conditions
NASA Astrophysics Data System (ADS)
Buffoni, B.
2012-09-01
In a region D in {{R}^2} or {{R}^3}, the classical Euler equation for the regular motion of an inviscid and incompressible fluid of constant density is given by partial_t v+(v\\cdot nabla_x)v=-nabla_x p, div_x v=0, where v( t, x) is the velocity of the particle located at {xin D} at time t and {p(t,x)in{R}} is the pressure. Solutions v and p to the Euler equation can be obtained by solving \\{begin{array}{l} nabla_x\\{partial_tφ(t,x,a) + p(t,x)+(1/2)|nabla_xφ(t,x,a)|^2 \\}=0 at a=kappa(t,x),\\ v(t,x)=nabla_x φ(t,x,a) at a=kappa(t,x), \\ partial_tkappa(t,x)+(v\\cdotnabla_x)kappa(t,x)=0, \\ div_x v(t,x)=0, . quadquadquadquadquad(0.1) where φ:{R}× D× {R}^l→{R} and kappa:{R}× D → {R}^l are additional unknown mappings ( l ≥ 1 is prescribed). The third equation in the system says that {kappain{R}^l} is convected by the flow and the second one that {φ} can be interpreted as some kind of velocity potential. However vorticity is not precluded thanks to the dependence on a. With the additional condition κ(0, x) = x on D (and thus l = 2 or 3), this formulation was developed by Brenier (Commun Pure Appl Math 52:411-452, 1999) in his Eulerian-Lagrangian variational approach to the Euler equation. He considered generalized flows that do not cross {partial D} and that carry each "particle" at time t = 0 at a prescribed location at time t = T > 0, that is, κ( T, x) is prescribed in D for all {xin D}. We are concerned with flows that are periodic in time and with prescribed flux through each point of the boundary {partial D} of the bounded region D (a two- or three-dimensional straight pipe). More precisely, the boundary condition is on the flux through {partial D} of particles labelled by each value of κ at each point of {partial D}. One of the main novelties is the introduction of a prescribed "generalized" Bernoulli's function {H:{R}^l→ {R}}, namely, we add to (0.1) the requirement that partial_tφ(t,x,a) +p(t,x)+(1/2)|nabla_xφ(t,x,a)|^2=H(a) at a
A Smoothed Boundary Condition for Reducing Nonphysical Field Effects
NASA Technical Reports Server (NTRS)
Smith, Arlynn W.; Parks, Joseph W., Jr.; Haralson, Joe N., II; Brennan, Kevin F.
1997-01-01
In this paper, we examine the problem associated with abruptly mixing boundary conditions in the context of a two-dimensional semiconductor device simulator. Explicitly, this paper addresses the transition between an ohmic-type Dirichlet condition and a passivated Neumann boundary. In the traditional setting, the details or the transition between the two boundary types are not addressed and an abrupt transition is assumed. Subsequently, the calculated observables (most notably the potential) exhibit discontinuous derivatives near the surface at the point where the boundary type switches. This paper proposes an alternative condition which models the progression between the two boundary types through the use of a finite length, smoothed boundary whereby the numerical discontinuities are eliminated. The physical and mathematical basis for this smoothed boundary condition is discussed and examples of the technique's implementation given. It is found that the proposed boundary condition is numerically efficient and can be implemented in pre-existing device simulators with relative ease.
Long-time behaviour of absorbing boundary conditions
NASA Technical Reports Server (NTRS)
Engquist, B.; Halpern, L.
1990-01-01
A new class of computational far-field boundary conditions for hyperbolic partial differential equations was recently introduced by the authors. These boundary conditions combine properties of absorbing conditions for transient solutions and properties of far-field conditions for steady states. This paper analyses the properties of the wave equation coupled with these new boundary conditions: well-posedness, dissipativity and convergence in time.
NASA Astrophysics Data System (ADS)
Deryabin, M. S.; Kasyanov, D. A.; Kurin, V. V.; Garasyov, M. A.
2016-05-01
We show that a significant energy redistribution occurs in the spectrum of reflected nonlinear waves, when an intense acoustic beam is reflected from an acoustically soft boundary, which manifests itself at short wave distances from a reflecting boundary. This effect leads to the appearance of extrema in the distributions of the amplitude and intensity of the field of the reflected acoustic beam near the reflecting boundary. The results of physical experiments are confirmed by numerical modeling of the process of transformation of nonlinear waves reflected from an acoustically soft boundary. Numerical modeling was performed by means of the Khokhlov—Zabolotskaya—Kuznetsov (KZK) equation.
NASA Astrophysics Data System (ADS)
Deryabin, M. S.; Kasyanov, D. A.; Kurin, V. V.; Garasyov, M. A.
2016-06-01
We show that a significant energy redistribution occurs in the spectrum of reflected nonlinear waves, when an intense acoustic beam is reflected from an acoustically soft boundary, which manifests itself at short wave distances from a reflecting boundary. This effect leads to the appearance of extrema in the distributions of the amplitude and intensity of the field of the reflected acoustic beam near the reflecting boundary. The results of physical experiments are confirmed by numerical modeling of the process of transformation of nonlinear waves reflected from an acoustically soft boundary. Numerical modeling was performed by means of the Khokhlov—Zabolotskaya—Kuznetsov (KZK) equation.
NASA Astrophysics Data System (ADS)
Bennewitz, John William
This research investigation encompasses experimental tests demonstrating the control of a high-frequency combustion instability by acoustically modulating the propellant flow. A model rocket combustor burned gaseous oxygen and methane using a single-element, pentad-style injector. Flow conditions were established that spontaneously excited a 2430 Hz first longitudinal combustion oscillation at an amplitude up to p'/pc ≈ 6%. An acoustic speaker was placed at the base of the oxidizer supply to modulate the flow and alter the oscillatory behavior of the combustor. Two speaker modulation approaches were investigated: (1) Bands of white noise and (2) Pure sinusoidal tones. The first approach adjusted 500 Hz bands of white noise ranging from 0-500 Hz to 2000-2500 Hz, while the second implemented single-frequency signals with arbitrary phase swept from 500-2500 Hz. The results showed that above a modulation signal amplitude threshold, both approaches suppressed 95+% of the spontaneous combustion oscillation. By increasing the applied signal amplitude, a wider frequency range of instability suppression became present for these two acoustic modulation approaches. Complimentary to these experiments, a linear modal analysis was undertaken to investigate the effects of acoustic modulation at the inlet boundary on the longitudinal instability modes of a dump combustor. The modal analysis employed acoustically consistent matching conditions with a specific impedance boundary condition at the inlet to represent the acoustic modulation. From the modal analysis, a naturally unstable first longitudinal mode was predicted in the absence of acoustic modulation, consistent with the spontaneously excited 2430 Hz instability observed experimentally. Subsequently, a detailed investigation involving variation of the modulation signal from 0-2500 Hz and mean combustor temperature from 1248-1685 K demonstrated the unstable to stable transition of a 2300-2500 Hz first longitudinal mode. The
Eutectic growth under acoustic levitation conditions
NASA Astrophysics Data System (ADS)
Xie, W. J.; Cao, C. D.; Lü, Y. J.; Wei, B.
2002-12-01
Samples of Pb-Sn eutectic alloy with a high density of 8.5×103 kg/m3 are levitated with a single-axis acoustic levitator, and containerlessly melted and then solidified in argon atmosphere. High undercoolings up to 38 K are obtained, which results in a microstructural transition of ``lamellas-broken lamellas-dendrites.'' This transition is further investigated in the light of the coupled zone for eutectic growth and the effects of ultrasound. The breaking of regular eutectic lamellas and suppression of gravity-induced macrosegregation of (Pb) and (Sn) dendrites are explained by the complicated internal flow inside the levitated drop, which is jointly induced by the shape oscillation, bulk vibration and rotation of the levitated drop. The ultrasonic field is also found to drive forced surface vibration, which subsequently excites capillary ripples and catalyzes nucleation on the sample surface.
Eutectic growth under acoustic levitation conditions.
Xie, W J; Cao, C D; Lü, Y J; Wei, B
2002-12-01
Samples of Pb-Sn eutectic alloy with a high density of 8.5 x 10(3) kg/m(3) are levitated with a single-axis acoustic levitator, and containerlessly melted and then solidified in argon atmosphere. High undercoolings up to 38 K are obtained, which results in a microstructural transition of "lamellas-broken lamellas-dendrites." This transition is further investigated in the light of the coupled zone for eutectic growth and the effects of ultrasound. The breaking of regular eutectic lamellas and suppression of gravity-induced macrosegregation of (Pb) and (Sn) dendrites are explained by the complicated internal flow inside the levitated drop, which is jointly induced by the shape oscillation, bulk vibration and rotation of the levitated drop. The ultrasonic field is also found to drive forced surface vibration, which subsequently excites capillary ripples and catalyzes nucleation on the sample surface. PMID:12513291
Absorbing boundary conditions for second-order hyperbolic equations
NASA Technical Reports Server (NTRS)
Jiang, Hong; Wong, Yau Shu
1989-01-01
A uniform approach to construct absorbing artificial boundary conditions for second-order linear hyperbolic equations is proposed. The nonlocal boundary condition is given by a pseudodifferential operator that annihilates travelling waves. It is obtained through the dispersion relation of the differential equation by requiring that the initial-boundary value problem admits the wave solutions travelling in one direction only. Local approximation of this global boundary condition yields an nth-order differential operator. It is shown that the best approximations must be in the canonical forms which can be factorized into first-order operators. These boundary conditions are perfectly absorbing for wave packets propagating at certain group velocities. A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. These examples illustrate that the absorbing boundary conditions are easy to derive, and the effectiveness is demonstrated by the numerical experiments.
Absorbing boundary conditions for second-order hyperbolic equations
NASA Technical Reports Server (NTRS)
Jiang, Hong; Wong, Yau Shu
1990-01-01
A uniform approach to construct absorbing artificial boundary conditions for second-order linear hyperbolic equations is proposed. The nonlocal boundary condition is given by a pseudodifferential operator that annihilates travelling waves. It is obtained through the dispersion relation of the differential equation by requiring that the initial-boundary value problem admits the wave solutions travelling in one direction only. Local approximation of this global boundary condition yields an nth-order differential operator. It is shown that the best approximations must be in the canonical forms which can be factorized into first-order operators. These boundary conditions are perfectly absorbing for wave packets propagating at certain group velocities. A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. These examples illustrate that the absorbing boundary conditions are easy to derive, and the effectiveness is demonstrated by the numerical experiments.
Receptivity of Hypersonic Boundary Layers to Distributed Roughness and Acoustic Disturbances
NASA Technical Reports Server (NTRS)
Balakumar, P.
2013-01-01
Boundary-layer receptivity and stability of Mach 6 flows over smooth and rough seven-degree half-angle sharp-tipped cones are numerically investigated. The receptivity of the boundary layer to slow acoustic disturbances, fast acoustic disturbances, and vortical disturbances is considered. The effects of three-dimensional isolated roughness on the receptivity and stability are also simulated. The results for the smooth cone show that the instability waves are generated in the leading edge region and that the boundary layer is much more receptive to slow acoustic waves than to the fast acoustic waves. Vortical disturbances also generate unstable second modes, however the receptivity coefficients are smaller than that of the slow acoustic wave. Distributed roughness elements located near the nose region decreased the receptivity of the second mode generated by the slow acoustic wave by a small amount. Roughness elements distributed across the continuous spectrum increased the receptivity of the second mode generated by the slow and fast acoustic waves and the vorticity wave. The largest increase occurred for the vorticity wave. Roughness elements distributed across the synchronization point did not change the receptivity of the second modes generated by the acoustic waves. The receptivity of the second mode generated by the vorticity wave increased in this case, but the increase is lower than that occurred with the roughness elements located across the continuous spectrum. The simulations with an isolated roughness element showed that the second mode waves generated by the acoustic disturbances are not influenced by the small roughness element. Due to the interaction, a three-dimensional wave is generated. However, the amplitude is orders of magnitude smaller than the two-dimensional wave.
Lateral boundary conditions for the Klein-Gordon-Fock equation
NASA Astrophysics Data System (ADS)
Tulenov, Kanat S.; Dauitbek, Dostilek
2016-08-01
In this paper we consider an initial-boundary value problem for the Klein-Gordon-Fock equation. We prove the uniqueness of the solution and find lateral boundary conditions for the Klein-Gordon-Fock equation.
Effective surface and boundary conditions for heterogeneous surfaces with mixed boundary conditions
NASA Astrophysics Data System (ADS)
Guo, Jianwei; Veran-Tissoires, Stéphanie; Quintard, Michel
2016-01-01
To deal with multi-scale problems involving transport from a heterogeneous and rough surface characterized by a mixed boundary condition, an effective surface theory is developed, which replaces the original surface by a homogeneous and smooth surface with specific boundary conditions. A typical example corresponds to a laminar flow over a soluble salt medium which contains insoluble material. To develop the concept of effective surface, a multi-domain decomposition approach is applied. In this framework, velocity and concentration at micro-scale are estimated with an asymptotic expansion of deviation terms with respect to macro-scale velocity and concentration fields. Closure problems for the deviations are obtained and used to define the effective surface position and the related boundary conditions. The evolution of some effective properties and the impact of surface geometry, Péclet, Schmidt and Damköhler numbers are investigated. Finally, comparisons are made between the numerical results obtained with the effective models and those from direct numerical simulations with the original rough surface, for two kinds of configurations.
Verification Assessment of Flow Boundary Conditions for CFD Analysis of Supersonic Inlet Flows
NASA Technical Reports Server (NTRS)
Slater, John W.
2002-01-01
Boundary conditions for subsonic inflow, bleed, and subsonic outflow as implemented into the WIND CFD code are assessed with respect to verification for steady and unsteady flows associated with supersonic inlets. Verification procedures include grid convergence studies and comparisons to analytical data. The objective is to examine errors, limitations, capabilities, and behavior of the boundary conditions. Computational studies were performed on configurations derived from a "parameterized" supersonic inlet. These include steady supersonic flows with normal and oblique shocks, steady subsonic flow in a diffuser, and unsteady flow with the propagation and reflection of an acoustic disturbance.
Acoustic Receptivity of Mach 4.5 Boundary Layer with Leading- Edge Bluntness
NASA Technical Reports Server (NTRS)
Malik, Mujeeb R.; Balakumar, Ponnampalam
2007-01-01
Boundary layer receptivity to two-dimensional slow and fast acoustic waves is investigated by solving Navier-Stokes equations for Mach 4.5 flow over a flat plate with a finite-thickness leading edge. Higher order spatial and temporal schemes are employed to obtain the solution whereby the flat-plate leading edge region is resolved by providing a sufficiently refined grid. The results show that the instability waves are generated in the leading edge region and that the boundary-layer is much more receptive to slow acoustic waves (by almost a factor of 20) as compared to the fast waves. Hence, this leading-edge receptivity mechanism is expected to be more relevant in the transition process for high Mach number flows where second mode instability is dominant. Computations are performed to investigate the effect of leading-edge thickness and it is found that bluntness tends to stabilize the boundary layer. Furthermore, the relative significance of fast acoustic waves is enhanced in the presence of bluntness. The effect of acoustic wave incidence angle is also studied and it is found that the receptivity of the boundary layer on the windward side (with respect to the acoustic forcing) decreases by more than a factor of 4 when the incidence angle is increased from 0 to 45 deg. However, the receptivity coefficient for the leeward side is found to vary relatively weakly with the incidence angle.
Receptivity of Hypersonic Boundary Layers to Distributed Roughness and Acoustic Disturbances
NASA Technical Reports Server (NTRS)
Balakumar, Ponnampalam
2012-01-01
Boundary-layer receptivity and stability of Mach 6 flow over smooth and rough 7 half-angle sharp-tipped cones are numerically investigated. The receptivity of the boundary layer to slow acoustic disturbances, fast acoustic disturbances, and vortical disturbances are considered. The effects of two-dimensional isolated and distributed roughness on the receptivity and stability are also simulated. The results show that the instability waves are generated in the leading edge region and that the boundary layer is much more receptive to slow acoustic waves than to the fast waves. Vortical disturbances also generate unstable second modes, however the receptivity coefficients are smaller than that of the slow acoustic wave. An isolated two-dimensional roughness element of height h/delta =1/4 did not produce any difference in the receptivity or in the stability of the boundary layer. Distributed roughness elements produced a small decrease in the receptivity coefficient and also stabilized the boundary layer by small amounts.
NASA Technical Reports Server (NTRS)
Tam, Christopher K. W.; Webb, Jay C.
1994-01-01
In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The
Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations
NASA Astrophysics Data System (ADS)
Ehrlacher, V.; Ortner, C.; Shapeev, A. V.
2016-06-01
Numerical simulations of crystal defects are necessarily restricted to finite computational domains, supplying artificial boundary conditions that emulate the effect of embedding the defect in an effectively infinite crystalline environment. This work develops a rigorous framework within which the accuracy of different types of boundary conditions can be precisely assessed. We formulate the equilibration of crystal defects as variational problems in a discrete energy space and establish qualitatively sharp regularity estimates for minimisers. Using this foundation we then present rigorous error estimates for (i) a truncation method (Dirichlet boundary conditions), (ii) periodic boundary conditions, (iii) boundary conditions from linear elasticity, and (iv) boundary conditions from nonlinear elasticity. Numerical results confirm the sharpness of the analysis.
Najafi-Yazdi, A; Mongeau, L
2012-09-15
The Lattice Boltzmann Method (LBM) is a well established computational tool for fluid flow simulations. This method has been recently utilized for low Mach number computational aeroacoustics. Robust and nonreflective boundary conditions, similar to those used in Navier-Stokes solvers, are needed for LBM-based aeroacoustics simulations. The goal of the present study was to develop an absorbing boundary condition based on the perfectly matched layer (PML) concept for LBM. The derivation of formulations for both two and three dimensional problems are presented. The macroscopic behavior of the new formulation is discussed. The new formulation was tested using benchmark acoustic problems. The perfectly matched layer concept appears to be very well suited for LBM, and yielded very low acoustic reflection factor. PMID:23526050
Najafi-Yazdi, A.; Mongeau, L.
2012-01-01
The Lattice Boltzmann Method (LBM) is a well established computational tool for fluid flow simulations. This method has been recently utilized for low Mach number computational aeroacoustics. Robust and nonreflective boundary conditions, similar to those used in Navier-Stokes solvers, are needed for LBM-based aeroacoustics simulations. The goal of the present study was to develop an absorbing boundary condition based on the perfectly matched layer (PML) concept for LBM. The derivation of formulations for both two and three dimensional problems are presented. The macroscopic behavior of the new formulation is discussed. The new formulation was tested using benchmark acoustic problems. The perfectly matched layer concept appears to be very well suited for LBM, and yielded very low acoustic reflection factor. PMID:23526050
On the boundary conditions in slope stability analysis
NASA Astrophysics Data System (ADS)
Chugh, Ashok K.
2003-09-01
Boundary conditions can affect computed factor of safety results in two- and three-dimensional stability analyses of slopes. Commonly used boundary conditions in two- and three-dimensional slope stability analyses via limit-equilibrium and continuum-mechanics based solution procedures are described. A sample problem is included to illustrate the importance of boundary conditions in slope stability analyses. The sample problem is solved using two- and three-dimensional numerical models commonly used in engineering practice.
Absorbing boundary conditions for relativistic quantum mechanics equations
Antoine, X.; Sater, J.; Fillion-Gourdeau, F.; Bandrauk, A.D.
2014-11-15
This paper is devoted to the derivation of absorbing boundary conditions for the Klein–Gordon and Dirac equations modeling quantum and relativistic particles subject to classical electromagnetic fields. Microlocal analysis is the main ingredient in the derivation of these boundary conditions, which are obtained in the form of pseudo-differential equations. Basic numerical schemes are derived and analyzed to illustrate the accuracy of the derived boundary conditions.
Divergence Boundary Conditions for Vector Helmholtz Equations with Divergence Constraints
NASA Technical Reports Server (NTRS)
Kangro, Urve; Nicolaides, Roy
1997-01-01
The idea of replacing a divergence constraint by a divergence boundary condition is investigated. The connections between the formulations are considered in detail. It is shown that the most common methods of using divergence boundary conditions do not always work properly. Necessary and sufficient conditions for the equivalence of the formulations are given.
New boundary conditions for the c=-2 ghost system
Creutzig, Thomas; Quella, Thomas; Schomerus, Volker
2008-01-15
We investigate a novel boundary condition for the bc system with central charge c=-2. Its boundary state is constructed and tested in detail. It appears to give rise to the first example of a local logarithmic boundary sector within a bulk theory whose Virasoro zero modes are diagonalizable.
Simulation of boundary conditions for testing of masonry shear walls
NASA Astrophysics Data System (ADS)
Salmanpour, Amir Hosein; Mojsilović, Nebojša
2015-12-01
This paper is focused on the simulation of the fixed-ends boundary conditions in shear testing of unreinforced masonry walls. Two different approaches to simulate the fixed-ends boundary conditions, i.e. the static and kinematic approaches, are introduced, and their validity is discussed with the help of our own recent experimental data. It is shown that the static approach can result in unrealistic boundary conditions, and it is not a proper way to simulate the fixed-ends boundary conditions.
Receptivity and Forced Response to Acoustic Disturbances in High-Speed Boundary Layers
NASA Technical Reports Server (NTRS)
Balakumar, P.; King, Rudolph A.; Chou, Amanda; Owens, Lewis R.; Kegerise, Michael A.
2016-01-01
Supersonic boundary-layer receptivity to freestream acoustic disturbances is investigated by solving the Navier-Stokes equations for Mach 3.5 flow over a sharp flat plate and a 7-deg half-angle cone. The freestream disturbances are generated from a wavy wall placed at the nozzle wall. The freestream acoustic disturbances radiated by the wavy wall are obtained by solving the linearized Euler equations. The results for the flat plate show that instability modes are generated at all the incident angles ranging from zero to highly oblique. However, the receptivity coefficient decreases by about 20 times when the incident angle increases from zero to a highly oblique angle of 68 degrees. The results for the cone show that no instability modes are generated when the acoustic disturbances impinge the cone obliquely. The results show that the perturbations generated inside the boundary layer by the acoustic disturbances are the response of the boundary layer to the external forcing. The amplitude of the forced disturbances inside the boundary layer are about 2.5 times larger than the incoming field for zero azimuthal wavenumber and they are about 1.5 times for large azimuthal wavenumbers.
Receptivity of Hypersonic Boundary Layers Due to Acoustic Disturbances over Blunt Cone
NASA Technical Reports Server (NTRS)
Kara, K.; Balakumar, P.; Kandil, O. A.
2007-01-01
The transition process induced by the interaction of acoustic disturbances in the free-stream with boundary layers over a 5-degree straight cone and a wedge with blunt tips is numerically investigated at a free-stream Mach number of 6.0. To compute the shock and the interaction of shock with the instability waves the Navier-Stokes equations are solved in axisymmetric coordinates. The governing equations are solved using the 5th -order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. After the mean flow field is computed, acoustic disturbances are introduced at the outer boundary of the computational domain and unsteady simulations are performed. Generation and evolution of instability waves and the receptivity of boundary layer to slow and fast acoustic waves are investigated. The mean flow data are compared with the experimental results. The results show that the instability waves are generated near the leading edge and the non-parallel effects are stronger near the nose region for the flow over the cone than that over a wedge. It is also found that the boundary layer is much more receptive to slow acoustic wave (by almost a factor of 67) as compared to the fast wave.
Belyaev, Mikhail A.; Rafikov, Roman R.; Stone, James M.
2013-06-10
The nature of angular momentum transport in the boundary layers of accretion disks has been one of the central and long-standing issues of accretion disk theory. In this work we demonstrate that acoustic waves excited by supersonic shear in the boundary layer serve as an efficient mechanism of mass, momentum, and energy transport at the interface between the disk and the accreting object. We develop the theory of angular momentum transport by acoustic modes in the boundary layer, and support our findings with three-dimensional hydrodynamical simulations, using an isothermal equation of state. Our first major result is the identification of three types of global modes in the boundary layer. We derive dispersion relations for each of these modes that accurately capture the pattern speeds observed in simulations to within a few percent. Second, we show that angular momentum transport in the boundary layer is intrinsically nonlocal, and is driven by radiation of angular momentum away from the boundary layer into both the star and the disk. The picture of angular momentum transport in the boundary layer by waves that can travel large distances before dissipating and redistributing angular momentum and energy to the disk and star is incompatible with the conventional notion of local transport by turbulent stresses. Our results have important implications for semianalytical models that describe the spectral emission from boundary layers.
Effect of Far-Field Boundary Conditions on Boundary-Layer Transition
NASA Technical Reports Server (NTRS)
Bertolotti, Fabio P.; Joslin, Ronald D.
1994-01-01
The effect of far-field boundary conditions on the evolution of a finite-amplitude two-dimensional wave in the Blasius boundary layer is assessed. With the use of the parabolized stability equations (PSE) theory for the numerical computations, either asymptotic, Dirichlet, Neumann or mixed boundary conditions are imposed at various distances from the wall. The results indicate that asymptotic and mixed boundary conditions yield the most accurate mean-flow distortion and unsteady instability modes in comparison with the results obtained with either Dirichlet or Neumann conditions.
Effect of Far-Field Boundary Conditions on Boundary-Layer Transition
NASA Technical Reports Server (NTRS)
Bertolotti, Fabio P.; Joslin, Ronald D.
1995-01-01
The effect of far-field boundary conditions on the evolution of a finite-amplitude two-dimensional wave in the Blasius boundary layer is assessed. With the use of the parabolized stability equations (PSE) theory for the numerical computations, either asymptotic, Dirichlet, Neumann or mixed boundary conditions are imposed at various distances from the wall. The results indicate that asymptotic and mixed boundary conditions yield the most accurate mean-flow distortion and unsteady instability modes in comparison with the results obtained with either Dirichlet or Neumann conditions.
The influence of the boundary conditions on longitudinal wave propagation in a viscoelastic medium.
Eskandari, Hani; Baghani, Ali; Salcudean, Septimiu E; Rohling, Robert
2009-07-01
In this paper, the effect of the boundary conditions and excitation dimensions on the speed of longitudinal waves in a medium is investigated. It is shown that with appropriate boundary conditions, a low-speed longitudinal wave can be generated in the medium which can be tracked by standard pulse-echo ultrasound motion tracking techniques. Three different cases of boundary conditions are explored in which the longitudinal wave speed in an incompressible material can be as high as the acoustic wave speed or as low as the shear wave speed. It is shown that the displacement spectrum can be used to estimate the wave speed in a viscoelastic medium. Numerical simulations with 3D viscoelastic finite element models and experiments on tissue-mimicking phantoms are performed to validate the theory. PMID:19502703
Numerical boundary condition procedure for the transonic axisymmetric inverse problem
NASA Technical Reports Server (NTRS)
Shankar, V.
1981-01-01
Two types of boundary condition procedures for the axisymmetric inverse problem are described. One is a Neumann type boundary condition (analogous to the analysis problem) and the other is a Dirichlet type boundary conditon, both requiring special treatments to make the inverse scheme numerically stable. The dummy point concept is utilized in implementing both. Results indicate the Dirichlet type inverse boundary condition is more robust and conceptually simpler to implement than the Neumann type procedure. A few results demonstrating the powerful capability of the newly developed inverse method that can handle both shocked as well as shockless body design are included.
Boundary-Layer Effects on Acoustic Transmission Through Narrow Slit Cavities
NASA Astrophysics Data System (ADS)
Ward, G. P.; Lovelock, R. K.; Murray, A. R. J.; Hibbins, A. P.; Sambles, J. R.; Smith, J. D.
2015-07-01
We explore the slit-width dependence of the resonant transmission of sound in air through both a slit array formed of aluminum slats and a single open-ended slit cavity in an aluminum plate. Our experimental results accord well with Lord Rayleigh's theory concerning how thin viscous and thermal boundary layers at a slit's walls affect the acoustic wave across the whole slit cavity. By measuring accurately the frequencies of the Fabry-Perot-like cavity resonances, we find a significant 5% reduction in the effective speed of sound through the slits when an individual viscous boundary layer occupies only 5% of the total slit width. Importantly, this effect is true for any airborne slit cavity, with the reduction being achieved despite the slit width being on a far larger scale than an individual boundary layer's thickness. This work demonstrates that the recent prevalent loss-free treatment of narrow slit cavities within acoustic metamaterials is unrealistic.
NASA Astrophysics Data System (ADS)
Mimura, Masakazu; Tamazaki, Daisuke; Yamane, Takashi; Kando, Hajime
2012-07-01
In this paper, we describe a new boundary acoustic wave structure employing multilayered metal electrodes with a high-density metal and a low-density metal. By using this structure, such as Pt/Al/Pt, the electromechanical coupling coefficient (k2) and temperature coefficient of frequency (TCF) of the boundary acoustic wave can be changed. We theoretically studied the dependence of the energy distribution of the boundary wave on the position of the total electrode gravity center when the electrode layer structure is changed. It was experimentally confirmed that k2 and TCF can be changed simultaneously. By using this structure, we developed a novel filter with good electrical characteristics, and a very small variation of the filter characteristic with temperature (almost zero TCF) was successfully realized.
NASA Technical Reports Server (NTRS)
Schopper, M. R.
1982-01-01
The hot-wire anemometer amplitude data contained in the 1977 report of P. J. Shapiro entitled, ""The Influence of Sound Upon Laminar Boundary'' were reevaluated. Because the low-Reynolds number boundary layer disturbance data were misinterpreted, an effort was made to improve the corresponding disturbance growth rate curves. The data are modeled as the sum of upstream and downstream propagating acoustic waves and a wave representing the Tollmien-Schlichting (TS) wave. The amplitude and phase velocity of the latter wave were then adjusted so that the total signal reasonably matched the amplitude and phase angle hot-wire data along the plate laminar boundary layer. The revised rates show growth occurring further upstream than Shapiro found. It appears that the premature growth is due to the adverse pressure gradient created by the shape of the plate. Basic elements of sound propagation in ducts and the experimental and theoretical acoustic-stability literature are reviewed.
Finite difference time domain implementation of surface impedance boundary conditions
NASA Technical Reports Server (NTRS)
Beggs, John H.; Luebbers, Raymond J.; Yee, Kane S.; Kunz, Karl S.
1991-01-01
Surface impedance boundary conditions are employed to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In the finite difference solution, they also can be utilized to avoid using small cells, made necessary by shorter wavelengths in conducting media throughout the solution volume. The standard approach is to approximate the surface impedance over a very small bandwidth by its value at the center frequency, and then use that result in the boundary condition. Here, two implementations of the surface impedance boundary condition are presented. One implementation is a constant surface impedance boundary condition and the other is a dispersive surface impedance boundary condition that is applicable over a very large frequency bandwidth and over a large range of conductivities. Frequency domain results are presented in one dimension for two conductivity values and are compared with exact results. Scattering width results from an infinite square cylinder are presented as a two dimensional demonstration. Extensions to three dimensions should be straightforward.
Periodic Boundary Conditions in the ALEGRA Finite Element Code
AIDUN,JOHN B.; ROBINSON,ALLEN C.; WEATHERBY,JOE R.
1999-11-01
This document describes the implementation of periodic boundary conditions in the ALEGRA finite element code. ALEGRA is an arbitrary Lagrangian-Eulerian multi-physics code with both explicit and implicit numerical algorithms. The periodic boundary implementation requires a consistent set of boundary input sets which are used to describe virtual periodic regions. The implementation is noninvasive to the majority of the ALEGRA coding and is based on the distributed memory parallel framework in ALEGRA. The technique involves extending the ghost element concept for interprocessor boundary communications in ALEGRA to additionally support on- and off-processor periodic boundary communications. The user interface, algorithmic details and sample computations are given.
NASA Technical Reports Server (NTRS)
Choudhari, Meelan
1994-01-01
The Goldstein-Ruban theory has been extended within the framework of Zavol'skii et al. to study the acoustic receptivity of compressible boundary layers. We consider the receptivity produced in a region of localized, small-amplitude variation in the surface temperature and compare it with the receptivity that is induced through a similar mechanism by a variation in the suction velocity at the surface. It is found that the orientation of the acoustic wave can have a significant impact on the receptivity process, with the maximum receptivity at a given sound-pressure level being produced by upstream oriented acoustic waves. At sufficiently low Mach numbers, the variation of receptivity with the acoustic-wave orientation can be predicted analytically and is the same for both surface suction and surface heating. However, as a result of the acoustic refraction across the mean boundary layer, the above dependence can become rather complex and, also, dependent on the type of surface nonuniformity. The results also suggest that the receptivity caused by temperature nonuniformities may turn out to be more significant than that produced by the mean-flow perturbations associated with strip suction.
Accurate boundary conditions for exterior problems in gas dynamics
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas; Hariharan, S. I.
1988-01-01
The numerical solution of exterior problems is typically accomplished by introducing an artificial, far field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory.
Accurate boundary conditions for exterior problems in gas dynamics
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas; Hariharan, S. I.
1988-01-01
The numerical solution of exterior problems is typically accomplished by introducing an artificial, far-field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far-field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory.
A Advanced Boundary Element Formulation for Acoustic Radiation and Scattering in Three Dimensions.
NASA Astrophysics Data System (ADS)
Soenarko, Benjamin
A computational method is presented for determining acoustic fields produced by arbitrary shaped three-dimensional bodies. The formulation includes both radiation and scattering problems. In particular an isoparametric element formulation is introduced in which both the surface geometry and the acoustic variables on the surface of the body are represented by second order shape functions within the local coordinate system. A general result for the surface velocity potential and the exterior field is derived. This result is applicable to non-smooth bodies, i.e. it includes the case where the surface may have a non-unique normal (e.g. at the edge of a cube). Test cases are shown involving spherical, cylindrical and cubical geometry for both radiation and scattering problems. The present formulation is also extended to include half-space problems in which the effect of the reflected wave from an infinite plane is taken into account. By selecting an appropriate Green's function, the surface integral over the plane is nullified; thus all the computational efforts can be performed only on the radiating or scattering body at issue and thereby greatly simplify the solution. A special formulation involving axisymmetric bodies and boundary conditions is also presented. For this special case, the surface integrals are reduced to line integrals and an integral over the angle of revolution. The integration over the angle is performed partly analytically in terms of elliptic integrals and partly numerically using simple Gaussian quadrature formula. Since the rest of the integrals involve only line integrals along the generator of the body, any discretization scheme can be easily obtained to achieve a desired degree of accuracy in evaluating these integrals.
Daeva, S.G.; Setukha, A.V.
2015-03-10
A numerical method for solving a problem of diffraction of acoustic waves by system of solid and thin objects based on the reduction the problem to a boundary integral equation in which the integral is understood in the sense of finite Hadamard value is proposed. To solve this equation we applied piecewise constant approximations and collocation methods numerical scheme. The difference between the constructed scheme and earlier known is in obtaining approximate analytical expressions to appearing system of linear equations coefficients by separating the main part of the kernel integral operator. The proposed numerical scheme is tested on the solution of the model problem of diffraction of an acoustic wave by inelastic sphere.
NASA Technical Reports Server (NTRS)
Kachanov, Y. S.; Kozlov, V. V.; Levchenko, V. Y.
1985-01-01
A low-turbulence subsonic wind tunnel was used to study the influence of acoustic disturbances on the development of small sinusoidal oscillations (Tollmien-Schlichting waves) which constitute the initial phase of turbulent transition. It is found that acoustic waves propagating opposite to the flow generate vibrations of the model (plate) in the flow. Neither the plate vibrations nor the acoustic field itself have any appreciable influence on the stability of the laminar boundary layer. The influence of an acoustic field on laminar boundary layer disturbances is limited to the generation of Tollmien-Schlichting waves at the leading-edge of the plate.
NASA Astrophysics Data System (ADS)
Zheng, Chang-Jun; Chen, Hai-Bo; Chen, Lei-Lei
2013-04-01
This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/plane-symmetric acoustic wave problems. The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only. Moreover, a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived, and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating, translating and saving the multipole/local expansion coefficients of the image domain. The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems. As for exterior acoustic problems, the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method. Details on the implementation of the present method are described, and numerical examples are given to demonstrate its accuracy and efficiency.
Breaking integrability at the boundary: the sine-Gordon model with Robin boundary conditions
NASA Astrophysics Data System (ADS)
Arthur, Robert; Dorey, Patrick; Parini, Robert
2016-04-01
We explore boundary scattering in the sine-Gordon model with a non-integrable family of Robin boundary conditions. The soliton content of the field after collision is analysed using a numerical implementation of the direct scattering problem associated with the inverse scattering method. We find that an antikink may be reflected into various combinations of an antikink, a kink, and one or more breathers, depending on the values of the initial antikink velocity and a parameter associated with the boundary condition. In addition we observe regions with an intricate resonance structure arising from the creation of an intermediate breather whose recollision with the boundary is highly dependent on the breather phase.
Boundary condition effects on maximum groundwater withdrawal in coastal aquifers.
Lu, Chunhui; Chen, Yiming; Luo, Jian
2012-01-01
Prevention of sea water intrusion in coastal aquifers subject to groundwater withdrawal requires optimization of well pumping rates to maximize the water supply while avoiding sea water intrusion. Boundary conditions and the aquifer domain size have significant influences on simulating flow and concentration fields and estimating maximum pumping rates. In this study, an analytical solution is derived based on the potential-flow theory for evaluating maximum groundwater pumping rates in a domain with a constant hydraulic head landward boundary. An empirical correction factor, which was introduced by Pool and Carrera (2011) to account for mixing in the case with a constant recharge rate boundary condition, is found also applicable for the case with a constant hydraulic head boundary condition, and therefore greatly improves the usefulness of the sharp-interface analytical solution. Comparing with the solution for a constant recharge rate boundary, we find that a constant hydraulic head boundary often yields larger estimations of the maximum pumping rate and when the domain size is five times greater than the distance between the well and the coastline, the effect of setting different landward boundary conditions becomes insignificant with a relative difference between two solutions less than 2.5%. These findings can serve as a preliminary guidance for conducting numerical simulations and designing tank-scale laboratory experiments for studying groundwater withdrawal problems in coastal aquifers with minimized boundary condition effects. PMID:22050244
Electrodynamic boundary conditions for planar arrays of thin magnetic elements
Lisenkov, Ivan; Tyberkevych, Vasyl; Slavin, Andrei; Nikitov, Sergei
2015-08-24
Approximate electrodynamic boundary conditions are derived for an array of dipolarly coupled magnetic elements. It is assumed that the elements' thickness is small compared to the wavelength of an electromagnetic wave in a free space. The boundary conditions relate electric and magnetic fields existing at the top and bottom sides of the array through the averaged uniform dynamic magnetization of the array. This dynamic magnetization is determined by the collective dynamic eigen-excitations (spin wave modes) of the array and is found using the external magnetic susceptibility tensor. The problem of oblique scattering of a plane electromagnetic wave on the array is considered to illustrate the use of the derived boundary conditions.
Improved Boundary Conditions for Cell-centered Difference Schemes
NASA Technical Reports Server (NTRS)
VanderWijngaart, Rob F.; Klopfer, Goetz H.; Chancellor, Marisa K. (Technical Monitor)
1997-01-01
Cell-centered finite-volume (CCFV) schemes have certain attractive properties for the solution of the equations governing compressible fluid flow. Among others, they provide a natural vehicle for specifying flux conditions at the boundaries of the physical domain. Unfortunately, they lead to slow convergence for numerical programs utilizing them. In this report a method for investigating and improving the convergence of CCFV schemes is presented, which focuses on the effect of the numerical boundary conditions. The key to the method is the computation of the spectral radius of the iteration matrix of the entire demoralized system of equations, not just of the interior point scheme or the boundary conditions.
Large Eddy Simulation in a Channel with Exit Boundary Conditions
NASA Technical Reports Server (NTRS)
Cziesla, T.; Braun, H.; Biswas, G.; Mitra, N. K.
1996-01-01
The influence of the exit boundary conditions (vanishing first derivative of the velocity components and constant pressure) on the large eddy simulation of the fully developed turbulent channel flow has been investigated for equidistant and stretched grids at the channel exit. Results show that the chosen exit boundary conditions introduce some small disturbance which is mostly damped by the grid stretching. The difference between the fully developed turbulent channel flow obtained with LES with periodicity condition and the inlet and exit and the LES with fully developed flow at the inlet and the exit boundary condition is less than 10% for equidistant grids and less than 5% for the case grid stretching. The chosen boundary condition is of interest because it may be used in complex flows with backflow at exit.
Internal gravity-shear waves in the atmospheric boundary layer from acoustic remote sensing data
NASA Astrophysics Data System (ADS)
Lyulyukin, V. S.; Kallistratova, M. A.; Kouznetsov, R. D.; Kuznetsov, D. D.; Chunchuzov, I. P.; Chirokova, G. Yu.
2015-03-01
The year-round continuous remote sounding of the atmospheric boundary layer (ABL) by means of the Doppler acoustic radar (sodar) LATAN-3 has been performed at the Zvenigorod Scientific Station of the Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, since 2008. A visual analysis of sodar echograms for four years revealed a large number of wavelike patterns in the intensity field of a scattered sound signal. Similar patterns were occasionally identified before in sodar, radar, and lidar sounding data. These patterns in the form of quasi-periodic inclined stripes, or cat's eyes, arise under stable stratification and significant vertical wind shears and result from the loss of the dynamic stability of the flow. In the foreign literature, these patterns, which we call internal gravity-shear waves, are often associated with Kelvin-Helmholtz waves. In the present paper, sodar echograms are classified according to the presence or absence of wavelike patterns, and a statistical analysis of the frequency of their occurrence by the year and season was performed. A relationship between the occurrence of the patterns and wind shear and between the wave length and amplitude was investigated. The criteria for the identification of gravity-shear waves, meteorological conditions of their excitation, and issues related to their observations were discussed.
Acoustic Receptivity of a Blasius Boundary Layer with 2-D and Oblique Surface Waviness
NASA Technical Reports Server (NTRS)
King, Rudolph A.; Breuer, Kenneth S.
2000-01-01
An experimental investigation was conducted to examine acoustic receptivity and subsequent boundary-layer instability evolution for a Blasius boundary layer formed on a flat plate in the presence of two-dimensional (2-D) and oblique (3-D) surface waviness. The effect of the non-localized surface roughness geometry and acoustic wave amplitude on the receptivity process was explored. The surface roughness had a well defined wavenumber spectrum with fundamental wavenumber k (sub w). A planar downstream traveling acoustic wave was created to temporally excite the flow near the resonance frequency of an unstable eigenmode corresponding to k (sub ts) = k (sub w). The range of acoustic forcing levels, epsilon, and roughness heights, DELTA h, examined resulted in a linear dependence of receptivity coefficients; however, the larger values of the forcing combination epsilon dot DELTA h resulted in subsequent nonlinear development of the Tollmien-Schlichting (T-S) wave. This study provided the first experimental evidence of a marked increase in the receptivity coefficient with increasing obliqueness of the surface waviness in excellent agreement with theory. Detuning of the 2-D and oblique disturbances was investigated by varying the streamwise wall-roughness wavenumber a,, and measuring the T-S response. For the configuration where laminar-to-turbulent breakdown occurred, the breakdown process was found to be dominated by energy at the fundamental and harmonic frequencies, indicative of K-type breakdown.
NASA Astrophysics Data System (ADS)
Kwon, K.; Loh, B.-G.; Lee, D.-R.
2007-12-01
Acoustic streaming patterns, velocity fields, which is induced by a cylindrical ultrasonic exciter vibrating at 28.4kHz in an open physical boundaries, is analytically and experimentally investigated using Particle Imaging Velocimetry (PIV). Induced acoustic streaming patterns and velocity fields for the gaps of 18mm at which the irrotational tangential velocity becomes a maximum, resulting in a substantial increase in the acoustic streaming velocity and pronounced visualization of streaming patterns between the vibrator and quiescent glass plate are presented. The overall air flow patterns at the gaps of 24, 30, 36mm are similar to the gap of 18 mm but as the gap increases the frequency of occurrence and irregularity of vortices in the gap appear to increase. The symmetric definite steady circular flow with local vortices is observed. The maximum streaming velocity measured stands at 0.16 cm/s with a vibration amplitude of 50 micrometers. Theoretical analysis indicates that the pattern of air flow in the gap is determined by the top and bottom limiting velocities induced by acoustic streaming within the Stokes boundary layer and that the streaming pattern is symmetrical with respect to the center axis of the vibrator by reason of symmetry. The comparison between the experimental data and the theoretical estimation based on Nyborg and Jackson is performed.
Boundary-element shape sensitivity analysis for thermal problems with nonlinear boundary conditions
NASA Technical Reports Server (NTRS)
Kane, James H.; Wang, Hua
1991-01-01
Implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solid objects subjected to nonlinear boundary conditions is shown to generate an accurate and economical approach for the computation of shape sensitivities for this class of problems. This approach involves the employment of analytical derivatives of boundary-element kernel functions with respect to shape design variables. A formulation is presented that can consistently account for both temperature-dependent convection and radiation boundary conditions. Several iterative strategies are presented for the solution of the resulting sets of nonlinear equations and the computational performances examined in detail. Multizone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized nonlinear boundary conditions or regions of geometric insensitivity to design variables. A series of nonlinear example problems are presented that have closed-form solutions.
Two Baryons with Twisted Boundary Conditions
Briceno, Raul; Davoudi, Zohreh; Luu, Thomas; Savage, Martin
2014-04-01
The quantization condition for two particle systems with arbitrary number of two-body open coupled-channels, spin and masses in a finite cubic volume is presented. The condition presented is in agreement with all previous studies of two-body systems in a finite volume. The result is fully relativistic and holds for all momenta below inelastic thresholds and is exact up to exponential volume corrections that are governed by m{sub {pi}} L, where m{sub {pi}} is the pion mass and L is the spatial extent of my box. Its implication for the studies of coupled-channel baryon-baryon systems is discussed, and the necessary tools for implementing the formalism are review.
NASA Technical Reports Server (NTRS)
Hu, Fang Q.; Manthey, Joe L.
1997-01-01
Accurate numerical non-reflecting boundary conditions are important in all the proposed benchmark problems of the Second Workshop. Recently, a new absorbing boundary condition has been developed using Perfectly Matched Layer (PML) equations for the Euler equations. In this approach, a region with a width of a few grid points is introduced adjacent to the non-reflecting boundaries. In the added region, Perfectly Matched Layer equations are constructed and applied so that the out-going waves are absorbed inside the layer with little reflection to the interior domain. It will be demonstrated in the present paper that the proposed absorbing boundary condition is quite general and versatile, applicable to radiation boundaries as well as inflow and outflow boundaries. It is also easy to implement. The emphasis of the paper will be on the application of the PML absorbing boundary condition to problems in Categories 1, 2, and 3. In Category 1, solutions of problems 1 and 2 are presented. Both problems are solved using a multi-domain polar grid system. Perfectly Matched Layer equations for a circular boundary are constructed and their effectiveness assessed. In Category 2, solutions of problem 2 are presented. Here, in addition to the radiation boundary conditions at the far field in the axisymmetric coordinate system, the inflow boundary condition at the duct inlet is also dealt with using the proposed Perfectly Match Layer equations. At the inlet, a PML domain is introduced in which the incident duct mode is simulated while the waves reflected from the open end of the duct are absorbed at the same time. In Category 3, solutions of all three problems are presented. Again, the PML absorbing boundary condition is used at the inflow boundary so that the incoming vorticity wave is simulated while the outgoing acoustic waves are absorbed with very little numerical reflection. All the problems are solved using central difference schemes for spatial discretizations and the
Acoustical conditions of typical classrooms in Hong Kong
NASA Astrophysics Data System (ADS)
Li, Kai Ming; Lam, Coriolanus C. L.
2005-04-01
This paper presents measurement results of the acoustical environments of local schools in Hong Kong. In the measurements, several acoustical aspects that affect verbal communication in classrooms have been studied. These conditions include outdoor and indoor ambient noise levels, signal-to-noise ratios, reverberation time and the speech transmission index. Typical classrooms in many different schools and other higher-education institutions have been selected in the present study. Experimental results are compared with such national standards as USA (ANSI S 12.60 V 2002), Australian/New Zealand (AS/NZS 2107:2000), China (GB/T 15508 V 1995) and other national and industrial standards. This study will form the basis of devising acceptable standards for use in Hong Kong. [Work supported by the Research Grants Council of the SAR Government, the Research Committee of the Hong Kong Polytechnic University and Architectural Services Department of the Hong Kong SAR Government.
Propagation of acoustic shock waves between parallel rigid boundaries and into shadow zones
NASA Astrophysics Data System (ADS)
Desjouy, C.; Ollivier, S.; Marsden, O.; Dragna, D.; Blanc-Benon, P.
2015-10-01
The study of acoustic shock propagation in complex environments is of great interest for urban acoustics, but also for source localization, an underlying problematic in military applications. To give a better understanding of the phenomenon taking place during the propagation of acoustic shocks, laboratory-scale experiments and numerical simulations were performed to study the propagation of weak shock waves between parallel rigid boundaries, and into shadow zones created by corners. In particular, this work focuses on the study of the local interactions taking place between incident, reflected, and diffracted waves according to the geometry in both regular or irregular - also called Von Neumann - regimes of reflection. In this latter case, an irregular reflection can lead to the formation of a Mach stem that can modify the spatial distribution of the acoustic pressure. Short duration acoustic shock waves were produced by a 20 kilovolts electric spark source and a schlieren optical method was used to visualize the incident shockfront and the reflection/diffraction patterns. Experimental results are compared to numerical simulations based on the high-order finite difference solution of the two dimensional Navier-Stokes equations.
Propagation of acoustic shock waves between parallel rigid boundaries and into shadow zones
Desjouy, C. Ollivier, S.; Dragna, D.; Blanc-Benon, P.; Marsden, O.
2015-10-28
The study of acoustic shock propagation in complex environments is of great interest for urban acoustics, but also for source localization, an underlying problematic in military applications. To give a better understanding of the phenomenon taking place during the propagation of acoustic shocks, laboratory-scale experiments and numerical simulations were performed to study the propagation of weak shock waves between parallel rigid boundaries, and into shadow zones created by corners. In particular, this work focuses on the study of the local interactions taking place between incident, reflected, and diffracted waves according to the geometry in both regular or irregular – also called Von Neumann – regimes of reflection. In this latter case, an irregular reflection can lead to the formation of a Mach stem that can modify the spatial distribution of the acoustic pressure. Short duration acoustic shock waves were produced by a 20 kilovolts electric spark source and a schlieren optical method was used to visualize the incident shockfront and the reflection/diffraction patterns. Experimental results are compared to numerical simulations based on the high-order finite difference solution of the two dimensional Navier-Stokes equations.
Effect of boundary conditions on thermal plume growth
NASA Astrophysics Data System (ADS)
Kondrashov, A.; Sboev, I.; Rybkin, K.
2016-07-01
We have investigated the influence of boundary conditions on the growth rate of convective plumes. Temperature and rate fields were studied in a rectangular convective cell heated by a spot heater. The results of the full-scale test were compared with the numerical data calculated using the ANSYS CFX software package. The relationship between the heat plume growth rate and heat boundary conditions, the width and height of the cell, size of heater for different kinds of liquid was established.
Absorbing Boundary Conditions For Optical Pulses In Dispersive, Nonlinear Materials
NASA Technical Reports Server (NTRS)
Goorjian, Peter M.; Kwak, Dochan (Technical Monitor)
1995-01-01
This paper will present results in computational nonlinear optics. An algorithm will be described that provides absorbing boundary conditions for optical pulses in dispersive, nonlinear materials. A new numerical absorber at the boundaries has been developed that is responsive to the spectral content of the pulse. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of "light bullet" like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. Comparisons will be shown of calculations that use the standard boundary conditions and the new ones.
The Fokker-Planck Equation with Absorbing Boundary Conditions
NASA Astrophysics Data System (ADS)
Hwang, Hyung Ju; Jang, Juhi; Velázquez, Juan J. L.
2014-10-01
We study the initial-boundary value problem for the Fokker-Planck equation in an interval with absorbing boundary conditions. We develop a theory of well-posedness of classical solutions for the problem. We also prove that the resulting solutions decay exponentially for long times. To prove these results we obtain several crucial estimates, which include hypoellipticity away from the singular set for the Fokker-Planck equation with absorbing boundary conditions, as well as the Hölder continuity of the solutions up to the singular set.
A novel periodic boundary condition for computational hemodynamics studies.
Bahramian, Fereshteh; Mohammadi, Hadi
2014-07-01
In computational fluid dynamics models for hemodynamics applications, boundary conditions remain one of the major issues in obtaining accurate fluid flow predictions. For major cardiovascular models, the realistic boundary conditions are not available. In order to address this issue, the whole computational domain needs to be modeled, which is practically impossible. For simulating fully developed turbulent flows using the large eddy simulation and dynamic numerical solution methods, which are very popular in hemodynamics studies, periodic boundary conditions are suitable. This is mainly because the computational domain can be reduced considerably. In this study, a novel periodic boundary condition is proposed, which is based on mass flow condition. The proposed boundary condition is applied on a square duct for the sake of validation. The mass-based condition was shown to obtain the solution in 15% less time. As such, the mass-based condition has two decisive advantages: first, the solution for a given Reynolds number can be obtained in a single simulation because of the direct specification of the mass flow, and second, simulations can be made more quickly. PMID:25015666
Scattering through a straight quantum waveguide with combined boundary conditions
Briet, Ph. Soccorsi, E.; Dittrich, J.
2014-11-15
Scattering through a straight two-dimensional quantum waveguide R×(0,d) with Dirichlet boundary conditions on (R{sub −}{sup *}×(y=0))∪(R{sub +}{sup *}×(y=d)) and Neumann boundary condition on (R{sub −}{sup *}×(y=d))∪(R{sub +}{sup *}×(y=0)) is considered using stationary scattering theory. The existence of a matching conditions solution at x = 0 is proved. The use of stationary scattering theory is justified showing its relation to the wave packets motion. As an illustration, the matching conditions are also solved numerically and the transition probabilities are shown.
Formation of an interphase boundary under highly nonequilibrium conditions
Belyaev, A. P.; Rubets, V. P.; Antipov, V. V.
2007-12-15
The results of comparison studies of the CdTe-CdS interphase boundary in Au/CdTe/CdS sandwich structures synthesized on a substrate of artificial fluorophlogopite mica in highly nonequilibrium conditions (with a substrate temperature T{sub s} = 125 K) and in quasi-equilibrium conditions (T{sub s} > 720 K) are reported. The X-ray diffraction patterns and a capacitance-voltage characteristic are also reported. It is shown that highly nonequilibrium conditions allow synthesis of structures with excellent crystalline quality and with an interphase boundary that is no worse than in the structures grown under equilibrium conditions.
Belyaev, Mikhail A.; Stone, James M.; Rafikov, Roman R.
2012-11-20
Disk accretion onto a weakly magnetized central object, e.g., a star, is inevitably accompanied by the formation of a boundary layer near the surface, in which matter slows down from the highly supersonic orbital velocity of the disk to the rotational velocity of the star. We perform high-resolution two-dimensional hydrodynamical simulations in the equatorial plane of an astrophysical boundary layer with the goal of exploring the dynamics of non-axisymmetric structures that form there. We generically find that the supersonic shear in the boundary layer excites non-axisymmetric quasi-stationary acoustic modes that are trapped between the surface of the star and a Lindblad resonance in the disk. These modes rotate in a prograde fashion, are stable for hundreds of orbital periods, and have a pattern speed that is less than and of the order of the rotational velocity at the inner edge of the disk. The origin of these intrinsically global modes is intimately related to the operation of a corotation amplifier in the system. Dissipation of acoustic modes in weak shocks provides a universal mechanism for angular momentum and mass transport even in purely hydrodynamic (i.e., non-magnetized) boundary layers. We discuss the possible implications of these trapped modes for explaining the variability seen in accreting compact objects.
Optimizing acoustical conditions for speech intelligibility in classrooms
NASA Astrophysics Data System (ADS)
Yang, Wonyoung
High speech intelligibility is imperative in classrooms where verbal communication is critical. However, the optimal acoustical conditions to achieve a high degree of speech intelligibility have previously been investigated with inconsistent results, and practical room-acoustical solutions to optimize the acoustical conditions for speech intelligibility have not been developed. This experimental study validated auralization for speech-intelligibility testing, investigated the optimal reverberation for speech intelligibility for both normal and hearing-impaired listeners using more realistic room-acoustical models, and proposed an optimal sound-control design for speech intelligibility based on the findings. The auralization technique was used to perform subjective speech-intelligibility tests. The validation study, comparing auralization results with those of real classroom speech-intelligibility tests, found that if the room to be auralized is not very absorptive or noisy, speech-intelligibility tests using auralization are valid. The speech-intelligibility tests were done in two different auralized sound fields---approximately diffuse and non-diffuse---using the Modified Rhyme Test and both normal and hearing-impaired listeners. A hybrid room-acoustical prediction program was used throughout the work, and it and a 1/8 scale-model classroom were used to evaluate the effects of ceiling barriers and reflectors. For both subject groups, in approximately diffuse sound fields, when the speech source was closer to the listener than the noise source, the optimal reverberation time was zero. When the noise source was closer to the listener than the speech source, the optimal reverberation time was 0.4 s (with another peak at 0.0 s) with relative output power levels of the speech and noise sources SNS = 5 dB, and 0.8 s with SNS = 0 dB. In non-diffuse sound fields, when the noise source was between the speaker and the listener, the optimal reverberation time was 0.6 s with
Nonlinear activity of acoustically driven gas bubble near a rigid boundary
Maksimov, Alexey
2015-10-28
The presence of a boundary can produce considerable changes in the oscillation amplitude of the bubble and its scattered echo. The present study fills a gap in the literature, in that it is concerned theoretically with the bubble activity at relatively small distances from the rigid boundary. It was shown that the bi-spherical coordinates provide separation of variables and are more suitable for analysis of the dynamics of these constrained bubbles. Explicit formulas have been derived which describe the dependence of the bubble emission near a rigid wall on its size and the separation distance between the bubble and the boundary. As applications, time reversal technique for gas leakage detection and radiation forces that are induced by an acoustic wave on a constrained bubble were analyzed.
Classification of heart valve condition using acoustic measurements
Clark, G.
1994-11-15
Prosthetic heart valves and the many great strides in valve design have been responsible for extending the life spans of many people with serious heart conditions. Even though the prosthetic valves are extremely reliable, they are eventually susceptible to long-term fatigue and structural failure effects expected from mechanical devices operating over long periods of time. The purpose of our work is to classify the condition of in vivo Bjork-Shiley Convexo-Concave (BSCC) heart valves by processing acoustic measurements of heart valve sounds. The structural failures of interest for Bscc valves is called single leg separation (SLS). SLS can occur if the outlet strut cracks and separates from the main structure of the valve. We measure acoustic opening and closing sounds (waveforms) using high sensitivity contact microphones on the patient`s thorax. For our analysis, we focus our processing and classification efforts on the opening sounds because they yield direct information about outlet strut condition with minimal distortion caused by energy radiated from the valve disc.
A hybrid absorbing boundary condition for frequency-domain finite-difference modelling
NASA Astrophysics Data System (ADS)
Ren, Zhiming; Liu, Yang
2013-10-01
Liu and Sen (2010 Geophysics 75 A1-6 2012 Geophys. Prospect. 60 1114-32) proposed an efficient hybrid scheme to significantly absorb boundary reflections for acoustic and elastic wave modelling in the time domain. In this paper, we extend the hybrid absorbing boundary condition (ABC) into the frequency domain and develop specific strategies for regular-grid and staggered-grid modelling, respectively. Numerical modelling tests of acoustic, visco-acoustic, elastic and vertically transversely isotropic (VTI) equations show significant absorptions for frequency-domain modelling. The modelling results of the Marmousi model and the salt model also demonstrate the effectiveness of the hybrid ABC. For elastic modelling, the hybrid Higdon ABC and the hybrid Clayton and Engquist (CE) ABC are implemented, respectively. Numerical simulations show that the hybrid Higdon ABC gets better absorption than the hybrid CE ABC, especially for S-waves. We further compare the hybrid ABC with the classical perfectly matched layer (PML). Results show that the two ABCs cost the same computation time and memory space for the same absorption width. However, the hybrid ABC is more effective than the PML for the same small absorption width and the absorption effects of the two ABCs gradually become similar when the absorption width is increased.
Asymptotic boundary conditions for dissipative waves: General theory
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas
1990-01-01
An outstanding issue in the computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.
Asymptotic boundary conditions for dissipative waves - General theory
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas
1991-01-01
An outstanding issue in computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.
Pressure boundary conditions for incompressible flow using unstructured meshes
Mathur, S.R.; Murthy, J.Y.
1997-10-01
A large variety of industrial problems require the specification of pressure boundary conditions. In many industrial pipe flows, for example, the mass flow rate is not known a priori; the flow is driven by a specified pressure difference between inlet and outlet. This article presents a numerical method for computing incompressible flows with given pressure boundary conditions. Unstructured meshes composed of arbitrary polyhedra are considered in a cell-centered, co-located pressure-velocity formulation. The SIMPLE algorithm of Patankar and Spalding is extended to develop correction equations for boundary static pressure and boundary mass flux through an added-dissipation scheme. The procedure is validated against published benchmarks and shown to perform satisfactorily.
Derivation and application of a class of generalized boundary conditions
NASA Technical Reports Server (NTRS)
Senior, Thomas B. A.; Volakis, John L.
1989-01-01
Boundary conditions involving higher order derivatives are presented for simulating surfaces whose reflection coefficients are known analytically, numerically, or experimentally. Procedures for determining the coefficients of the derivatives are discussed, along with the effect of displacing the surface where the boundary conditions are applied. Provided the coefficients satisfy a duality relation, equivalent forms of the boundary conditions involving tangential field components are deduced, and these provide the natural extension to nonplanar surfaces. As an illustration, the simulation of metal-backed uniform and three-layer dielectric coatings is given. It is shown that fourth order conditions are capable of providing an accurate simulation for uniform coating at least a quarter of a wavelength in thickness.
DNS of Turbulent Boundary Layers under Highenthalpy Conditions
NASA Astrophysics Data System (ADS)
Duan, Lian; Martín, Pino
2010-11-01
To study real-gas effects and turbulence-chemistry interaction, direct numerical simulations (DNS) of hypersonic boundary layers are conducted under typical hypersonic conditions. We consider the boundary layer on a lifting-body consisting of a flat plate at an angle of attack, which flies at altitude 30km with a Mach number 21. Two different inclined angles, 35^o and 8^o, are considered,representing blunt and slender bodies. Both noncatalytic and supercatalytic wall conditions are considered. The DNS data are studied to assess the validity of Morkovin's hypothesis, the strong Reynolds analogy, as well as the behaviors of turbulence structures under high-enthalpy conditions.Relative to low-enthalpy conditions [1], significant differences in typical scalings are observed. [4pt] [1] L. Duan and I. Beekman and M. P. Mart'in, Direct numerical simulation of hypersonic turbulent boundary layers. Part 2: Effect of temperature, J. Fluid Mech. 655 (2010), 419-445.
Boundary conditions for free interfaces with the lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Bogner, Simon; Ammer, Regina; Rüde, Ulrich
2015-09-01
In this paper we analyze the boundary treatment of the lattice Boltzmann method (LBM) for simulating 3D flows with free surfaces. The widely used free surface boundary condition of Körner et al. [27] is shown to be first order accurate. The article presents a new free surface boundary scheme that is suitable for second order accurate simulations based on the LBM. The new method takes into account the free surface position and its orientation with respect to the computational lattice. Numerical experiments confirm the theoretical findings and illustrate the different behavior of the original method and the new method.
Response of a hypersonic boundary layer to freestream pulse acoustic disturbance.
Wang, Zhenqing; Tang, Xiaojun; Lv, Hongqing
2014-01-01
The response of hypersonic boundary layer over a blunt wedge to freestream pulse acoustic disturbance was investigated. The stability characteristics of boundary layer for freestream pulse wave and continuous wave were analyzed comparatively. Results show that freestream pulse disturbance changes the thermal conductivity characteristics of boundary layer. For pulse wave, the number of main disturbance clusters decreases and the frequency band narrows along streamwise. There are competition and disturbance energy transfer among different modes in boundary layer. The dominant mode of boundary layer has an inhibitory action on other modes. Under continuous wave, the disturbance modes are mainly distributed near fundamental and harmonic frequencies, while under pulse wave, the disturbance modes are widely distributed in different modes. For both pulse and continuous waves, most of disturbance modes slide into a lower-growth or decay state in downstream, which is tending towards stability. The amplitude of disturbance modes in boundary layer under continuous wave is considerably larger than pulse wave. The growth rate for the former is also considerably larger than the later the disturbance modes with higher growth are mainly distributed near fundamental and harmonic frequencies for the former, while the disturbance modes are widely distributed in different frequencies for the latter. PMID:24737993
Response of a Hypersonic Boundary Layer to Freestream Pulse Acoustic Disturbance
Wang, Zhenqing; Tang, Xiaojun; Lv, Hongqing
2014-01-01
The response of hypersonic boundary layer over a blunt wedge to freestream pulse acoustic disturbance was investigated. The stability characteristics of boundary layer for freestream pulse wave and continuous wave were analyzed comparatively. Results show that freestream pulse disturbance changes the thermal conductivity characteristics of boundary layer. For pulse wave, the number of main disturbance clusters decreases and the frequency band narrows along streamwise. There are competition and disturbance energy transfer among different modes in boundary layer. The dominant mode of boundary layer has an inhibitory action on other modes. Under continuous wave, the disturbance modes are mainly distributed near fundamental and harmonic frequencies, while under pulse wave, the disturbance modes are widely distributed in different modes. For both pulse and continuous waves, most of disturbance modes slide into a lower-growth or decay state in downstream, which is tending towards stability. The amplitude of disturbance modes in boundary layer under continuous wave is considerably larger than pulse wave. The growth rate for the former is also considerably larger than the later the disturbance modes with higher growth are mainly distributed near fundamental and harmonic frequencies for the former, while the disturbance modes are widely distributed in different frequencies for the latter. PMID:24737993
Ambarzumyan's theorem for the quasi-periodic boundary conditions
NASA Astrophysics Data System (ADS)
Kıraç, Alp Arslan
2015-10-01
We obtain the classical Ambarzumyan's theorem for the Sturm-Liouville operators Lt(q) with qin L1[0,1] and quasi-periodic boundary conditions, tin [0,2π ) , when there is not any additional condition on the potential q.
NASA Astrophysics Data System (ADS)
Wagenhoffer, Nathan; Moored, Keith; Jaworski, Justin
2015-11-01
Animals have evolved flexible wings and fins to efficiently and quietly propel themselves through the air and water. The design of quiet and efficient bio-inspired propulsive concepts requires a rapid, unified computational framework that integrates three essential features: the fluid mechanics, the elastic structural response, and the noise generation. This study focuses on the development, validation, and demonstration of a transient, two-dimensional acoustic boundary element solver accelerated by a fast multipole algorithm. The resulting acoustic solver is used to characterize the acoustic signature produced by a vortex street advecting over a NACA 0012 airfoil, which is representative of vortex-body interactions that occur in schools of swimming fish. Both 2S and 2P canonical vortex streets generated by fish are investigated over the range of Strouhal number 0 . 2 < St < 0 . 4 , and the acoustic signature of the airfoil is quantified. This study provides the first estimate of the noise signature of a school of swimming fish. Lehigh University CORE Grant.
Magnetization boundary conditions at a ferromagnetic interface of finite thickness.
Kruglyak, V V; Gorobets, O Yu; Gorobets, Yu I; Kuchko, A N
2014-10-01
We develop a systematic approach to derive boundary conditions at an interface between two ferromagnetic materials in the continuous medium approximation. The approach treats the interface as a two-sublattice material, although the final equations connect magnetizations outside of the interface and therefore do not explicitly depend on its structure. Instead, the boundary conditions are defined in terms of some average properties of the interface, which may also have a finite thickness. In addition to the interface anisotropy and symmetric exchange coupling, this approach allows us to take into account coupling resulting from inversion symmetry breaking in the vicinity of the interface, such as the Dzyaloshinskii-Moriya antisymmetric exchange interaction. In the case of negligible interface anisotropy and Dzyaloshinskii-Moriya exchange parameters, the derived boundary conditions represent a generalization of those proposed earlier by Barnaś and Mills and are therefore named 'generalized Barnaś-Mills boundary conditions'. We demonstrate how one could use the boundary conditions to extract parameters of the interface via fitting of appropriate experimental data. The developed theory could be applied to modeling of both linear and non-linear spin waves, including exchange, dipole-exchange, magnetostatic, and retarded modes, as well as to calculations of non-uniform equilibrium micromagnetic configurations near the interface, with a direct impact on the research in magnonics and micromagnetism. PMID:25219663
Kac boundary conditions of the logarithmic minimal models
NASA Astrophysics Data System (ADS)
Pearce, Paul A.; Tartaglia, Elena; Couvreur, Romain
2015-01-01
We develop further the implementation and analysis of Kac boundary conditions in the general logarithmic minimal models { {LM}}(p,p\\prime) with 1 ⩽ p < p‧ and p, p‧ coprime. Specifically, working in a strip geometry, we consider the (r, s) Kac boundary conditions. These boundary conditions are organized into infinitely extended Kac tables labeled by the Kac labels r, s = 1, 2, 3, …. They are conjugate to Virasoro Kac representations with conformal dimensions Δr, s given by the usual Kac formula. On a finite strip of width N, built from a square lattice, the associated integrable boundary conditions are constructed by acting on the vacuum (1, 1) boundary with an s-type seam of width s - 1 columns and an r-type seam of width ρ - 1 columns. The r-type seam contains an arbitrary boundary field ξ. While the usual fusion construction of the r-type seam relies on the existence of Wenzl-Jones projectors restricting its application to r ⩽ ρ < p‧, this limitation was recently removed by Pearce et al who further conjectured that the conformal boundary conditions labeled by r are realized, in particular, for ρ=ρ(r)=\\lfloor \\frac{rp\\prime}{p}\\rfloor . In this paper, we confirm this conjecture by performing extensive numerics on the commuting double row transfer matrices and their associated quantum Hamiltonian chains. Letting [x] denote the fractional part, we fix the boundary field to the specialized values ξ=\\fracπ{2} if [\\fracρ{p\\prime}]=0 and ξ=[\\fracρ p}{p\\prime}]\\frac{π{2} otherwise. For these boundary conditions, we obtain the Kac conformal weights Δr, s by numerically extrapolating the finite-size corrections to the lowest eigenvalue of the quantum Hamiltonians out to sizes N ⩽ 32 - ρ - s. Additionally, by solving local inversion relations, we obtain general analytic expressions for the boundary free energies allowing for more accurate estimates of the conformal data. This paper is dedicated to Jean-Bernard Zuber on the occassion
Modeling sea-water intrusion with open boundary conditions
Padilla, F.; Cruz-Sanjulian, J.
1997-07-01
The present study concerns the application of a new numerical approach to describe the fresh-water/sea-water relationships in coastal aquifers. Essentially, a solution to the partial differential equation governing the regional motion of a phreatic surface and the resulting interface between fresh water and salt water is analyzed by a Galerkin finite-element formulation. A single-phase steady numerical model was applied to approximate, with simple triangular elements, the regional behavior of a coastal aquifer under appropriate sinks, sources, Neumann, outflow face, and open boundary conditions. On the one hand, outflow open boundaries at the coastline were not treated with other classical boundary conditions, but instead with a formal numerical approach for open boundaries inspired in this particular case by the Dupuit approximation of horizontal outflow at the boundary. The solution to this numerical model, together with the Ghyben-Herzberg principle, allows the correct simulation of fresh-water heads and the position of the salt-water interface for a steeply sloping coast. Although the solutions were precise and do not present classical numerical oscillations, this approach requires a previous solution with Dirichlet boundary conditions at the coastline in order to find a good convergence of the solution algorithm. On the other hand, the same precise results were obtained with a more restrictive open boundary condition, similar in a way to the outflow face approach, which required less computer time, did not need a prior numerical solution and could be extended to different coastline conditions. The steady-state problem was solved for different hypothetical coastal aquifers and fresh-water usage through three types of numerical tests.
Experiments on hypersonic boundary layer transition on blunt cones with acoustic-absorption coating
NASA Astrophysics Data System (ADS)
Shiplyuk, A.; Lukashevich, S.; Bountin, D.; Maslov, A.; Knaus, H.
2012-01-01
The laminar-turbulent transition is studied experimentally on a cone with an acoustic-absorption coating and with different nose bluntness in a high-speed flow. The acoustic-absorption coating is a felt metal sheet with a random microstructure. Experiments were carried out on a 1-meter length 7 degree cone at free-stream Mach number M = 8 and zero angle of attack. Locations of the laminar-turbulent transition are detected using heat flux distributions registered by calorimeter sensors. In addition, boundary layer pulsations are measured by means of ultrafast heat flux sensors. It is shown that the laminar-turbulent transition is caused by the second-mode instability, and the laminar run extends as the bluntness is increased. The porous coating effectively suppresses this instability for all tested bluntness values and 1.3-1.85 times extends the laminar run.
Lenhart, S. |; Protopopescu, V.; Yong, J.
1997-12-31
The authors apply optimal control techniques to find approximate solutions to an inverse problem for the acoustic wave equation. The inverse problem (assumed here to have a solution) is to determine the boundary reflection coefficient from partial measurements of the acoustic signal. The sought reflection coefficient is treated as a control and the goal--quantified by an approximate functional--is to drive the model solution close to the experimental data by adjusting this coefficient. The problem is solved by finding the optimal control that minimizes the approximate functional. Then by driving the cost of the control to zero one proves that the corresponding sequence of optimal controls represents a converging sequence of estimates for the solution of the inverse problem. Compared to classical regularization methods (e.g., Tikhonov coupled with optimization schemes), their approach yields: (1) a systematic procedure to solve inverse problems of identification type and (ii) an explicit expression for the approximations of the solution.
Critical effects of downstream boundary conditions on vortex breakdown
NASA Technical Reports Server (NTRS)
Kandil, Osama; Kandil, Hamdy A.; Liu, C. H.
1992-01-01
The unsteady, compressible, full Navier-Stokes (NS) equations are used to study the critical effects of the downstream boundary conditions on the supersonic vortex breakdown. The present study is applied to two supersonic vortex breakdown cases. In the first case, quasi-axisymmetric supersonic swirling flow is considered in a configured circular duct, and in the second case, quasi-axisymmetric supersonic swirling jet, that is issued from a nozzle into a supersonic jet of lower Mach number, is considered. For the configured duct flow, four different types of downstream boundary conditions are used, and for the swirling jet flow from the nozzle, two types of downstream boundary conditions are used. The solutions are time accurate which are obtained using an implicit, upwind, flux-difference splitting, finite-volume scheme.
Boundary conditions and the simulation of low Mach number flows
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas; Lorenz, Jens
1993-01-01
The problem of accurately computing low Mach number flows, with the specific intent of studying the interaction of sound waves with incompressible flow structures, such as concentrations of vorticity is considered. This is a multiple time (and/or space) scales problem, leading to various difficulties in the design of numerical methods. Concentration is on one of these difficulties - the development of boundary conditions at artificial boundaries which allow sound waves and vortices to radiate to the far field. Nonlinear model equations are derived based on assumptions about the scaling of the variables. Then these are linearized about a uniform flow and exact boundary conditions are systematically derived using transform methods. Finally, useful approximations to the exact conditions which are valid for small Mach number and small viscosity are computed.
Quarks with Twisted Boundary Conditions in the Epsilon Regime
Thomas Mehen; Brian C. Tiburzi
2005-05-01
We study the effects of twisted boundary conditions on the quark fields in the epsilon regime of chiral perturbation theory. We consider the SU(2){sub L} x SU(2){sub R} chiral theory with non-degenerate quarks and the SU(3){sub L} x SU(3){sub R} chiral theory with massless up and down quarks and massive strange quarks. The partition function and condensate are derived for each theory. Because flavor-neutral Goldstone bosons are unaffected by twisted boundary conditions chiral symmetry is still restored in finite volumes. The dependence of the condensate on the twisting parameters can be used to extract the pion decay constant from simulations in the epsilon regime. The relative contribution to the partition function from sectors of different topological charge is numerically insensitive to twisted boundary conditions.
Boundary conditions on internal three-body wave functions
Mitchell, Kevin A.; Littlejohn, Robert G.
1999-10-01
For a three-body system, a quantum wave function {Psi}{sub m}{sup {ell}} with definite {ell} and m quantum numbers may be expressed in terms of an internal wave function {chi}{sub k}{sup {ell}} which is a function of three internal coordinates. This article provides necessary and sufficient constraints on {chi}{sub k}{sup {ell}} to ensure that the external wave function {Psi}{sub k}{sup {ell}} is analytic. These constraints effectively amount to boundary conditions on {chi}{sub k}{sup {ell}} and its derivatives at the boundary of the internal space. Such conditions find similarities in the (planar) two-body problem where the wave function (to lowest order) has the form r{sup |m|} at the origin. We expect the boundary conditions to prove useful for constructing singularity free three-body basis sets for the case of nonvanishing angular momentum.
Viscosity in molecular dynamics with periodic boundary conditions
NASA Astrophysics Data System (ADS)
Viscardy, S.; Gaspard, P.
2003-10-01
We report a study of viscosity by the method of Helfand moment in systems with periodic boundary conditions. We propose a new definition of Helfand moment which takes into account the minimum image convention used in molecular dynamics with periodic boundary conditions. Our Helfand-moment method is equivalent to the method based on the Green-Kubo formula and is not affected by ambiguities due to the periodic boundary conditions. Moreover, in hard-ball systems, our method is equivalent to that developed by Alder, Gass, and Wainwright [J. Chem. Phys. 53, 3813 (1970)]. We apply and verify our method in a fluid composed of N⩾2 hard disks in elastic collisions. We show that the viscosity coefficients already take values in good agreement with Enskog’s theory for N=2 hard disks in a hexagonal geometry.
Viscosity in molecular dynamics with periodic boundary conditions.
Viscardy, S; Gaspard, P
2003-10-01
We report a study of viscosity by the method of Helfand moment in systems with periodic boundary conditions. We propose a new definition of Helfand moment which takes into account the minimum image convention used in molecular dynamics with periodic boundary conditions. Our Helfand-moment method is equivalent to the method based on the Green-Kubo formula and is not affected by ambiguities due to the periodic boundary conditions. Moreover, in hard-ball systems, our method is equivalent to that developed by Alder, Gass, and Wainwright [J. Chem. Phys. 53, 3813 (1970)]. We apply and verify our method in a fluid composed of N> or =2 hard disks in elastic collisions. We show that the viscosity coefficients already take values in good agreement with Enskog's theory for N=2 hard disks in a hexagonal geometry. PMID:14682933
A multigrid fluid pressure solver handling separating solid boundary conditions.
Chentanez, Nuttapong; Müller-Fischer, Matthias
2012-08-01
We present a multigrid method for solving the linear complementarity problem (LCP) resulting from discretizing the Poisson equation subject to separating solid boundary conditions in an Eulerian liquid simulation’s pressure projection step. The method requires only a few small changes to a multigrid solver for linear systems. Our generalized solver is fast enough to handle 3D liquid simulations with separating boundary conditions in practical domain sizes. Previous methods could only handle relatively small 2D domains in reasonable time, because they used expensive quadratic programming (QP) solvers. We demonstrate our technique in several practical scenarios, including nonaxis-aligned containers and moving solids in which the omission of separating boundary conditions results in disturbing artifacts of liquid sticking to solids. Our measurements show, that the convergence rate of our LCP solver is close to that of a standard multigrid solver. PMID:22411885
Analysis of the boundary conditions of the spline filter
NASA Astrophysics Data System (ADS)
Tong, Mingsi; Zhang, Hao; Ott, Daniel; Zhao, Xuezeng; Song, John
2015-09-01
The spline filter is a standard linear profile filter recommended by ISO/TS 16610-22 (2006). The main advantage of the spline filter is that no end-effects occur as a result of the filter. The ISO standard also provides the tension parameter β =0.625 24 to make the transmission characteristic of the spline filter approximately similar to the Gaussian filter. However, when the tension parameter β is not zero, end-effects appear. To resolve this problem, we analyze 14 different combinations of boundary conditions of the spline filter and propose a set of new boundary conditions in this paper. The new boundary conditions can provide satisfactory end portions of the output form without end-effects for the spline filter while still maintaining the value of β =0.625 24 .
Magnetization boundary conditions at a ferromagnetic interface of finite thickness
NASA Astrophysics Data System (ADS)
Kruglyak, V. V.; Gorobets, O. Yu; Gorobets, Yu I.; Kuchko, A. N.
2014-10-01
We develop a systematic approach to derive boundary conditions at an interface between two ferromagnetic materials in the continuous medium approximation. The approach treats the interface as a two-sublattice material, although the final equations connect magnetizations outside of the interface and therefore do not explicitly depend on its structure. Instead, the boundary conditions are defined in terms of some average properties of the interface, which may also have a finite thickness. In addition to the interface anisotropy and symmetric exchange coupling, this approach allows us to take into account coupling resulting from inversion symmetry breaking in the vicinity of the interface, such as the Dzyaloshinskii-Moriya antisymmetric exchange interaction. In the case of negligible interface anisotropy and Dzyaloshinskii-Moriya exchange parameters, the derived boundary conditions represent a generalization of those proposed earlier by Barnaś and Mills and are therefore named ‘generalized Barnaś-Mills boundary conditions’. We demonstrate how one could use the boundary conditions to extract parameters of the interface via fitting of appropriate experimental data. The developed theory could be applied to modeling of both linear and non-linear spin waves, including exchange, dipole-exchange, magnetostatic, and retarded modes, as well as to calculations of non-uniform equilibrium micromagnetic configurations near the interface, with a direct impact on the research in magnonics and micromagnetism.
Transport synthetic acceleration with opposing reflecting boundary conditions
Zika, M.R.; Adams, M.L.
2000-02-01
The transport synthetic acceleration (TSA) scheme is extended to problems with opposing reflecting boundary conditions. This synthetic method employs a simplified transport operator as its low-order approximation. A procedure is developed that allows the use of the conjugate gradient (CG) method to solve the resulting low-order system of equations. Several well-known transport iteration algorithms are cast in a linear algebraic form to show their equivalence to standard iterative techniques. Source iteration in the presence of opposing reflecting boundary conditions is shown to be equivalent to a (poorly) preconditioned stationary Richardson iteration, with the preconditioner defined by the method of iterating on the incident fluxes on the reflecting boundaries. The TSA method (and any synthetic method) amounts to a further preconditioning of the Richardson iteration. The presence of opposing reflecting boundary conditions requires special consideration when developing a procedure to realize the CG method for the proposed system of equations. The CG iteration may be applied only to symmetric positive definite matrices; this condition requires the algebraic elimination of the boundary angular corrections from the low-order equations. As a consequence of this elimination, evaluating the action of the resulting matrix on an arbitrary vector involves two transport sweeps and a transmission iteration. Results of applying the acceleration scheme to a simple test problem are presented.
Orbiter Boundary Layer Transition Stability Modeling at Flight Entry Conditions
NASA Technical Reports Server (NTRS)
Bartkowicz, Matt; Johnson, Heath; Candler, Graham; Campbell, Charles H.
2009-01-01
State of the art boundary layer stability modeling capabilities are increasingly seeing application to entry flight vehicles. With the advent of user friendly and robust implementations of two-dimensional chemical nonequilibrium stability modeling with the STABL/PSE-CHEM software, the need for flight data to calibrate such analyses capabilities becomes more critical. Recent efforts to perform entry flight testing with the Orbiter geometry related to entry aerothermodynamics and boundary layer transition is allowing for a heightened focus on the Orbiter configuration. A significant advancement in the state of the art can likely be achieved by establishing a basis of understanding for the occurrence of boundary layer transition on the Orbiter due to discrete protruding gap fillers and the nominal distributed roughness of the actual thermal protection system. Recent success in demonstrating centerline two-dimensional stability modeling on the centerline of the Orbiter at flight entry conditions provides a starting point for additional investigations. The more detailed paper will include smooth Orbiter configuration boundary layer stability results for several typical orbiter entry conditions. In addition, the numerical modeling approach for establishing the mean laminar flow will be reviewed and the method for determining boundary layer disturbance growth will be overviewed. In addition, if actual Orbiter TPS surface data obtained via digital surface scans become available, it may be possible to investigate the effects of an as-flown flight configuration on boundary layer transition compared to a smooth CAD reference.
Maxwell boundary condition and velocity dependent accommodation coefficient
Struchtrup, Henning
2013-11-15
A modification of Maxwell's boundary condition for the Boltzmann equation is developed that allows to incorporate velocity dependent accommodation coefficients into the microscopic description. As a first example, it is suggested to consider the wall-particle interaction as a thermally activated process with three parameters. A simplified averaging procedure leads to jump and slip boundary conditions for hydrodynamics. Coefficients for velocity slip, temperature jump, and thermal transpiration flow are identified and compared with those resulting from the original Maxwell model and the Cercignani-Lampis model. An extension of the model leads to temperature dependent slip and jump coefficients.
Quantum communication through a spin ring with twisted boundary conditions
NASA Astrophysics Data System (ADS)
Bose, S.; Jin, B.-Q.; Korepin, V. E.
2005-08-01
We investigate quantum communication between the sites of a spin ring with twisted boundary conditions. Such boundary conditions can be achieved by a magnetic flux through the ring. We find that a nonzero twist can improve communication through finite odd-numbered rings and enable high-fidelity multiparty quantum communication through spin rings (working near perfectly for rings of five and seven spins). We show that in certain cases, the twist results in the complete blockage of quantum-information flow to a certain site of the ring. This effect can be exploited to interface and entangle a flux qubit and a spin qubit without embedding the latter in a magnetic field.
Intermediate boundary conditions for LOD, ADI and approximate factorization methods
NASA Technical Reports Server (NTRS)
Leveque, R. J.
1985-01-01
A general approach to determining the correct intermediate boundary conditions for dimensional splitting methods is presented. The intermediate solution U is viewed as a second order accurate approximation to a modified equation. Deriving the modified equation and using the relationship between this equation and the original equation allows us to determine the correct boundary conditions for U*. This technique is illustrated by applying it to locally one dimensional (LOD) and alternating direction implicit (ADI) methods for the heat equation in two and three space dimensions. The approximate factorization method is considered in slightly more generality.
Thermodynamically admissible boundary conditions for the regularized 13 moment equations
NASA Astrophysics Data System (ADS)
Rana, Anirudh Singh; Struchtrup, Henning
2016-02-01
A phenomenological approach to the boundary conditions for linearized R13 equations is derived using the second law of thermodynamics. The phenomenological coefficients appearing in the boundary conditions are calculated by comparing the slip, jump, and thermal creep coefficients with linearized Boltzmann solutions for Maxwell's accommodation model for different values of the accommodation coefficient. For this, the linearized R13 equations are solved for viscous slip, thermal creep, and temperature jump problems and the results are compared to the solutions of the linearized Boltzmann equation. The influence of different collision models (hard-sphere, Bhatnagar-Gross-Krook, and Maxwell molecules) and accommodation coefficients on the phenomenological coefficients is studied.
Boundary conditions in a meshless staggered particle code
Libersky, L.D.; Randles, P.W.
1998-07-01
A meshless method utilizing two sets of particles and generalized boundary conditions is introduced. Companion sets of particles, one carrying velocity and the other carrying stress, are employed to reduce the undesirable effects of colocation of all field variables and increase accuracy. Boundary conditions implemented within this staggered framework include contact, stress-free, stress, velocity, and symmetry constraints. Several test problems are used to evaluate the method. Of particular importance is the motion of stress particles relative to velocity particles in higher dimensions. Early results show promise, but difficulties remain that must be overcome if the staggered technique is to be successful.
Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions.
Alase, Abhijeet; Cobanera, Emilio; Ortiz, Gerardo; Viola, Lorenza
2016-08-12
We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D-1. The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s-wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4π-periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary. PMID:27563986
Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions
NASA Astrophysics Data System (ADS)
Alase, Abhijeet; Cobanera, Emilio; Ortiz, Gerardo; Viola, Lorenza
2016-08-01
We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D -1 . The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s -wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4 π -periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary.
Burton-Miller-type singular boundary method for acoustic radiation and scattering
NASA Astrophysics Data System (ADS)
Fu, Zhuo-Jia; Chen, Wen; Gu, Yan
2014-08-01
This paper proposes the singular boundary method (SBM) in conjunction with Burton and Miller's formulation for acoustic radiation and scattering. The SBM is a strong-form collocation boundary discretization technique using the singular fundamental solutions, which is mathematically simple, easy-to-program, meshless and introduces the concept of source intensity factors (SIFs) to eliminate the singularities of the fundamental solutions. Therefore, it avoids singular numerical integrals in the boundary element method (BEM) and circumvents the troublesome placement of the fictitious boundary in the method of fundamental solutions (MFS). In the present method, we derive the SIFs of exterior Helmholtz equation by means of the SIFs of exterior Laplace equation owing to the same order of singularities between the Laplace and Helmholtz fundamental solutions. In conjunction with the Burton-Miller formulation, the SBM enhances the quality of the solution, particularly in the vicinity of the corresponding interior eigenfrequencies. Numerical illustrations demonstrate efficiency and accuracy of the present scheme on some benchmark examples under 2D and 3D unbounded domains in comparison with the analytical solutions, the boundary element solutions and Dirichlet-to-Neumann finite element solutions.
Fatigue crack damage detection using subharmonic component with nonlinear boundary condition
NASA Astrophysics Data System (ADS)
Wu, Weiliang; Shen, Yanfeng; Qu, Wenzhong; Xiao, Li; Giurgiutiu, Victor
2015-03-01
In recent years, researchers have focused on structural health monitoring (SHM) and damage detection techniques using nonlinear vibration and nonlinear ultrasonic methods. Fatigue cracks may exhibit contact acoustic nonlinearity (CAN) with distinctive features such as superharmonics and subharmonics in the power spectrum of the sensing signals. However, challenges have been noticed in the practical applications of the harmonic methods. For instance, superharmonics can also be generated by the piezoelectric transducers and the electronic equipment; super/subharmonics may also stem from the nonlinear boundary conditions such as structural fixtures and joints. It is hard to tell whether the nonlinear features come from the structural damage or the intrinsic nonlinear boundary conditions. The objective of this paper is to demonstrate the application of nonlinear ultrasonic subharmonic method for detecting fatigue cracks with nonlinear boundary conditions. The fatigue crack was qualitatively modeled as a single-degree-of-freedom (SDOF) system with non-classical hysteretic nonlinear interface forces at both sides of the crack surfaces. The threshold of subharmonic generation was studied, and the influence of crack interface parameters on the subharmonic resonance condition was investigated. The different threshold behaviors between the nonlinear boundary condition and the fatigue crack was found, which can be used to distinguish the source of nonlinear subharmonic features. To evaluate the proposed method, experiments of an aluminum plate with a fatigue crack were conducted to quantitatively verify the subharmonic resonance range. Two surface-bonded piezoelectric transducers were used to generate and receive ultrasonic wave signals. The fatigue damage was characterized in terms of a subharmonic damage index. The experimental results demonstrated that the subharmonic component of the sensing signal can be used to detect the fatigue crack and further distinguish it from
Fatigue crack damage detection using subharmonic component with nonlinear boundary condition
Wu, Weiliang Qu, Wenzhong E-mail: xiaoli6401@126.com; Xiao, Li E-mail: xiaoli6401@126.com; Shen, Yanfeng Giurgiutiu, Victor
2015-03-31
In recent years, researchers have focused on structural health monitoring (SHM) and damage detection techniques using nonlinear vibration and nonlinear ultrasonic methods. Fatigue cracks may exhibit contact acoustic nonlinearity (CAN) with distinctive features such as superharmonics and subharmonics in the power spectrum of the sensing signals. However, challenges have been noticed in the practical applications of the harmonic methods. For instance, superharmonics can also be generated by the piezoelectric transducers and the electronic equipment; super/subharmonics may also stem from the nonlinear boundary conditions such as structural fixtures and joints. It is hard to tell whether the nonlinear features come from the structural damage or the intrinsic nonlinear boundary conditions. The objective of this paper is to demonstrate the application of nonlinear ultrasonic subharmonic method for detecting fatigue cracks with nonlinear boundary conditions. The fatigue crack was qualitatively modeled as a single-degree-of-freedom (SDOF) system with non-classical hysteretic nonlinear interface forces at both sides of the crack surfaces. The threshold of subharmonic generation was studied, and the influence of crack interface parameters on the subharmonic resonance condition was investigated. The different threshold behaviors between the nonlinear boundary condition and the fatigue crack was found, which can be used to distinguish the source of nonlinear subharmonic features. To evaluate the proposed method, experiments of an aluminum plate with a fatigue crack were conducted to quantitatively verify the subharmonic resonance range. Two surface-bonded piezoelectric transducers were used to generate and receive ultrasonic wave signals. The fatigue damage was characterized in terms of a subharmonic damage index. The experimental results demonstrated that the subharmonic component of the sensing signal can be used to detect the fatigue crack and further distinguish it from
NASA Astrophysics Data System (ADS)
Gélat, P.; ter Haar, G.; Saffari, N.
2014-04-01
High intensity focused ultrasound (HIFU) enables highly localised, non-invasive tissue ablation and its efficacy has been demonstrated in the treatment of a range of cancers, including those of the kidney, prostate and breast. HIFU offers the ability to treat deep-seated tumours locally, and potentially bears fewer side effects than more established treatment modalities such as resection, chemotherapy and ionising radiation. There remains however a number of significant challenges which currently hinder its widespread clinical application. One of these challenges is the need to transmit sufficient energy through the ribcage to ablate tissue at the required foci whilst minimising the formation of side lobes and sparing healthy tissue. Ribs both absorb and reflect ultrasound strongly. This sometimes results in overheating of bone and overlying tissue during treatment, leading to skin burns. Successful treatment of a patient with tumours in the upper abdomen therefore requires a thorough understanding of the way acoustic and thermal energy is deposited. Previously, a boundary element (BE) approach based on a Generalised Minimal Residual (GMRES) implementation of the Burton-Miller formulation was developed to predict the field of a multi-element HIFU array scattered by human ribs, the topology of which was obtained from CT scan data [1]. Dissipative mechanisms inside the propagating medium have since been implemented, together with a complex surface impedance condition at the surface of the ribs. A reformulation of the boundary element equations as a constrained optimisation problem was carried out to determine the complex surface velocities of a multi-element HIFU array which generated the acoustic pressure field that best fitted a required acoustic pressure distribution in a least-squares sense. This was done whilst ensuring that an acoustic dose rate parameter at the surface of the ribs was kept below a specified threshold. The methodology was tested at an
NASA Technical Reports Server (NTRS)
Pates, Carl S., III
1991-01-01
A boundary element formulation, along with detailed solution procedure for determining the acoustic field inside a three-dimensional, rectangular duct is presented in this paper. The results of classical and boundary element solutions are compared for a typical rectangular duct by restricting the input frequency in such a way that only plane wave propagation is possible. The effect of changing the type and number of discrete boundary elements on the computed sound pressure levels inside the duct is also presented.
Acoustic characteristics of phonation in “wet voice” conditions
Murugappan, Shanmugam; Boyce, Suzanne; Khosla, Sid; Kelchner, Lisa; Gutmark, Ephraim
2010-01-01
A perceptible change in phonation characteristics after a swallow has long been considered evidence that food and∕or drink material has entered the laryngeal vestibule and is on the surface of the vocal folds as they vibrate. The current paper investigates the acoustic characteristics of phonation when liquid material is present on the vocal folds, using ex vivo porcine larynges as a model. Consistent with instrumental examinations of swallowing disorders or dysphagia in humans, three liquids of different Varibar viscosity (“thin liquid,” “nectar,” and “honey”) were studied at constant volume. The presence of materials on the folds during phonation was generally found to suppress the higher frequency harmonics and generate intermittent additional frequencies in the low and high end of the acoustic spectrum. Perturbation measures showed a higher percentage of jitter and shimmer when liquid material was present on the folds during phonation, but they were unable to differentiate statistically between the three fluid conditions. The finite correlation dimension and positive Lyapunov exponent measures indicated that the presence of materials on the vocal folds excited a chaotic system. Further, these measures were able to reliably differentiate between the baseline and different types of liquid on the vocal folds. PMID:20370039
Computation of dispersion curves for embedded waveguides using a dashpot boundary condition.
Gravenkamp, Hauke; Birk, Carolin; Song, Chongmin
2014-03-01
In this paper a numerical approach is presented to compute dispersion curves for solid waveguides coupled to an infinite medium. The derivation is based on the scaled boundary finite element method that has been developed previously for waveguides with stress-free surfaces. The effect of the surrounding medium is accounted for by introducing a dashpot boundary condition at the interface between the waveguide and the adjoining medium. The damping coefficients are derived from the acoustic impedances of the surrounding medium. Results are validated using an improved implementation of an absorbing region. Since no discretization of the surrounding medium is required for the dashpot approach, the required number of degrees of freedom is typically 10 to 50 times smaller compared to the absorbing region. When compared to other finite element based results presented in the literature, the number of degrees of freedom can be reduced by as much as a factor of 4000. PMID:24606256
Transparent boundary conditions for iterative high-order parabolic equations
NASA Astrophysics Data System (ADS)
Petrov, P. S.; Ehrhardt, M.
2016-05-01
Recently a new approach to the construction of high-order parabolic approximations for the Helmholtz equation was developed. These approximations have the form of the system of iterative parabolic equations, where the solution of the n-th equation is used as an input term for the (n + 1)-th equation. In this study the transparent boundary conditions for such systems of coupled parabolic equations are derived. The existence and uniqueness of the solution of the initial boundary value problem for the system of iterative parabolic equations with the derived boundary conditions are proved. The well-posedness of this problem is also established and an unconditionally stable finite difference scheme for its solution is proposed.
A Robust Absorbing Boundary Condition for Compressible Flows
NASA Technical Reports Server (NTRS)
Loh, Ching Y.; orgenson, Philip C. E.
2005-01-01
An absorbing non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented with theoretical proof. This paper is a continuation and improvement of a previous paper by the author. The absorbing NRBC technique is based on a first principle of non reflecting, which contains the essential physics that a plane wave solution of the Euler equations remains intact across the boundary. The technique is theoretically shown to work for a large class of finite volume approaches. When combined with the hyperbolic conservation laws, the NRBC is simple, robust and truly multi-dimensional; no additional implementation is needed except the prescribed physical boundary conditions. Several numerical examples in multi-dimensional spaces using two different finite volume schemes are illustrated to demonstrate its robustness in practical computations. Limitations and remedies of the technique are also discussed.
Boundary conditions for the Boltzmann equation for rough walls
NASA Astrophysics Data System (ADS)
Brull, Stéphane; Charrier, Pierre
2014-12-01
In some applications, rarefied gases have to considered in a domain whose boundary presents some nanoscale roughness. That is why, we have considered (Brull,2014) a new derivation of boundary conditions for the Boltzmann equation, where the wall present some nanoscale roughness. In this paper, the interaction between the gas and the wall is represented by a kinetic equation defined in a surface layer at the scale of the nanometer close to the wall. The boundary conditions are obtained from a formal asymptotic expansion and are describded by a scattering kernel satisfying classical properties (non-negativeness, normalization, reciprocity). Finally, we present some numerical simulations of scattering diagrams showing the importance of the consideration of roughness for small scales in the model.
Curvature boundary condition for a moving contact line
NASA Astrophysics Data System (ADS)
Luo, J.; Hu, X. Y.; Adams, N. A.
2016-04-01
Effective wall boundary conditions are very important for simulating multi-phase flows involving a moving contact line. In this paper we present a curvature boundary condition to circumvent the difficulties of previous approaches on explicitly imposing the contact angle and with respect to mass-loss artifacts near the wall boundary. While employing the asymptotic theory of Cox for imposing an effective curvature directly at the wall surface, the present method avoids a mismatch between the exact and the numerical contact angles. Test simulations on drop spreading and multi-phase flow in a channel show that the present method achieves grid-convergent results and ensures mass conservation, and delivers good agreement with theoretical, numerical and experimental data.
NASA Technical Reports Server (NTRS)
Balakumar, Ponnampalam; King, Rudolph A.
2011-01-01
The receptivity and interaction of stationary and traveling crossflow instability of three-dimensional supersonic boundary layers over a swept biconvex wing with a blunt leading edge are numerically investigated for a freestream Mach number of 3. The steady and unsteady flow fields are obtained by solving the full Navier-Stokes equations. The receptivity of the boundary layer to surface roughness, freestream acoustic waves, and freestream vorticity waves are numerically investigated. The initial amplitudes of the stationary vortices generated by 1 micron roughness elements is about 2000 times larger than the initial amplitudes of the traveling disturbances generated by vortical disturbances. The interaction of stationary and traveling disturbances was investigated by solving the equations with both surface roughness and vortical disturbances. When the initial amplitudes of the stationary disturbances are large compared to the traveling disturbances, the stationary vortex dominates the perturbation field. When the amplitudes are comparable, the traveling vortex prevails and the stationary vortex is suppressed.
NASA Astrophysics Data System (ADS)
Arias-Ramirez, Walter; Olson, Britton; Wolf, William; Lawrence Livermore National Laboratory Team; University of Campinas Team
2015-11-01
The suitability of a continuing forcing immersed boundary method (IBM) combined with a high-order finite difference method is examined on several acoustic scattering problems. A suite of two-dimensional numerical simulations of canonical cases are conducted with the aim of analyzing the error behavior associated with the IBM, through wave reflection, wave diffraction, and the shock-boundary layer interaction phenomena. The compressible Navier-Stokes equations are solved using the Miranda code developed at Lawrence Livermore National Laboratory. Comparison of analytical solution against numerical results is shown for different flow parameters. Preliminary results indicate that the continuing forcing approach has the largest error in wave reflection compared to analytical solution. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344.
Multicomponent Gas Diffusion and an Appropriate Momentum Boundary Condition
NASA Technical Reports Server (NTRS)
Noever, David A.
1994-01-01
Multicomponent gas diffusion is reviewed with particular emphasis on gas flows near solid boundaries-the so-called Kramers-Kistemaker effect. The aim is to derive an appropriate momentum boundary condition which governs many gaseous species diffusing together. The many species' generalization of the traditional single gas condition, either as slip or stick (no-slip), is not obvious, particularly for technologically important cases of lower gas pressures and very dissimilar molecular weight gases. No convincing theoretical case exists for why two gases should interact with solid boundaries equally but in opposite flow directions, such that the total gas flow exactly vanishes. ln this way, the multicomponent no-slip boundary requires careful treatment The approaches discussed here generally adopt a microscopic model for gas-solid contact. The method has the advantage that the mathematics remain tractable and hence experimentally testable. Two new proposals are put forward, the first building in some molecular collision physics, the second drawing on a detailed view of surface diffusion which does not unphysically extrapolate bulk gas properties to govern the adsorbed molecules. The outcome is a better accounting of previously anomalous experiments. Models predict novel slip conditions appearing even for the case of equal molecular weight components. These approaches become particularly significant in view of a conceptual contradiction found to arise in previous derivations of the appropriate boundary conditions. The analogous case of three gases, one of which is uniformly distributed and hence non-diffusing, presents a further refinement which gives unexpected flow reversals near solid boundaries. This case is investigated alone and for aggregating gas species near their condensation point. In addition to predicting new physics, this investigation carries practical implications for controlling vapor diffusion in the growth of crystals used in medical diagnosis (e
Dirac operator on a disk with global boundary conditions
Falomir, H.; Gamboa Saravi, R.E.; Santangelo, E.M.
1998-01-01
We compute the functional determinant for a Dirac operator in the presence of an Abelian gauge field on a bidimensional disk, under global boundary conditions of the type introduced by Atiyah{endash}Patodi{endash}Singer. We also discuss the connection between our result and the index theorem. {copyright} {ital 1998 American Institute of Physics.}
Investigation of Boundary Conditions for Flexible Multibody Spacecraft Dynamics
NASA Technical Reports Server (NTRS)
MacLean, John R.; Huynh, An; Quiocho, Leslie J.
2007-01-01
In support of both the Space Shuttle and International Space Station programs, a set of generic multibody dynamics algorithms integrated within the Trick simulation environment have addressed the variety of on-orbit manipulator simulation requirements for engineering analysis, procedures development and crew familiarization/training at the NASA Johnson Space Center (JSC). Enhancements to these dynamics algorithms are now being driven by a new set of Constellation program requirements for flexible multibody spacecraft simulation. One particular issue that has been discussed within the NASA community is the assumption of cantilever-type flexible body boundary conditions. This assumption has been commonly utilized within manipulator multibody dynamics formulations as it simplifies the computation of relative motion for articulated flexible topologies. Moreover, its use for modeling of space-based manipulators such as the Shuttle Remote Manipulator System (SRMS) and Space Station Remote Manipulator System (SSRMS) has been extensively validated against flight data. For more general flexible spacecraft applications, however, the assumption of cantilever-type boundary conditions may not be sufficient. This paper describes the boundary condition assumptions that were used in the original formulation, demonstrates that this formulation can be augmented to accommodate systems in which the assumption of cantilever boundary conditions no longer applies, and verifies the approach through comparison with an independent model previously validated against experimental hardware test data from a spacecraft flexible dynamics emulator.
Calculation of Multistage Turbomachinery Using Steady Characteristic Boundary Conditions
NASA Technical Reports Server (NTRS)
Chima, Rodrick V.
1998-01-01
A multiblock Navier-Stokes analysis code for turbomachinery has been modified to allow analysis of multistage turbomachines. A steady averaging-plane approach was used to pass information between blade rows. Characteristic boundary conditions written in terms of perturbations about the mean flow from the neighboring blade row were used to allow close spacing between the blade rows without forcing the flow to be axisymmetric. In this report the multiblock code is described briefly and the characteristic boundary conditions and the averaging-plane implementation are described in detail. Two approaches for averaging the flow properties are also described. A two-dimensional turbine stator case was used to compare the characteristic boundary conditions with standard axisymmetric boundary conditions. Differences were apparent but small in this low-speed case. The two-stage fuel turbine used on the space shuttle main engines was then analyzed using a three-dimensional averaging-plane approach. Computed surface pressure distributions on the stator blades and endwalls and computed distributions of blade surface heat transfer coefficient on three blades showed very good agreement with experimental data from two tests.
Poroelastic modeling of seismic boundary conditions across a fracture.
Nakagawa, Seiji; Schoenberg, Michael A
2007-08-01
Permeability of a fracture can affect how the fracture interacts with seismic waves. To examine this effect, a simple mathematical model that describes the poroelastic nature of wave-fracture interaction is useful. In this paper, a set of boundary conditions is presented which relate wave-induced particle velocity (or displacement) and stress including fluid pressure across a compliant, fluid-bearing fracture. These conditions are derived by modeling a fracture as a thin porous layer with increased compliance and finite permeability. Assuming a small layer thickness, the boundary conditions can be derived by integrating the governing equations of poroelastic wave propagation. A finite jump in the stress and velocity across a fracture is expressed as a function of the stress and velocity at the boundaries. Further simplification for a thin fracture yields a set of characteristic parameters that control the seismic response of single fractures with a wide range of mechanical and hydraulic properties. These boundary conditions have potential applications in simplifying numerical models such as finite-difference and finite-element methods to compute seismic wave scattering off nonplanar (e.g., curved and intersecting) fractures. PMID:17672634
Outer boundary conditions for evolving cool white dwarfs
NASA Astrophysics Data System (ADS)
Rohrmann, R. D.; Althaus, L. G.; García-Berro, E.; Córsico, A. H.; Miller Bertolami, M. M.
2012-10-01
Context. White dwarf evolution is essentially a gravothermal cooling process, which, for cool white dwarfs, depends on the treatment of the outer boundary conditions. Aims: We provide detailed outer boundary conditions that are appropriate to computing the evolution of cool white dwarfs by employing detailed nongray model atmospheres for pure hydrogen composition. We also explore the impact on the white dwarf cooling times of different assumptions for energy transfer in the atmosphere of cool white dwarfs. Methods: Detailed nongray model atmospheres were computed by considering nonideal effects in the gas equation of state and chemical equilibrium, collision-induced absorption from molecules, and the Lyman α quasi-molecular opacity. We explored the impact of outer boundary conditions provided by updated model atmospheres on the cooling times of 0.60 and 0.90 M⊙ white dwarf sequences. Results: Our results show that the use of detailed outer boundary conditions becomes relevant for effective temperatures lower than 5800 K for sequences with 0.60 M⊙ and 6100 K with 0.90 M⊙. Detailed model atmospheres predict ages that are up to ≈10% shorter at log (L/L⊙) = -4 when compared with the ages derived using Eddington-like approximations at τRoss = 2/3. We also analyze the effects of various assumptions and physical processes that are relevant in the calculation of outer boundary conditions. In particular, we find that the Lyα red wing absorption does not substantially affect the evolution of white dwarfs. Conclusions: White dwarf cooling timescales are sensitive to the surface boundary conditions for Teff ≲ 6000 K. Interestingly enough, nongray effects have few consequences on these cooling times at observable luminosities. In fact, collision-induced absorption processes, which significantly affect the spectra and colors of old white dwarfs with hydrogen-rich atmospheres, have no noticeable effects on their cooling rates, except throughout the Rosseland mean
A novel formulation for Neumann inflow boundary conditions in biomechanics.
Gravemeier, Volker; Comerford, Andrew; Yoshihara, Lena; Ismail, Mahmoud; Wall, Wolfgang A
2012-05-01
Neumann boundary conditions prescribing the total momentum flux at inflow boundaries of biomechanical problems are proposed in this study. This approach enables the simultaneous application of velocity/flow rate and pressure curves at inflow boundaries. As the basic numerical method, a residual-based variational multiscale (or stabilized) finite element method is presented. The focus of the numerical examples in this work is on respiratory flows with complete flow reversals. However, the proposed formulation is just as well suited for cardiovascular flow problems with partial retrograde flow. Instabilities, which were reported for such problems in the literature, are resolved by the present approach without requiring the additional consideration of a Lagrange multiplier technique. The suitability of the approach is demonstrated for two respiratory flow examples, a rather simple tube and complex tracheobronchial airways (up to the fourth generation, segmented from end-expiratory CT images). For the latter example, the boundary conditions are generated from mechanical ventilation data obtained from an intensive care unit patient suffering from acute lung injury. For the tube, analytical pressure profiles can be replicated, and for the tracheobronchial airways, a correct distribution of the prescribed total momentum flux at the inflow boundary into velocity and pressure part is observed. PMID:25099458
Internal friction and boundary conditions in lossy fluid seabeds
Deane, G.B.
1997-01-01
There are two distinct mechanisms associated with compressional wave absorption in lossy media, internal relaxation and internal friction. For the special case of propagation in an homogeneous, unbounded medium, both mechanisms can be modeled by adopting the convention of a complex sound speed and are, in this sense, equivalent. For the more realistic case of propagation in a stratified medium, the convention of complex sound speed does not give a correct description for losses which modify the linearized equation of motion, such as internal friction. In the presence of boundaries, internal friction can be modeled by the introduction of a complex quiescent density in addition to complex sound speed. Propagation models which use complex sound speed only in the presence of boundaries make the tacit assumption that seafloor losses are caused by internal relaxations only. A solution is developed for propagation in a lossy Pekeris channel where absorption in the lower fluid is caused by internal friction. The example that has been considered yields a sound level 3 dB less than the standard description over a 50-km path. {copyright} {ital 1997 Acoustical Society of America.}
NASA Astrophysics Data System (ADS)
Husain, S. Z.; Floryan, J. M.
2008-04-01
A fully implicit, spectral algorithm for the analysis of moving boundary problem is described. The algorithm is based on the concept of immersed boundary conditions (IBC), i.e., the computational domain is fixed while the time dependent physical domain is submerged inside the computational domain, and is described in the context of the diffusion-type problems. The physical conditions along the edges of the physical domain are treated as internal constraints. The method eliminates the need for adaptive grid generation that follows evolution of the physical domain and provides sharp resolution of the location of the boundary. Various tests confirm the spectral accuracy in space and the first- and second-order accuracy in time. The computational cost advantage of the IBC method as compared with the more traditional algorithm based on the mapping concept is demonstrated.
Nonlinear Stefan problem with convective boundary condition in Storm's materials
NASA Astrophysics Data System (ADS)
Briozzo, Adriana C.; Natale, Maria F.
2016-04-01
We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material x > 0, with phase change temperature T f . We assume that the heat capacity and the thermal conductivity satisfy a Storm's condition, and we assume a convective boundary condition at the fixed face x = 0. A unique explicit solution of similarity type is obtained. Moreover, asymptotic behavior of the solution when {h→ + ∞} is studied.
Zhang, Honghu
2006-04-01
The acoustical radiosity method is a computationally expensive acoustical simulation algorithm that assumes an enclosure with ideal diffuse reflecting boundaries. Miles observed that for such an enclosure, the sound energy decay of every point on the boundaries will gradually converge to exponential manner with a uniform decay rate. Therefore, the ratio of radiosity between every pair of points on the boundaries will converge to a constant, and the radiosity across the boundaries will approach a fixed distribution during the sound decay process, where radiosity is defined as the acoustic power per unit area leaving (or being received by) a point on a boundary. We call this phenomenon the "relaxation" of the sound field. In this paper, we study the relaxation in rooms of different shapes with different boundary absorptions. Criteria based on the relaxation of the sound field are proposed to terminate the costly and unnecessary radiosity computation in the later phase, which can then be replaced by a fast regression step to speed up the acoustical radiosity simulation. PMID:16642833
On the Huygens absorbing boundary conditions for electromagnetics
Berenger, Jean-Pierre
2007-09-10
A new absorbing boundary condition (ABC) is presented for the solution of Maxwell equations in unbounded spaces. Called the Huygens ABC, this condition is a generalization of two previously published ABCs, namely the multiple absorbing surfaces (MAS) and the re-radiating boundary condition (rRBC). The properties of the Huygens ABC are derived theoretically in continuous spaces and in the finite-difference (FDTD) discretized space. A solution is proposed to render the Huygens ABC effective for the absorption of evanescent waves. Numerical experiments with the FDTD method show that the effectiveness of the Huygens ABC is close to that of the PML ABC in some realistic problems of numerical electromagnetics. It is also shown in the paper that a combination of the Huygens ABC with the PML ABC is very well suited to the solution of some particular problems.
Surface Acoustic Wave (SAW) Resonators for Monitoring Conditioning Film Formation.
Hohmann, Siegfried; Kögel, Svea; Brunner, Yvonne; Schmieg, Barbara; Ewald, Christina; Kirschhöfer, Frank; Brenner-Weiß, Gerald; Länge, Kerstin
2015-01-01
We propose surface acoustic wave (SAW) resonators as a complementary tool for conditioning film monitoring. Conditioning films are formed by adsorption of inorganic and organic substances on a substrate the moment this substrate comes into contact with a liquid phase. In the case of implant insertion, for instance, initial protein adsorption is required to start wound healing, but it will also trigger immune reactions leading to inflammatory responses. The control of the initial protein adsorption would allow to promote the healing process and to suppress adverse immune reactions. Methods to investigate these adsorption processes are available, but it remains difficult to translate measurement results into actual protein binding events. Biosensor transducers allow user-friendly investigation of protein adsorption on different surfaces. The combination of several transduction principles leads to complementary results, allowing a more comprehensive characterization of the adsorbing layer. We introduce SAW resonators as a novel complementary tool for time-resolved conditioning film monitoring. SAW resonators were coated with polymers. The adsorption of the plasma proteins human serum albumin (HSA) and fibrinogen onto the polymer-coated surfaces were monitored. Frequency results were compared with quartz crystal microbalance (QCM) sensor measurements, which confirmed the suitability of the SAW resonators for this application. PMID:26007735
Surface Acoustic Wave (SAW) Resonators for Monitoring Conditioning Film Formation
Hohmann, Siegfried; Kögel, Svea; Brunner, Yvonne; Schmieg, Barbara; Ewald, Christina; Kirschhöfer, Frank; Brenner-Weiß, Gerald; Länge, Kerstin
2015-01-01
We propose surface acoustic wave (SAW) resonators as a complementary tool for conditioning film monitoring. Conditioning films are formed by adsorption of inorganic and organic substances on a substrate the moment this substrate comes into contact with a liquid phase. In the case of implant insertion, for instance, initial protein adsorption is required to start wound healing, but it will also trigger immune reactions leading to inflammatory responses. The control of the initial protein adsorption would allow to promote the healing process and to suppress adverse immune reactions. Methods to investigate these adsorption processes are available, but it remains difficult to translate measurement results into actual protein binding events. Biosensor transducers allow user-friendly investigation of protein adsorption on different surfaces. The combination of several transduction principles leads to complementary results, allowing a more comprehensive characterization of the adsorbing layer. We introduce SAW resonators as a novel complementary tool for time-resolved conditioning film monitoring. SAW resonators were coated with polymers. The adsorption of the plasma proteins human serum albumin (HSA) and fibrinogen onto the polymer-coated surfaces were monitored. Frequency results were compared with quartz crystal microbalance (QCM) sensor measurements, which confirmed the suitability of the SAW resonators for this application. PMID:26007735
Assignment of boundary conditions in embedded ground water flow models
Leake, S.A.
1998-01-01
Many small-scale ground water models are too small to incorporate distant aquifer boundaries. If a larger-scale model exists for the area of interest, flow and head values can be specified for boundaries in the smaller-scale model using values from the larger-scale model. Flow components along rows and columns of a large-scale block-centered finite-difference model can be interpolated to compute horizontal flow across any segment of a perimeter of a small-scale model. Head at cell centers of the larger-scale model can be interpolated to compute head at points on a model perimeter. Simple linear interpolation is proposed for horizontal interpolation of horizontal-flow components. Bilinear interpolation is proposed for horizontal interpolation of head values. The methods of interpolation provided satisfactory boundary conditions in tests using models of hypothetical aquifers.Many small-scale ground water models are too small to incorporate distant aquifer boundaries. If a larger-scale model exists for the area of interest, flow and head values can be specified for boundaries in the smaller-scale model using values from the larger-scale model. Flow components along rows and columns of a large-scale block-centered finite-difference model can be interpolated to compute horizontal flow across any segment of a perimeter of a small-scale model. Head at cell centers of the larger.scale model can be interpolated to compute head at points on a model perimeter. Simple linear interpolation is proposed for horizontal interpolation of horizontal-flow components. Bilinear interpolation is proposed for horizontal interpolation of head values. The methods of interpolation provided satisfactory boundary conditions in tests using models of hypothetical aquifers.
Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre M.
2014-02-15
Robin boundary condition for the Navier-Stokes equations is used to model slip conditions at the fluid-solid boundaries. A novel Continuous Boundary Force (CBF) method is proposed for solving the Navier-Stokes equations subject to Robin boundary condition. In the CBF method, the Robin boundary condition at boundary is replaced by the homogeneous Neumann boundary condition at the boundary and a volumetric force term added to the momentum conservation equation. Smoothed Particle Hydrodynamics (SPH) method is used to solve the resulting Navier-Stokes equations. We present solutions for two-dimensional and three-dimensional flows in domains bounded by flat and curved boundaries subject to various forms of the Robin boundary condition. The numerical accuracy and convergence are examined through comparison of the SPH-CBF results with the solutions of finite difference or finite element method. Taken the no-slip boundary condition as a special case of slip boundary condition, we demonstrate that the SPH-CBF method describes accurately both no-slip and slip conditions.