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.
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.
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.
Zhao, Shan; Wei, G. W.
2010-01-01
SUMMARY High-order central finite difference schemes encounter great difficulties in implementing complex boundary conditions. This paper introduces the matched interface and boundary (MIB) method as a novel boundary scheme to treat various general boundary conditions in arbitrarily high-order central finite difference schemes. To attain arbitrarily high order, the MIB method accurately extends the solution beyond the boundary by repeatedly enforcing only the original set of boundary conditions. The proposed approach is extensively validated via boundary value problems, initial-boundary value problems, eigenvalue problems, and high-order differential equations. Successful implementations are given to not only Dirichlet, Neumann, and Robin boundary conditions, but also more general ones, such as multiple boundary conditions in high-order differential equations and time-dependent boundary conditions in evolution equations. Detailed stability analysis of the MIB method is carried out. The MIB method is shown to be able to deliver high-order accuracy, while maintaining the same or similar stability conditions of the standard high-order central difference approximations. The application of the proposed MIB method to the boundary treatment of other non-standard high-order methods is also considered. PMID:20485574
A general approach for high order absorbing boundary conditions for the Helmholtz equation
NASA Astrophysics Data System (ADS)
Zarmi, Asaf; Turkel, Eli
2013-06-01
When solving a scattering problem in an unbounded space, one needs to implement the Sommerfeld condition as a boundary condition at infinity, to ensure no energy penetrates the system. In practice, solving a scattering problem involves truncating the region and implementing a boundary condition on an artificial outer boundary. Bayliss, Gunzburger and Turkel (BGT) suggested an Absorbing Boundary Condition (ABC) as a sequence of operators aimed at annihilating elements from the solution's series representation. Their method was practical only up to a second order condition. Later, Hagstrom and Hariharan (HH) suggested a method which used auxiliary functions and enabled implementation of higher order conditions. We compare various absorbing boundary conditions (ABCs) and introduce a new method to construct high order ABCs, generalizing the HH method. We then derive from this general method ABCs based on different series representations of the solution to the Helmholtz equation - in polar, elliptical and spherical coordinates. Some of these ABCs are generalizations of previously constructed ABCs and some are new. These new ABCs produce accurate solutions to the Helmholtz equation, which are much less dependent on the various parameters of the problem, such as the value of k, or the eccentricity of the ellipse. In addition to constructing new ABCs, our general method sheds light on the connection between various ABCs. Computations are presented to verify the high accuracy of these new ABCs.
Gibbons-Hawking boundary terms and junction conditions for higher-order brane gravity models
Balcerzak, Adam; Dabrowski, Mariusz P. E-mail: mpdabfz@wmf.univ.szczecin.pl
2009-01-15
We derive the most general junction conditions for the fourth-order brane gravity constructed of arbitrary functions of curvature invariants. We reduce these fourth-order theories to second order theories at the expense of introducing new scalar and tensor fields - the scalaron and the tensoron. In order to obtain junction conditions we apply the method of generalized Gibbons-Hawking boundary terms which are appended to the appropriate actions. After assuming the continuity of the scalaron and the tensoron on the brane, we recover junction conditions for such general brane universe models previously obtained by different methods. The derived junction conditions can serve studying the cosmological implications of the higher-order brane gravity models.
Generalized second-order slip boundary condition for nonequilibrium gas flows.
Guo, Zhaoli; Qin, Jishun; Zheng, Chuguang
2014-01-01
It is a challenging task to model nonequilibrium gas flows within a continuum-fluid framework. Recently some extended hydrodynamic models in the Navier-Stokes formulation have been developed for such flows. A key problem in the application of such models is that suitable boundary conditions must be specified. In the present work, a generalized second-order slip boundary condition is developed in which an effective mean-free path considering the wall effect is used. By combining this slip scheme with certain extended Navier-Stokes constitutive relation models, we obtained a method for nonequilibrium gas flows with solid boundaries. The method is applied to several rarefied gas flows involving planar or curved walls, including the Kramers' problem, the planar Poiseuille flow, the cylindrical Couette flow, and the low speed flow over a sphere. The results show that the proposed method is able to give satisfied predictions, indicating the good potential of the method for nonequilibrium flows. PMID:24580334
High-order Two-way Artificial Boundary Conditions for Nonlinear Wave Propagation with Backscattering
NASA Technical Reports Server (NTRS)
Fibich, Gadi; Tsynkov, Semyon
2000-01-01
When solving linear scattering problems, one typically first solves for the impinging wave in the absence of obstacles. Then, by linear superposition, the original problem is reduced to one that involves only the scattered waves driven by the values of the impinging field at the surface of the obstacles. In addition, when the original domain is unbounded, special artificial boundary conditions (ABCs) that would guarantee the reflectionless propagation of waves have to be set at the outer boundary of the finite computational domain. The situation becomes conceptually different when the propagation equation is nonlinear. In this case the impinging and scattered waves can no longer be separated, and the problem has to be solved in its entirety. In particular, the boundary on which the incoming field values are prescribed, should transmit the given incoming waves in one direction and simultaneously be transparent to all the outgoing waves that travel in the opposite direction. We call this type of boundary conditions two-way ABCs. In the paper, we construct the two-way ABCs for the nonlinear Helmholtz equation that models the laser beam propagation in a medium with nonlinear index of refraction. In this case, the forward propagation is accompanied by backscattering, i.e., generation of waves in the direction opposite to that of the incoming signal. Our two-way ABCs generate no reflection of the backscattered waves and at the same time impose the correct values of the incoming wave. The ABCs are obtained for a fourth-order accurate discretization to the Helmholtz operator; the fourth-order grid convergence is corroborated experimentally by solving linear model problems. We also present solutions in the nonlinear case using the two-way ABC which, unlike the traditional Dirichlet boundary condition, allows for direct calculation of the magnitude of backscattering.
The impedance problem of wave diffraction by a strip with higher order boundary conditions
Castro, L. P.; Simões, A. M.
2013-10-17
This work is devoted to analyse an impedance boundary-transmission problem for the Helmholtz equation originated by a problem of wave diffraction by an infinite strip with higher order imperfect boundary conditions. A constructive approach of operator relations is built, which allows a transparent interpretation of the problem in an operator theory framework. In particular, different types of operator relations are exhibited for different types of operators acting between Lebesgue and Sobolev spaces on a finite interval and the positive half-line. All this has consequences in the understanding of the structure of this type of problems. In particular, a Fredholm characterization of the problem is obtained in terms of the initial space order parameters. At the request of the author and the Proceedings Editor the above article has been replaced with a corrected version. The original PDF file supplied to AIP Publishing contained an error in the title of the article. The original title appeared as: 'The Impedance Problem of Wave Diffraction by a trip with Higher Order Boundary Conditions.' This article has been replaced and the title now appears correctly online. The corrected article was published on 8 November 2013.
Constraint-preserving boundary conditions in the 3+1 first-order approach
Bona, C.; Bona-Casas, C.
2010-09-15
A set of energy-momentum constraint-preserving boundary conditions is proposed for the first-order Z4 case. The stability of a simple numerical implementation is tested in the linear regime (robust stability test), both with the standard corner and vertex treatment and with a modified finite-differences stencil for boundary points which avoids corners and vertices even in Cartesian-like grids. Moreover, the proposed boundary conditions are tested in a strong-field scenario, the Gowdy waves metric, showing the expected rate of convergence. The accumulated amount of energy-momentum constraint violations is similar or even smaller than the one generated by either periodic or reflection conditions, which are exact in the Gowdy waves case. As a side theoretical result, a new symmetrizer is explicitly given, which extends the parametric domain of symmetric hyperbolicity for the Z4 formalism. The application of these results to first-order Baumgarte-Shapiro-Shibata-Nakamura-like formalisms is also considered.
Compact high order schemes with gradient-direction derivatives for absorbing boundary conditions
NASA Astrophysics Data System (ADS)
Gordon, Dan; Gordon, Rachel; Turkel, Eli
2015-09-01
We consider several compact high order absorbing boundary conditions (ABCs) for the Helmholtz equation in three dimensions. A technique called "the gradient method" (GM) for ABCs is also introduced and combined with the high order ABCs. GM is based on the principle of using directional derivatives in the direction of the wavefront propagation. The new ABCs are used together with the recently introduced compact sixth order finite difference scheme for variable wave numbers. Experiments on problems with known analytic solutions produced very accurate results, demonstrating the efficacy of the high order schemes, particularly when combined with GM. The new ABCs are then applied to the SEG/EAGE Salt model, showing the advantages of the new schemes.
NASA Astrophysics Data System (ADS)
Burlutskaya, M. Sh.
2014-01-01
The Fourier method is used to find a classical solution of the mixed problem for a first-order differential equation with involution and periodic boundary conditions. The application of the Fourier method is substantiated using refined asymptotic formulas obtained for the eigenvalues and eigenfunctions of the corresponding spectral problem. The Fourier series representing the formal solution is transformed using certain techniques, and the possibility of its term-by-term differentiation is proved. Minimal requirements are imposed on the initial data of the problem.
A High-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions
NASA Technical Reports Server (NTRS)
Sun, Xian-He; Zhuang, Yu
1997-01-01
In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains. Special treatments are then introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and separability. Finally, a Fast Fourier Transform (FFT) based technique is used to yield a fast direct solver. Analytical and experimental results show this newly proposed solver is comparable to the conventional second-order elliptic solver when accuracy is not a primary concern, and is significantly faster than that of the conventional solver if a highly accurate solution is required. In addition, this newly proposed fourth order Helmholtz solver is parallel in nature. It is readily available for parallel and distributed computers. The compact scheme introduced in this study is likely extendible for sixth-order accurate algorithms and for more general elliptic equations.
NASA Technical Reports Server (NTRS)
Nordstrom, Jan; Carpenter, Mark H.
1998-01-01
Boundary and interface conditions for high order finite difference methods applied to the constant coefficient Euler and Navier-Stokes equations are derived. The boundary conditions lead to strict and strong stability. The interface conditions are stable and conservative even if the finite difference operators and mesh sizes vary from domain to domain. Numerical experiments show that the new conditions also lead to good results for the corresponding nonlinear problems.
First-order corrections to approximate solutions to two-point boundary-condition problems
NASA Technical Reports Server (NTRS)
Andrus, J. F.; Greenleaf, W. G.
1973-01-01
A method, applicable to real time guidance, is developed for accurate solution to exo-atmospheric space flight optimization problems. In principle the method is applicable to many other two-point boundary-condition (TPBC) problems. The first step of the method is the iterative solution (using a shooting method) of a TPBC problem with differential equations simplified so that they may be solved analytically by means of a single closed-form solution over each stage of the flight. The second step is the addition of a closed-form correction to the solution to the TPBC problem obtained in the first step. The correction accounts (to first-order accuracy) for the errors due to the aforementioned simplifications. Numerical results are given for several orbital injection problems.
NASA Astrophysics Data System (ADS)
Raghupathy, Arun; Ghia, Karman; Ghia, Urmila
2008-11-01
Compact Thermal Models (CTM) to represent IC packages has been traditionally developed using the DELPHI-based (DEvelopment of Libraries of PHysical models for an Integrated design) methodology. The drawbacks of this method are presented, and an alternative method is proposed. A reduced-order model that provides the complete thermal information accurately with less computational resources can be effectively used in system level simulations. Proper Orthogonal Decomposition (POD), a statistical method, can be used to reduce the order of the degree of freedom or variables of the computations for such a problem. POD along with the Galerkin projection allows us to create reduced-order models that reproduce the characteristics of the system with a considerable reduction in computational resources while maintaining a high level of accuracy. The goal of this work is to show that this method can be applied to obtain a boundary condition independent reduced-order thermal model for complex components. The methodology is applied to the 1D transient heat equation.
Sobolev type equations of time-fractional order with periodical boundary conditions
NASA Astrophysics Data System (ADS)
Plekhanova, Marina
2016-08-01
The existence of a unique local solution for a class of time-fractional Sobolev type partial differential equations endowed by the Cauchy initial conditions and periodical with respect to every spatial variable boundary conditions on a parallelepiped is proved. General results are applied to study of the unique solvability for the initial boundary value problem to Benjamin-Bona-Mahony-Burgers and Allair partial differential equations.
NASA Astrophysics Data System (ADS)
Duru, Kenneth; Kozdon, Jeremy E.; Kreiss, Gunilla
2015-12-01
In computations, it is now common to surround artificial boundaries of a computational domain with a perfectly matched layer (PML) of finite thickness in order to prevent artificially reflected waves from contaminating a numerical simulation. Unfortunately, the PML does not give us an indication about appropriate boundary conditions needed to close the edges of the PML, or how those boundary conditions should be enforced in a numerical setting. Terminating the PML with an inappropriate boundary condition or an unstable numerical boundary procedure can lead to exponential growth in the PML which will eventually destroy the accuracy of a numerical simulation everywhere. In this paper, we analyze the stability and the well-posedness of boundary conditions terminating the PML for the elastic wave equation in first order form. First, we consider a vertical modal PML truncating a two space dimensional computational domain in the horizontal direction. We freeze all coefficients and consider a left half-plane problem with linear boundary conditions terminating the PML. The normal mode analysis is used to study the stability and well-posedness of the resulting initial boundary value problem (IBVP). The result is that any linear well-posed boundary condition yielding an energy estimate for the elastic wave equation, without the PML, will also lead to a well-posed IBVP for the PML. Second, we extend the analysis to the PML corner region where both a horizontal and vertical PML are simultaneously active. The challenge lies in constructing accurate and stable numerical approximations for the PML and the boundary conditions. Third, we develop a high order accurate finite difference approximation of the PML subject to the boundary conditions. To enable accurate and stable numerical boundary treatments for the PML we construct continuous energy estimates in the Laplace space for a one space dimensional problem and two space dimensional PML corner problem. We use summation
NASA Astrophysics Data System (ADS)
Shibata, Yoshihiro
2013-03-01
In this paper, we prove unique existence of solutions to the generalized resolvent problem of the Stokes operator with first order boundary condition in a general domain {Ω} of the N-dimensional Eulidean space {{R}^N, N ≥ 2}. This type of problem arises in the mathematical study of the flow of a viscous incompressible one-phase fluid with free surface. Moreover, we prove uniform estimates of solutions with respect to resolvent parameter {λ} varying in a sector {Σ_{σ, λ_0} = \\{λ in {C} mid |arg λ| < π-σ, enskip |λ| ≥ λ_0\\}}, where {0 < σ < π/2} and {λ_0 ≥ 1}. The essential assumption of this paper is the existence of a unique solution to a suitable weak Dirichlet problem, namely it is assumed the unique existence of solution {p in hat{W}^1_{q, Γ}(Ω)} to the variational problem: {(nabla p, nabla \\varphi) = (f, nabla \\varphi)} for any {\\varphi in hat W^1_{q', Γ}(Ω)}. Here, {1 < q < infty, q' = q/(q-1), hat W^1_{q, Γ}(Ω)} is the closure of {W^1_{q, Γ}(Ω) = \\{ p in W^1_q(Ω) mid p|_Γ = 0\\}} by the semi-norm {\\|nabla \\cdot \\|_{L_q(Ω)}}, and {Γ} is the boundary of {Ω}. In fact, we show that the unique solvability of such a Dirichlet problem is necessary for the unique existence of a solution to the resolvent problem with uniform estimate with respect to resolvent parameter varying in {(λ_0, infty)}. Our assumption is satisfied for any {q in (1, infty)} by the following domains: whole space, half space, layer, bounded domains, exterior domains, perturbed half space, perturbed layer, but for a general domain, we do not know any result about the unique existence of solutions to the weak Dirichlet problem except for q = 2.
NASA Astrophysics Data System (ADS)
van Joolen*, Vince; Givoli, Dan; Neta, Beny
2003-07-01
Among the many areas of research that Professor Kawahara has been active in is the subject of open boundaries in which linear time-dependent dispersive waves are considered in an unbounded domain. The infinite domain is truncated via an artificial boundary B on which an open boundary condition (OBC) is imposed. In this paper, Higdon OBCs and Hagstrom-Hariharan (HH) OBCs are considered. Higdon-type conditions, originally implemented as low-order OBCs, are made accessible for any desired order via a new scheme. The higher-order Higdon OBC is then reformulated using auxiliary variables and made compatible for use with finite element (FE) methods. Methodologies for selecting Higdon parameters are also proposed. The performances of these schemes are demonstrated in two numerical examples. This is followed by a discussion of the HH OBC, which is applicable to non-dispersive media on cylindrical and spherical geometries. The paper extends this OBC to the "slightly dispersive" case.
NASA Astrophysics Data System (ADS)
Ashyralyyev, Charyyar; Dedeturk, Mutlu
2016-08-01
Approximation of Dirichlet type overdetermined multidimensional elliptic problem with Dirichlet-Neumann boundary conditions are discussed. A third order of accuracy difference scheme for its approximate solution is proposed. The stability, almost coercive stability and coercive stability inequalities for the solution of constructed difference scheme are established. Test example for a two-dimensional elliptic problem is presented.
NASA Astrophysics Data System (ADS)
Ge, Wenjun; Modest, Michael F.; Roy, Somesh P.
2016-03-01
The high-order spherical harmonics (PN) method for 2-D Cartesian domains is extracted from the 3-D formulation. The number of equations and intensity coefficients reduces to (N + 1)2 / 4 in the 2-D Cartesian formulation compared with N(N + 1) / 2 for the general 3-D PN formulation. The Marshak boundary conditions are extended to solve problems with nonblack and mixed diffuse-specular surfaces. Additional boundary conditions for specified radiative wall flux, for symmetry/specular reflection boundaries have also been developed. The mathematical details of the formulations and their implementation in the OpenFOAM finite volume based CFD software platform are presented. The accuracy and computational cost of the 2-D Cartesian PN are compared with that of the 3-D PN solver and a Photon Monte Carlo solver for a square enclosure, as well as a 45° wedge geometry with variable radiative properties. The new boundary conditions have been applied for both test cases, and the boundary condition for mixed diffuse-specular surfaces is further illustrated by numerical examples of a rectangular geometry enclosed by walls with different surface characteristics.
NASA Astrophysics Data System (ADS)
Kushwaha, Hari Mohan; Sahu, S. K.
2014-12-01
In this paper, second order velocity slip and temperature jump boundary conditions are used to solve the momentum and energy equations along with isoflux thermal boundary condition at the surface of the micropipe. The flow is assumed to be hydrodynamically and thermally fully developed inside the micropipe and viscous dissipation is included in the analysis. The solution yields closed form expressions for the temperature field and Nusselt number ( Nu) as a function of various modeling parameters, namely, Knudsen number and Brinkman number ( Br). For the given values of Br, the maximum difference of Nu between continuum flow with first order slip model and continuum and, second order slip model is found to be 35.67 and 34.62 %, respectively. Present solution exhibits good agreement with the other theoretical models.
NASA Technical Reports Server (NTRS)
Zingg, D. W.; Lomax, H.
1993-01-01
A six-stage low-storage Runge-Kutta time-marching method is presented and shown to be an efficient method for use with high-accuracy spatial difference operators for wave propagation problems. The accuracy of the method for inhomogeneous ordinary differential equations is demonstrated through numerical solutions of the linear convection equation with forced boundary conditions. Numerical experiments are presented simulating a sine wave and a Gaussian pulse propagating into and through the domain. For practical levels of mesh refinement corresponding to roughly ten points per wavelength, the six-stage Runge-Kutta method is more accurate than the popular fourth-order Runge-Kutta method. Further numerical experiments are presented which show that the numerical boundary scheme at an inflow boundary can be a significant source of error when high-accuracy spatial discretizations are used.
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).
NASA Astrophysics Data System (ADS)
Alonso-Mallo, I.; Portillo, A. M.
2016-04-01
Klein-Gordon equations on an unbounded domain are considered in one dimensional and two dimensional cases. Numerical computation is reduced to a finite domain by using the Hagstrom-Warburton (H-W) high-order absorbing boundary conditions (ABCs). Time integration is made by means of exponential splitting schemes that are efficient and easy to implement. In this way, it is possible to achieve a negligible error due to the time integration and to study the behavior of the absorption error. Numerical experiments displaying the accuracy of the numerical solution for the two dimensional case are provided. The influence of the dispersion coefficient on the error is also studied.
NASA Astrophysics Data System (ADS)
Kanellopoulos, V. N.; Webb, J. P.
1993-03-01
A 3D vector analysis of plane wave scattering by a metallic sphere using finite elements and Absorbing Boundary Conditions (ABCs) is presented. The ABCs are applied on the outer surface that truncates the infinitely extending domain. Mixed order curvilinear covariantprojection elements are used to avoid spurious corruptions. The second order ABC is superior to the first at no extra computational cost. The errors due to incomplete absorption decrease as the outer surface is moved further away from the scatterer. An error of about 1% in near-field values was obtained with the second order ABC, when the outer surface was less than half a wavelength from the scatterer. Une analyse tridimensionnelle vectorielle de la diffusion d'onde plane sur une sphère métallique utilisant des éléments finis et des Conditions aux Limites Absorbantes (CLA) est présentée. Les CLA sont appliquées sur la surface exteme tronquant le domaine s'étendant à l'infini. Des éléments curvilignes mixtes utilisant des projections covariantes sont utilisés pour éviter des solutions parasites. La CLA de second ordre est supérieure à celle de premier ordre sans effort de calcul additionnel. Les erreurs dues à l'absorption incomplète décroissent à mesure que l'on déplace la surface externe à une distance croissante du diffuseur. Un taux d'erreur d'environ 1 % dans les valeurs du champ proche a été obtenu avec les CLA de second ordre lorsque la surface externe était placée à une distance inférieure à une demi-longueur de la source de diffusion.
NASA Technical Reports Server (NTRS)
Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul
1993-01-01
We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems. First, a roper summation-by-parts formula is found for the approximate derivative. A 'simultaneous approximation term' (SAT) is then introduced to treat the boundary conditions. This procedure leads to time-stable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach.
NASA Technical Reports Server (NTRS)
Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul
1994-01-01
We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems. First a proper summation-by-parts formula is found for the approximate derivative. A 'simultaneous approximation term' is then introduced to treat the boundary conditions. This procedure leads to time-stable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach.
Numerical 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.
NASA Astrophysics Data System (ADS)
Minale, Mario
2016-02-01
In this paper, a stress boundary condition at the interface between a porous medium saturated by a viscoelastic fluid and the free viscoelastic fluid is derived. The volume averages are used to upscale the problem. The boundary condition is obtained on the assumption that the free fluid stress is transferred partially to the fluid within the porous medium and partially to the solid skeleton. To this end the momentum balance on the solid skeleton saturated by the viscoelastic fluid is derived and a generalised Biot's equation is obtained, which is coupled with the generalised Brinkman's equation derived in Part I of the paper. They together state that the whole stress carried by the porous medium, sum of that of the fluid and that of the solid skeleton, is not dissipated. The boundary condition here derived does not show any stress jump and as in Part I, to emphasize the effect of elasticity, a second order fluid of Coleman and Noll is considered as viscoelastic fluid. Also the stress boundary condition at the interface between a homogeneous solid and the porous medium saturated by the viscoelastic fluid is obtained.
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.
NASA Astrophysics Data System (ADS)
Das, Dilip
2015-07-01
There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle these kind of mixed boundary-value problems associated with the Laplace's equation (or Helmholtz equation) arising in the study of waves propagating through solids or fluids. One of the widely used methods in wave structure interaction is the multipole expansion method. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace's equation or two-dimensional Helmholz equation. Construction of these wave-free potentials and multipoles are presented here in a systematic manner for a number of situations such as two-dimensional non-oblique and oblique waves, three dimensional waves in two-layer fluid with free surface condition with higher order partial derivative are considered. In particular, these are obtained taking into account of the effect of the presence of surface tension at the free surface and also in the presence of an ice-cover modelled as a thin elastic plate. Also for limiting case, it can be shown that the multipoles and wave-free potential functions go over to the single layer multipoles and wave-free potential.
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
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.
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.
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)
Volakis, John L.
1991-01-01
There are two tasks described in this report. First, an extension of a two dimensional formulation is presented for a three dimensional body of revolution. A Fourier series expansion of the vector electric and magnetic fields is employed to reduce the dimensionality of the system, and an exact boundary condition is employed to terminate the mesh. The mesh termination boundary is chosen such that it leads to convolutional boundary operators for low O(n) memory demand. Second, rigorous uniform geometrical theory of diffraction (UTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. Ray solutions are obtained which remain valid in the transition region and reduce uniformly those in the deep lit and shadow regions. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder.
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.
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.
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
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.
NASA Technical Reports Server (NTRS)
Volakis, John L.
1990-01-01
There are two tasks described in this report. First, an extension of a two dimensional formulation is presented for a three dimensional body of revolution. With the introduction of a Fourier expansion of the vector electric and magnetic fields, a coupled two dimensional system is generated and solved via the finite element method. An exact boundary condition is employed to terminate the mesh and the fast fourier transformation is used to evaluate the boundary integrals for low O(n) memory demand when an iterative solution algorithm is used. Second, the diffraction by a material discontinuity in a thick dielectric/ferrite layer is considered by modeling the layer as a distributed current sheet obeying generalized sheet transition conditions (GSTC's).
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.
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\
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.
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.
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.
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.
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.
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.
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.
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.
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 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.
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.
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.
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.
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.
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.
Uneven-order decentered Shapiro filters for boundary filtering
NASA Astrophysics Data System (ADS)
Falissard, F.
2015-07-01
This paper addresses the use of Shapiro filters for boundary filtering. A new class of uneven-order decentered Shapiro filters is proposed and compared to classical Shapiro filters and even-order decentered Shapiro filters. The theoretical analysis shows that the proposed boundary filters are more accurate than the centered Shapiro filters and more robust than the even-order decentered boundary filters usable at the same distance to the boundary. The benefit of the new boundary filters is assessed for computations using the compressible Euler equations.
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.
Inflow/Outflow Boundary Conditions with Application to FUN3D
NASA Technical Reports Server (NTRS)
Carlson, Jan-Renee
2011-01-01
Several boundary conditions that allow subsonic and supersonic flow into and out of the computational domain are discussed. These boundary conditions are demonstrated in the FUN3D computational fluid dynamics (CFD) code which solves the three-dimensional Navier-Stokes equations on unstructured computational meshes. The boundary conditions are enforced through determination of the flux contribution at the boundary to the solution residual. The boundary conditions are implemented in an implicit form where the Jacobian contribution of the boundary condition is included and is exact. All of the flows are governed by the calorically perfect gas thermodynamic equations. Three problems are used to assess these boundary conditions. Solution residual convergence to machine zero precision occurred for all cases. The converged solution boundary state is compared with the requested boundary state for several levels of mesh densities. The boundary values converged to the requested boundary condition with approximately second-order accuracy for all of the cases.
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.
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
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.
NASA Astrophysics Data System (ADS)
Huang, Juntao; Hu, Zexi; Yong, Wen-An
2016-04-01
In this paper, we present a kind of second-order curved boundary treatments for the lattice Boltzmann method solving two-dimensional convection-diffusion equations with general nonlinear Robin boundary conditions. The key idea is to derive approximate boundary values or normal derivatives on computational boundaries, with second-order accuracy, by using the prescribed boundary condition. Once the approximate information is known, the second-order bounce-back schemes can be perfectly adopted. Our boundary treatments are validated with a number of numerical examples. The results show the utility of our boundary treatments and very well support our theoretical predications on the second-order accuracy thereof. The idea is quite universal. It can be directly generalized to 3-dimensional problems, multiple-relaxation-time models, and the Navier-Stokes equations.
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.
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.
A dispersive boundary condition for microstrip component analysis using the FD-TD method
NASA Astrophysics Data System (ADS)
Bi, Zhiqiang; Wu, Keli; Wu, Chen; Litva, John
1992-04-01
A dispersive absorbing boundary condition (DBC) is presented, which allows the dispersion characteristics of waves to be used as a criterion for designing absorbing boundary conditions. Its absorbing quality is superior to that of the presently used Mur's first order boundary condition for microstrip component analysis, and, as well, its implementation is much simpler when compared to that of the 'super boundary condition' treatment. Due to the significant performance improvement of the new boundary condition, the memory requirement can be reduced greatly when applying this boundary condition to microstrip component analysis.
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
NASA Technical Reports Server (NTRS)
Biringen, S.; Cook, C.
1988-01-01
Pressure boundary conditions satisfying the normal momentum equation at solid boundaries with second-order accuracy are developed. Implementation of these conditions in an explicit numerical procedure for the two-dimensional incompressible Navier-Stokes equations enables convergent and accurate solutions for the driven cavity problem provided that the integral constraint of the Neumann boundary condtions is satisfied.
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.
10 CFR 590.402 - Conditional orders.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 10 Energy 4 2014-01-01 2014-01-01 false Conditional orders. 590.402 Section 590.402 Energy... WITH RESPECT TO THE IMPORT AND EXPORT OF NATURAL GAS Opinions and Orders § 590.402 Conditional orders. The Assistant Secretary may issue a conditional order at any time during a proceeding prior...
Atomically ordered solute segregation behaviour in an oxide grain boundary
NASA Astrophysics Data System (ADS)
Feng, Bin; Yokoi, Tatsuya; Kumamoto, Akihito; Yoshiya, Masato; Ikuhara, Yuichi; Shibata, Naoya
2016-03-01
Grain boundary segregation is a critical issue in materials science because it determines the properties of individual grain boundaries and thus governs the macroscopic properties of materials. Recent progress in electron microscopy has greatly improved our understanding of grain boundary segregation phenomena down to atomistic dimensions, but solute segregation is still extremely challenging to experimentally identify at the atomic scale. Here, we report direct observations of atomic-scale yttrium solute segregation behaviours in an yttria-stabilized-zirconia grain boundary using atomic-resolution energy-dispersive X-ray spectroscopy analysis. We found that yttrium solute atoms preferentially segregate to specific atomic sites at the core of the grain boundary, forming a unique chemically-ordered structure across the grain boundary.
Atomically ordered solute segregation behaviour in an oxide grain boundary
Feng, Bin; Yokoi, Tatsuya; Kumamoto, Akihito; Yoshiya, Masato; Ikuhara, Yuichi; Shibata, Naoya
2016-01-01
Grain boundary segregation is a critical issue in materials science because it determines the properties of individual grain boundaries and thus governs the macroscopic properties of materials. Recent progress in electron microscopy has greatly improved our understanding of grain boundary segregation phenomena down to atomistic dimensions, but solute segregation is still extremely challenging to experimentally identify at the atomic scale. Here, we report direct observations of atomic-scale yttrium solute segregation behaviours in an yttria-stabilized-zirconia grain boundary using atomic-resolution energy-dispersive X-ray spectroscopy analysis. We found that yttrium solute atoms preferentially segregate to specific atomic sites at the core of the grain boundary, forming a unique chemically-ordered structure across the grain boundary. PMID:27004614
Multiple Positive Solutions in the Second Order Autonomous Nonlinear Boundary Value Problems
NASA Astrophysics Data System (ADS)
Atslega, Svetlana; Sadyrbaev, Felix
2009-09-01
We construct the second order autonomous equations with arbitrarily large number of positive solutions satisfying homogeneous Dirichlet boundary conditions. Phase plane approach and bifurcation of solutions are the main tools.
10 CFR 590.402 - Conditional orders.
Code of Federal Regulations, 2012 CFR
2012-01-01
... WITH RESPECT TO THE IMPORT AND EXPORT OF NATURAL GAS Opinions and Orders § 590.402 Conditional orders... issuance of a final opinion and order. The conditional order shall include the basis for not issuing a final opinion and order at that time and a statement of findings and conclusions. The findings...
10 CFR 590.402 - Conditional orders.
Code of Federal Regulations, 2011 CFR
2011-01-01
... WITH RESPECT TO THE IMPORT AND EXPORT OF NATURAL GAS Opinions and Orders § 590.402 Conditional orders... issuance of a final opinion and order. The conditional order shall include the basis for not issuing a final opinion and order at that time and a statement of findings and conclusions. The findings...
An Explicit Time-Domain Hybrid Formulation Based on the Unified Boundary Condition
Madsen, N; Fasenfest, B J; White, D; Stowell, M; Jandhyala, V; Pingenot, J; Champagne, N J; Rockway, J D
2007-02-28
An approach to stabilize the two-surface, time domain FEM/BI hybrid by means of a unified boundary condition is presented. The first-order symplectic finite element formulation [1] is used along with a version of the unified boundary condition of Jin [2] reformulated for Maxwell's first-order equations in time to provide both stability and accuracy over the first-order ABC. Several results are presented to validate the numerical solutions. In particular the dipole in a free-space box is analyzed and compared to the Dirchlet boundary condition of Ziolkowski and Madsen [3] and to a Neuman boundary condition approach.
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.
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.
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.
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
Counterbalancing for Serial Order Carryover Effects in Experimental Condition Orders
ERIC Educational Resources Information Center
Brooks, Joseph L.
2012-01-01
Reactions of neural, psychological, and social systems are rarely, if ever, independent of previous inputs and states. The potential for serial order carryover effects from one condition to the next in a sequence of experimental trials makes counterbalancing of condition order an essential part of experimental design. Here, a method is proposed…
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.
Numerical solutions of telegraph equations with the Dirichlet boundary condition
NASA Astrophysics Data System (ADS)
Ashyralyev, Allaberen; Turkcan, Kadriye Tuba; Koksal, Mehmet Emir
2016-08-01
In this study, the Cauchy problem for telegraph equations in a Hilbert space is considered. Stability estimates for the solution of this problem are presented. The third order of accuracy difference scheme is constructed for approximate solutions of the problem. Stability estimates for the solution of this difference scheme are established. As a test problem to support theoretical results, one-dimensional telegraph equation with the Dirichlet boundary condition is considered. Numerical solutions of this equation are obtained by first, second and third order of accuracy difference schemes.
Hyporheic exchange controlled by dynamic hydrologic boundary conditions
NASA Astrophysics Data System (ADS)
Schmadel, Noah M.; Ward, Adam S.; Lowry, Christopher S.; Malzone, Jonathan M.
2016-05-01
The relative roles of dynamic hydrologic forcing and geomorphology as controls on the timescales and magnitudes of stream-aquifer exchange and hyporheic flow paths are unknown but required for management of stream corridors. We developed a comprehensive framework relating diel hydrologic fluctuations to hyporheic exchange in the absence of geomorphic complexity. We simulated groundwater flow through an aquifer bounded by a straight stream and hillslope and under time-varying boundary conditions. We found that diel fluctuations can produce hyporheic flow path lengths and residence times that span orders of magnitude. With these results, hyporheic flow path residence times and lengths can be predicted from the timing and magnitude of diel fluctuations and valley slope. Finally, we demonstrated that dynamic hydrologic boundary conditions can produce spatial and temporal scales of hyporheic flow paths equivalent to those driven by many well-studied geomorphic features, indicating that these controls must be considered together in future efforts of upscaling to stream networks.
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.
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.
Immersed boundary conditions method for computational fluid dynamics problems
NASA Astrophysics Data System (ADS)
Husain, Syed Zahid
This dissertation presents implicit spectrally-accurate algorithms based on the concept of immersed boundary conditions (IBC) for solving a range of computational fluid dynamics (CFD) problems where the physical domains involve boundary irregularities. Both fixed and moving irregularities are considered with particular emphasis placed on the two-dimensional moving boundary problems. The physical model problems considered are comprised of the Laplace operator, the biharmonic operator and the Navier-Stokes equations, and thus cover the most commonly encountered types of operators in CFD analyses. The IBC algorithm uses a fixed and regular computational domain with flow domain immersed inside the computational domain. Boundary conditions along the edges of the time-dependent flow domain enter the algorithm in the form of internal constraints. Spectral spatial discretization for two-dimensional problems is based on Fourier expansions in the stream-wise direction and Chebyshev expansions in the normal-to-the-wall direction. Up to fourth-order implicit temporal discretization methods have been implemented. The IBC algorithm is shown to deliver the theoretically predicted accuracy in both time and space. Construction of the boundary constraints in the IBC algorithm provides degrees of freedom in excess of that required to formulate a closed system of algebraic equations. The 'classical IBC formulation' works by retaining number boundary constraints that are just sufficient to form a closed system of equations. The use of additional boundary constraints leads to the 'over-determined formulation' of the IBC algorithm. Over-determined systems are explored in order to improve the accuracy of the IBC method and to expand its applicability to more extreme geometries. Standard direct over-determined solvers based on evaluation of pseudo-inverses of the complete coefficient matrices have been tested on three model problems, namely, the Laplace equation, the biharmonic equation
MULTIRESOLUTION REPRESENTATION OF OPERATORS WITH BOUNDARY CONDITIONS ON SIMPLE DOMAINS
Beylkin, Gregory; Fann, George I; Harrison, Robert J; Kurcz, Christopher E; Monzon, Lucas A
2011-01-01
We develop a multiresolution representation of a class of integral operators satisfying boundary conditions on simple domains in order to construct fast algorithms for their application. We also elucidate some delicate theoretical issues related to the construction of periodic Green s functions for Poisson s equation. By applying the method of images to the non-standard form of the free space operator, we obtain lattice sums that converge absolutely on all scales, except possibly on the coarsest scale. On the coarsest scale the lattice sums may be only conditionally convergent and, thus, allow for some freedom in their definition. We use the limit of square partial sums as a definition of the limit and obtain a systematic, simple approach to the construction (in any dimension) of periodized operators with sparse non-standard forms. We illustrate the results on several examples in dimensions one and three: the Hilbert transform, the projector on divergence free functions, the non-oscillatory Helmholtz Green s function and the Poisson operator. Remarkably, the limit of square partial sums yields a periodic Poisson Green s function which is not a convolution. Using a short sum of decaying Gaussians to approximate periodic Green s functions, we arrive at fast algorithms for their application. We further show that the results obtained for operators with periodic boundary conditions extend to operators with Dirichlet, Neumann, or mixed boundary conditions.
Lee, T.; Leaf, G. K.; Mathematics and Computer Science; The City Univ. of New York
2009-04-01
We propose an Eulerian description of the bounce-back boundary condition based on the high-order implicit time-marching schemes to improve the accuracy of lattice Boltzmann simulation in the vicinity of curved boundary. The Eulerian description requires only one grid spacing between fluid nodes when second-order accuracy in time and space is desired, although high-order accurate boundary conditions can be constructed on more grid-point support. The Eulerian description also provides an analytical framework for several different interpolation-based boundary conditions. For instance, the semi-Lagrangian, linear interpolation boundary condition is found to be a first-order upwind discretization that changes the time-marching schemes from implicit to explicit as the distance between the fluid boundary node and the solid boundary increases.
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.
Study on plate silencer with general boundary conditions
NASA Astrophysics Data System (ADS)
Liu, Gongmin; Zhao, Xiaochen; Zhang, Wenping; Li, Shuaijun
2014-09-01
A plate silencer consists of an expansion chamber with two side-branch rigid cavities covered by plates. Previous studies showed that, in a duct, the introduction of simply supported or clamped plates into an air conveying system could achieve broadband quieting from low to medium frequencies. In this study, analytical formulation is extended to the plate silencer with general boundary conditions. A set of static beam functions, which are a combination of sine series and third-order polynomial, is employed as the trial functions of the plate vibration velocity. Greens function and Kirchhoff-Helmholtz integral are used to solve the sound radiation in the duct and the cavity, and then the vibration velocity of the plate is obtained. Having obtained the vibration velocity, the pressure perturbations induced by the plate oscillation and the transmission loss are found. Optimization is carried out in order to obtain the widest stopband. The transmission loss calculated by the analytical method agrees closely with the result of the finite element method simulation. Further studies with regard to the plate under several different classical boundary conditions based on the validated model show that a clamped-free plate silencer has the worst stopband. Attempts to release the boundary restriction of the plate are also made to study its effect on sound reflection. Results show that a softer end for a clamped-clamped plate silencer helps increase the optimal bandwidth, while the same treatment for simply supported plate silencer will result in performance degradation.
P-stable boundary value methods for second order IVPs
NASA Astrophysics Data System (ADS)
Aceto, Lidia; Ghelardoni, Paolo; Magherini, Cecilia
2012-09-01
We introduce a family of Linear Multistep Methods used as Boundary Value Methods for the numerical solution of initial value problems for second order ordinary differential equations of special type. The aim is to obtain P-stable methods with arbitrary order of accuracy. This result allows to overcome the order barrier established by Lambert and Watson which limited to p = 2 the maximum order of a P-stable Linear Multistep Method. In addition, an extension of the methods in the Exponential Fitting framework is also considered.
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.
A second order accurate embedded boundary method for the wave equation with Dirichlet data
Kreiss, H O; Petersson, N A
2004-03-02
The accuracy of Cartesian embedded boundary methods for the second order wave equation in general two-dimensional domains subject to Dirichlet boundary conditions is analyzed. Based on the analysis, we develop a numerical method where both the solution and its gradient are second order accurate. We avoid the small-cell stiffness problem without sacrificing the second order accuracy by adding a small artificial term to the Dirichlet boundary condition. Long-time stability of the method is obtained by adding a small fourth order dissipative term. Several numerical examples are provided to demonstrate the accuracy and stability of the method. The method is also used to solve the two-dimensional TM{sub z} problem for Maxwell's equations posed as a second order wave equation for the electric field coupled to ordinary differential equations for the magnetic field.
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.
Applying twisted boundary conditions for few-body nuclear systems
NASA Astrophysics Data System (ADS)
Körber, Christopher; Luu, Thomas
2016-05-01
We describe and implement twisted boundary conditions for the deuteron and triton systems within finite volumes using the nuclear lattice EFT formalism. We investigate the finite-volume dependence of these systems with different twist angles. We demonstrate how various finite-volume information can be used to improve calculations of binding energies in such a framework. Our results suggests that with appropriate twisting of boundaries, infinite-volume binding energies can be reliably extracted from calculations using modest volume sizes with cubic length L ≈8 -14 fm. Of particular importance is our derivation and numerical verification of three-body analogs of "i-periodic" twist angles that eliminate the leading-order finite-volume effects to the three-body binding energy.
Structural Anisotropy in Polar Fluids Subjected to Periodic Boundary Conditions
2011-01-01
A heuristic model based on dielectric continuum theory for the long-range solvation free energy of a dipolar system possessing periodic boundary conditions (PBCs) is presented. The predictions of the model are compared to simulation results for Stockmayer fluids simulated using three different cell geometries. The boundary effects induced by the PBCs are shown to lead to anisotropies in the apparent dielectric constant and the long-range solvation free energy of as much as 50%. However, the sum of all of the anisotropic energy contributions yields a value that is very close to the isotropic one derived from dielectric continuum theory, leading to a total system energy close to the dielectric value. It is finally shown that the leading-order contribution to the energetic and structural anisotropy is significantly smaller in the noncubic simulation cell geometries compared to when using a cubic simulation cell. PMID:22303290
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.
10 CFR 590.402 - Conditional orders.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 10 Energy 4 2010-01-01 2010-01-01 false Conditional orders. 590.402 Section 590.402 Energy DEPARTMENT OF ENERGY (CONTINUED) NATURAL GAS (ECONOMIC REGULATORY ADMINISTRATION) ADMINISTRATIVE PROCEDURES WITH RESPECT TO THE IMPORT AND EXPORT OF NATURAL GAS Opinions and Orders § 590.402 Conditional...
High-Order Accurate Solutions to the Helmholtz Equation in the Presence of Boundary Singularities
NASA Astrophysics Data System (ADS)
Britt, Darrell Steven, Jr.
Problems of time-harmonic wave propagation arise in important fields of study such as geological surveying, radar detection/evasion, and aircraft design. These often involve highfrequency waves, which demand high-order methods to mitigate the dispersion error. We propose a high-order method for computing solutions to the variable-coefficient inhomogeneous Helmholtz equation in two dimensions on domains bounded by piecewise smooth curves of arbitrary shape with a finite number of boundary singularities at known locations. We utilize compact finite difference (FD) schemes on regular structured grids to achieve highorder accuracy due to their efficiency and simplicity, as well as the capability to approximate variable-coefficient differential operators. In this work, a 4th-order compact FD scheme for the variable-coefficient Helmholtz equation on a Cartesian grid in 2D is derived and tested. The well known limitation of finite differences is that they lose accuracy when the boundary curve does not coincide with the discretization grid, which is a severe restriction on the geometry of the computational domain. Therefore, the algorithm presented in this work combines high-order FD schemes with the method of difference potentials (DP), which retains the efficiency of FD while allowing for boundary shapes that are not aligned with the grid without sacrificing the accuracy of the FD scheme. Additionally, the theory of DP allows for the universal treatment of the boundary conditions. One of the significant contributions of this work is the development of an implementation that accommodates general boundary conditions (BCs). In particular, Robin BCs with discontinuous coefficients are studied, for which we introduce a piecewise parameterization of the boundary curve. Problems with discontinuities in the boundary data itself are also studied. We observe that the design convergence rate suffers whenever the solution loses regularity due to the boundary conditions. This is
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.
A boundary value problem for first order strictly hyperbolic systems on the plane
NASA Astrophysics Data System (ADS)
Soldatov, Alexander P.; Zhura, Nikolay A.
2015-11-01
Boundary value problems, more precisely Dirichlet's problem for a string equation, or for an equivalent system of first order equations have been first studied in the first half of last century ([1] - [9]). The interest to these problems has been big ever since, see e.g. [10, 11]. All these papers have looked into the boundary value problems in a finite domains in the plane. Strictly hyperbolic systems with more than two characteristics in infinite domains, have been studied in [12, 13]. The question of boundary value problems for a hyperbolic system of equations with more than two characteristics in finite domain on the plane, when a boundary conditions are prescribed at a whole boundary of the domain, evidently remained open. In this paper, we study this problem in a finite domain on the plane for a hyperbolic system of equations of the first order with constant coefficients and with three mutually distinct characteristics.
Livshits, Gideon I.
2014-02-15
Superpotentials offer a direct means of calculating conserved charges associated with the asymptotic symmetries of space-time. Yet superpotentials have been plagued with inconsistencies, resulting in nonphysical or incongruent values for the mass, angular momentum, and energy loss due to radiation. The approach of Regge and Teitelboim, aimed at a clear Hamiltonian formulation with a boundary, and its extension to the Lagrangian formulation by Julia and Silva have resolved these issues, and have resulted in a consistent, well-defined and unique variational equation for the superpotential, thereby placing it on a firm footing. A hallmark solution of this equation is the KBL superpotential obtained from the first-order Lovelock Lagrangian. Nevertheless, here we show that these formulations are still insufficient for Lovelock Lagrangians of higher orders. We present a paradox, whereby the choice of fields affects the superpotential for equivalent on-shell dynamics. We offer two solutions to this paradox: either the original Lagrangian must be effectively renormalized, or that boundary conditions must be imposed, so that space-time be asymptotically maximally symmetric. Non-metricity is central to this paradox, and we show how quadratic non-metricity in the bulk of space-time contributes to the conserved charges on the boundary, where it vanishes identically. This is a realization of the gravitational Higgs mechanism, proposed by Percacci, where the non-metricity is the analogue of the Goldstone boson.
NASA Astrophysics Data System (ADS)
Livshits, Gideon I.
2014-02-01
Superpotentials offer a direct means of calculating conserved charges associated with the asymptotic symmetries of space-time. Yet superpotentials have been plagued with inconsistencies, resulting in nonphysical or incongruent values for the mass, angular momentum, and energy loss due to radiation. The approach of Regge and Teitelboim, aimed at a clear Hamiltonian formulation with a boundary, and its extension to the Lagrangian formulation by Julia and Silva have resolved these issues, and have resulted in a consistent, well-defined and unique variational equation for the superpotential, thereby placing it on a firm footing. A hallmark solution of this equation is the KBL superpotential obtained from the first-order Lovelock Lagrangian. Nevertheless, here we show that these formulations are still insufficient for Lovelock Lagrangians of higher orders. We present a paradox, whereby the choice of fields affects the superpotential for equivalent on-shell dynamics. We offer two solutions to this paradox: either the original Lagrangian must be effectively renormalized, or that boundary conditions must be imposed, so that space-time be asymptotically maximally symmetric. Non-metricity is central to this paradox, and we show how quadratic non-metricity in the bulk of space-time contributes to the conserved charges on the boundary, where it vanishes identically. This is a realization of the gravitational Higgs mechanism, proposed by Percacci, where the non-metricity is the analogue of the Goldstone boson.
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.
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.
NASA Astrophysics Data System (ADS)
Novak, Jérôme; Bonazzola, Silvano
2004-06-01
We present a new formulation of the multipolar expansion of an exact boundary condition for the wave equation, which is truncated at the quadrupolar order. Using an auxiliary function, that is the solution of a wave equation on the sphere defining the outer boundary of the numerical grid, the absorbing boundary condition is simply written as a perturbation of the usual Sommerfeld radiation boundary condition. It is very easily implemented using spectral methods in spherical coordinates. Numerical tests of the method show that very good accuracy can be achieved and that this boundary condition has the same efficiency for dipolar and quadrupolar waves as the usual Sommerfeld boundary condition for monopolar ones. This is of particular importance for the simulation of gravitational waves, which have dominant quadrupolar terms, in General Relativity.
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.
Evaluation of Far-Field Boundary Conditions for the Gust Response Problem
NASA Technical Reports Server (NTRS)
Scott, James R.; Kreider, Kevin L.; Heminger, John A.
2002-01-01
This paper presents a detailed situ dy of four far-field boundary conditions used in solving the single airfoil gust response problem. The boundary conditions, examined are the partial Sommerfeld radiation condition with only radial derivatives, the full Sommerfeld radiation condition with both radial and tangential derivatives, the Bayliss-Turkel condition of order one, and the Hagstrom-Hariharan condition of order one. The main objectives of the study were to determine which far-field boundary condition was most accurate, which condition was least sensitive to changes in grid. and which condition was best overall in terms of both accuracy and efficiency. Through a systematic study of the flat plate gust response problem, it was determined that the Hagstrom-Hariharan condition was most accurate, the Bayliss-Turkel condition was least sensitive to changes in grid, and Bayliss-Turkel was best in terms of both accuracy and efficiency.
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 Astrophysics Data System (ADS)
Deniz, Sinan; Bildik, Necdet
2016-06-01
In this paper, we use Adomian Decomposition Method (ADM) to solve the singularly perturbed fourth order boundary value problem. In order to make the calculation process easier, first the given problem is transformed into a system of two second order ODEs, with suitable boundary conditions. Numerical illustrations are given to prove the effectiveness and applicability of this method in solving these kinds of problems. Obtained results shows that this technique provides a sequence of functions which converges rapidly to the accurate solution of the problems.
NASA Astrophysics Data System (ADS)
Chu, Yuchuan; Cao, Yong; He, Xiaoming; Luo, Min
2011-11-01
Many of the magnetostatic/electrostatic field problems encountered in aerospace engineering, such as plasma sheath simulation and ion neutralization process in space, are not confined to finite domain and non-interface problems, but characterized as open boundary and interface problems. Asymptotic boundary conditions (ABC) and immersed finite elements (IFE) are relatively new tools to handle open boundaries and interface problems respectively. Compared with the traditional truncation approach, asymptotic boundary conditions need a much smaller domain to achieve the same accuracy. When regular finite element methods are applied to an interface problem, it is necessary to use a body-fitting mesh in order to obtain the optimal convergence rate. However, immersed finite elements possess the same optimal convergence rate on a Cartesian mesh, which is critical to many applications. This paper applies immersed finite element methods and asymptotic boundary conditions to solve an interface problem arising from electric field simulation in composite materials with open boundary. Numerical examples are provided to demonstrate the high global accuracy of the IFE method with ABC based on Cartesian meshes, especially around both interface and boundary. This algorithm uses a much smaller domain than the truncation approach in order to achieve the same accuracy.
Second-Order Conditioning in "Drosophila"
ERIC Educational Resources Information Center
Tabone, Christopher J.; de Belle, J. Steven
2011-01-01
Associative conditioning in "Drosophila melanogaster" has been well documented for several decades. However, most studies report only simple associations of conditioned stimuli (CS, e.g., odor) with unconditioned stimuli (US, e.g., electric shock) to measure learning or establish memory. Here we describe a straightforward second-order conditioning…
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 manufactured solution for verifying CFD boundary conditions: part II.
Bond, Ryan Bomar; Ober, Curtis Curry; Knupp, Patrick Michael
2005-01-01
Order-of-accuracy verification is necessary to ensure that software correctly solves a given set of equations. One method to verify the order of accuracy of a code is the method of manufactured solutions. In this study, a manufactured solution has been derived and implemented that allows verification of not only the Euler, Navier-Stokes, and Reynolds-Averaged Navier-Stokes (RANS) equation sets, but also some of their associated boundary conditions (BC's): slip, no-slip (adiabatic and isothermal), and outflow (subsonic, supersonic, and mixed). Order-of-accuracy verification has been performed for the Euler and Navier-Stokes equations and these BC's in a compressible computational fluid dynamics code. All of the results shown are on skewed, non-uniform meshes. RANS results will be presented in a future paper. The observed order of accuracy was lower than the expected order of accuracy in two cases. One of these cases resulted in the identification and correction of a coding mistake in the CHAD gradient correction that was reducing the observed order of accuracy. This mistake would have been undetectable on a Cartesian mesh. During the search for the CHAD gradient correction problem, an unrelated coding mistake was found and corrected. The other case in which the observed order of accuracy was less than expected was a test of the slip BC; although no specific coding or formulation mistakes have yet been identified. After the correction of the identified coding mistakes, all of the aforementioned equation sets and BC's demonstrated the expected (or at least acceptable) order of accuracy except the slip condition.
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
Spatial heterogeneity of ocean surface boundary conditions under sea ice
NASA Astrophysics Data System (ADS)
Barthélemy, Antoine; Fichefet, Thierry; Goosse, Hugues
2016-06-01
The high heterogeneity of sea ice properties implies that its effects on the ocean are spatially variable at horizontal scales as small as a few meters. Previous studies have shown that taking this variability into account in models could be required to simulate adequately mixed layer processes and the upper ocean temperature and salinity structures. Although many advanced sea ice models include a subgrid-scale ice thickness distribution, potentially providing heterogeneous surface boundary conditions, the information is lost in the coupling with a unique ocean grid cell underneath. The present paper provides a thorough examination of boundary conditions at the ocean surface in the NEMO-LIM model, which can be used as a guideline for studies implementing subgrid-scale ocean vertical mixing schemes. Freshwater, salt, solar heat and non-solar heat fluxes are examined, as well as the norm of the surface stress. All of the thermohaline fluxes vary considerably between the open water and ice fractions of grid cells. To a lesser extent, this is also the case for the surface stress. Moreover, the salt fluxes in both hemispheres and the solar heat fluxes in the Arctic show a dependence on the ice thickness category, with more intense fluxes for thinner ice, which promotes further subgrid-scale heterogeneity. Our analysis also points out biases in the simulated open water fraction and in the ice thickness distribution, which should be investigated in more details in order to ensure that the latter is used to the best advantage.
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.
Actions, topological terms and boundaries in first-order gravity: A review
NASA Astrophysics Data System (ADS)
Corichi, Alejandro; Rubalcava-García, Irais; Vukašinac, Tatjana
2016-03-01
In this review, we consider first-order gravity in four dimensions. In particular, we focus our attention in formulations where the fundamental variables are a tetrad eaI and a SO(3, 1) connection ωaIJ. We study the most general action principle compatible with diffeomorphism invariance. This implies, in particular, considering besides the standard Einstein-Hilbert-Palatini term, other terms that either do not change the equations of motion, or are topological in nature. Having a well defined action principle sometimes involves the need for additional boundary terms, whose detailed form may depend on the particular boundary conditions at hand. In this work, we consider spacetimes that include a boundary at infinity, satisfying asymptotically flat boundary conditions and/or an internal boundary satisfying isolated horizons boundary conditions. We focus on the covariant Hamiltonian formalism where the phase space Γ is given by solutions to the equations of motion. For each of the possible terms contributing to the action, we consider the well-posedness of the action, its finiteness, the contribution to the symplectic structure, and the Hamiltonian and Noether charges. For the chosen boundary conditions, standard boundary terms warrant a well posed theory. Furthermore, the boundary and topological terms do not contribute to the symplectic structure, nor the Hamiltonian conserved charges. The Noether conserved charges, on the other hand, do depend on such additional terms. The aim of this manuscript is to present a comprehensive and self-contained treatment of the subject, so the style is somewhat pedagogical. Furthermore, along the way, we point out and clarify some issues that have not been clearly understood in the literature.
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.
An experiment of rainfall infiltration under different boundary conditions
NASA Astrophysics Data System (ADS)
Hao, Shuang; Tong, Fuguo; Xue, Song
2016-04-01
Rainfall infiltration is a two-phase flow of water and gas, which should be simulated through solving the nonlinear governing equations of gas and water flow. In order to avoid the three main problems, such as convergence, numerical stability and computational efficiency in the solution of the nonlinear governing equations, Richard equation was usually used to simulate rainfall infiltration when the effect of gas phase could be ignored. The purpose of this work is to study the effect of boundary condition on rainfall infiltration, and to know in which cases Richard equation is available for the simulation of rainfall infiltration. The sample of soil has a height of 1200 mm. It is tightly enclosed in a toughened glass sleeve. The gas pressure is equal to the atmospheric pressure on the top surface of the model. The gas tight of its bottom can be controlled by a tap to simulate two different gas boundary conditions, permeable boundary and impermeable boundary. When the bottom of the model is not gas tight, the water infiltration rate is entirely bigger than gas tight. There is a big difference over the long time of rainfall that infiltration rate tends to be stable to 0.05cm/min when permeable but it is only 0.002cm/min when impermeable. The dramatic contrast reflects that gas paly a hindered part during rainfall infiltration. In addition, the gas pressure is obviously lower when the model is not gas tight. Although the pore gas pressure rise a little bit when water block gas, it is still same with atmospheric pressure all time. The situation is different when gas tight, the pore gas pressure increases sharply in the early stage and stable to a higher value, such as 10cm gas pressure on 67cm depth. Therefore, people basically negate the correlation between gas pressure and rainfall infiltration rate, but the evidence points out that the effect of gas pressure is in a significant position and Richard equations are not accurate under gas impermeable condition.
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.
Inverse Lax-Wendroff procedure for numerical boundary conditions of convection-diffusion equations
NASA Astrophysics Data System (ADS)
Lu, Jianfang; Fang, Jinwei; Tan, Sirui; Shu, Chi-Wang; Zhang, Mengping
2016-07-01
We consider numerical boundary conditions for high order finite difference schemes for solving convection-diffusion equations on arbitrary geometry. The two main difficulties for numerical boundary conditions in such situations are: (1) the wide stencil of the high order finite difference operator requires special treatment for a few ghost points near the boundary; (2) the physical boundary may not coincide with grid points in a Cartesian mesh and may intersect with the mesh in an arbitrary fashion. For purely convection equations, the so-called inverse Lax-Wendroff procedure [28], in which we convert the normal derivatives into the time derivatives and tangential derivatives along the physical boundary by using the equations, has been quite successful. In this paper, we extend this methodology to convection-diffusion equations. It turns out that this extension is non-trivial, because totally different boundary treatments are needed for the diffusion-dominated and the convection-dominated regimes. We design a careful combination of the boundary treatments for the two regimes and obtain a stable and accurate boundary condition for general convection-diffusion equations. We provide extensive numerical tests for one- and two-dimensional problems involving both scalar equations and systems, including the compressible Navier-Stokes equations, to demonstrate the good performance of our numerical boundary conditions.
Derivation of generalized transition/boundary conditions for planar multiple-layer structures
NASA Technical Reports Server (NTRS)
Ricoy, M. A.; Volakis, J. L.
1990-01-01
Infinite-order generalized impedance boundary conditions (GIBCs) and generalized sheet transition conditions (GSTCs) for planar multilayer configurations are developed via the Taylor series expansion method. The conditions are derived in a matrix product form where each matrix corresponds to a specific layer. An overall composite boundary/transition condition is obtained by making finite-order approximations to the elements of each matrix for the cases of 'low-contrast' and 'high-contrast' material layers. The accuracy of the truncated boundary conditions is examined by comparing their implied reflection and transmission coefficients with the corresponding exact coefficients. Design curves are also given which relate the maximum order of the conditions required to simulate a coating or layer of specific thickness and contrast. Expressions are then derived for the reflection and transmission coefficients of the GIBC/GSTC sheets, and these are compared to exact coefficients to demonstrate the validity of the derived GIBCs/GSTCs.
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.
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.
NASA Technical Reports Server (NTRS)
Beggs, John H.; Luebbers, Raymond J.; Kunz, Karl S.; Yee, Kane S.
1991-01-01
Surface impedance boundary conditions are used to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In a finite difference solution, they also can be used to avoid using small cells, made necessary by shorter wavelengths in conducting media, throughout the solution volume. A one dimensional implementation is presented for a surface impedance boundary condition for good conductors in the Finite Difference Time Domain (FDTD) technique. In order to illustrate the FDTD surface impedance boundary condition, a planar air-lossy dielectric interface is considered.
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.
Boundary conditions of the lattice Boltzmann method for convection-diffusion equations
NASA Astrophysics Data System (ADS)
Huang, Juntao; Yong, Wen-An
2015-11-01
In this paper, we employ an asymptotic analysis technique and construct two boundary schemes accompanying the lattice Boltzmann method for convection-diffusion equations with general Robin boundary conditions. One scheme is for straight boundaries, with the boundary points locating at any distance from the lattice nodes, and has second-order accuracy. The other is for curved boundaries, has only first-order accuracy and is much simpler than the existing schemes. Unlike those in the literature, our schemes involve only the current lattice node. Such a "single-node" boundary schemes are highly desirable for problems with complex geometries. The two schemes are validated numerically with a number of examples. The numerical results show the utility of the constructed schemes and very well support our theoretical predications.
Derivation and application of a class of generalized impedance boundary conditions, part 2
NASA Technical Reports Server (NTRS)
Volakis, J. L.; Senior, T. B. A.; Jin, J.-M.
1989-01-01
Boundary conditions involving higher order derivatives are presented by 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 non-planar 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 the uniform coating at least a quarter of a wavelength in thickness. Provided, though, some compromise in accuracy is acceptable, it is also shown that a third order condition may be sufficient for practical purposes when simulating uniform coatings.
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.
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.
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.
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.
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
A hybrid FEM-BEM unified boundary condition with sub-cycling for electromagnetic radiation
Fasenfest, B; White, D; Stowell, M; Rieben, R; Sharpe, R; Madsen, N; Rockway, J; Champagne, N J; Jandhyala, V; Pingenot, J
2006-01-12
Hybrid solutions to time-domain electromagnetic problems offer many advantages when solving open-region scattering or radiation problems. Hybrid formulations use a finite-element or finite-difference discretization for the features of interest, then bound this region with a layer of planar boundary elements. The use of volume discretization allows for intricate features and many changes in material within the structure, while the boundary-elements provide a highly accurate radiating boundary condition. This concept has been implemented previously, using the boundary elements to set the E-field, H-field, or both for an FDTD grid, for example in [1][2][3], or as a mixed boundary condition for the second order wave equation solved by finite elements [4]. Further study has focused on using fast methods, such as the Plane Wave Time Domain method [3][4] to accelerate the BEM calculations. This paper details a hybrid solver using the coupled first-order equations for the E and H fields in the finite-element region. This formulation is explicit, with a restriction on the time step for stability. When this time step is used in conjunction with the boundary elements forming either a inhomogeneous Dirichlet or Neuman boundary condition on the finite-element mesh, late time instabilities occur. To combat this, a Unified Boundary Condition (UBC), similar to the one in [4] for the second-order wave equation, is used. Even when this UBC is used, the late time instabilities are merely delayed if standard testing in time is used. However, the late time instabilities can be removed by replacing centroid based time interpolation with quadrature point based time interpolation for the boundary elements, or by sub-cycling the boundary element portion of the formulation. This sub-cycling, used in [3] for FDTD to reduce complexity, is shown here to improve stability and overall accuracy of the technique.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Hübler, G.; Parrish, D. D.; Aikin, K. C.; Oltmans, S. J.; Johnson, B. J.; Ives, M.; Thouret, V.; Nédélec, P.; Cammas, J.; Team, A.
2009-12-01
Most detailed photochemical modeling must be carried out at regional or air basin scales in order to achieve the spatial resolution and detailed treatment of the chemical mechanisms required for realistic treatment of local air quality. Consequently these models must define upwind boundary conditions at the edge of the model domain. Uncertainty in the appropriate boundary conditions contributes significantly to the overall uncertainty of the photochemical modeling in California. Here we will investigate the available data sets to define to the extent possible the average summertime oceanic boundary conditions, the variability about that average, and the horizontal and vertical variability of the boundary conditions. The data sets considered will include ozone sondes launched from Trinidad Head CA, ozone and carbon monoxide profiles measured by MOZAIC aircraft flights into 4 west coast US cities, and the many chemical species measured on four aircraft flights conducted during the CARB-ARCTAS campaign during summer 2008
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.
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.
Flux Based Surface Boundary Conditions for Navier-Stokes Simulations
NASA Astrophysics Data System (ADS)
Fertig, M.; Auweter-Kurtz, M.
2005-02-01
During re-entry high thermal combined with mechanical loads arise at the TPS surface of a re-entry vehicle. Due to low gas density, high Knudsen Numbers arise, which indicate rarefaction effects such as thermo-chemical non-equilibrium as well as temperature and velocity slip. With increasing altitude, local Knudsen Numbers predict the failure of continuum equations starting in the bow shock and at the surface. While local failure of the equations in the shock can be neglected for the determination of surface loads, local failure at the surface is not negligible. The validity of continuum models can be extended by emploing surface boundary equations accounting for temperature and velocity slip. A new flux based model has been developed originating on the Boltzmann Equation. Making use of the Enskog Method perturbed partition functions for a multi-component gas are determined from the Boltzmann Equation. By introduction of the moments of Boltzmann's Equation, Maxwell's Transport Equation can be obtained. Particles approaching the surface are distinguished from particles leaving the surface depending on their molecular velocities. Hence, mass, momentum and energy fluxes to the surface can be determined employing the collisional invariants. Reactive as well as scattering models can be easily introduced in order to compute the fluxes from the surface. Finally, flux differences are balanced with the continuum fluxes from the Navier-Stokes equations. Hence, the model is able to predict temperature and velocity slip at the surface of a re-entry vehicle under rarefied conditions. Moreover, it is valid in the continuum regime as well. The boundary equations are solved fully implicit and fully coupled with the non-equilibrium Navier-Stokes Code URANUS. Results are compared to DSMC simulations for the re-entry of the US Space Shuttle orbiter at high altitudes. Key words: Navier-Stokes; re-entry; slip; non-equilibrium.
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.
Numerical Simulation of Time-Dependent Wave Propagation Using Nonreflective Boundary Conditions
NASA Astrophysics Data System (ADS)
Ionescu, D.; Muehlhaus, H.
2003-12-01
Solving numerically the wave equation for modelling wave propagation on an unbounded domain with complex geometry requires a truncation of the domain, to fit the infinite region on a finite computer. Minimizing the amount of spurious reflections requires in many cases the introduction of an artificial boundary and of associated nonreflecting boundary conditions. Here, a question arises, namely which boundary condition guarantees that the solution of the time dependent problem inside the artificial boundary coincides with the solution of the original problem in the infinite region. Recent investigations have shown that the accuracy and performance of numerical algorithms and the interpretation of the results critically depend on the proper treatment of external boundaries. Despite the computational speed of finite difference schemes and the robustness of finite elements in handling complex geometries the resulting numerical error consists of two independent contributions: the discretization error of the numerical method used and the spurious reflection generated at the artificial boundary. This spurious contribution travels back and substantially degrades the accuracy of the solution everywhere in the computational domain. Unless both error components are reduced systematically, the numerical solution does not converge to the solution of the original problem in the infinite region. In the present study we present and discuss absorbing boundary condition techniques for the time-dependent scalar wave equation in three spatial dimensions. In particular, exact conditions that annihilate wave harmonics on a spherical artificial boundary up to a given order are obtained and subsequently applied in numerical simulations by employing a finite differences implementation.
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.
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
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.
Mathematical analysis of the Navier-Stokes equations with non standard boundary conditions
NASA Technical Reports Server (NTRS)
Tidriri, M. D.
1995-01-01
One of the major applications of the domain decomposition time marching algorithm is the coupling of the Navier-Stokes systems with Boltzmann equations in order to compute transitional flows. Another important application is the coupling of a global Navier-Stokes problem with a local one in order to use different modelizations and/or discretizations. Both of these applications involve a global Navier-Stokes system with nonstandard boundary conditions. The purpose of this work is to prove, using the classical Leray-Schauder theory, that these boundary conditions are admissible and lead to a well posed problem.
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
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.
An energy absorbing far-field boundary condition for the elastic wave equation
Petersson, N A; Sjogreen, B
2008-07-15
The authors present an energy absorbing non-reflecting boundary condition of Clayton-Engquist type for the elastic wave equation together with a discretization which is stable for any ratio of compressional to shear wave speed. They prove stability for a second order accurate finite-difference discretization of the elastic wave equation in three space dimensions together with a discretization of the proposed non-reflecting boundary condition. The stability proof is based on a discrete energy estimate and is valid for heterogeneous materials. The proof includes all six boundaries of the computational domain where special discretizations are needed at the edges and corners. The stability proof holds also when a free surface boundary condition is imposed on some sides of the computational domain.
Frequency and Time Domain Modeling of Acoustic Liner Boundary Conditions
NASA Technical Reports Server (NTRS)
Bliss, Donald B.
1982-01-01
reacting layers as described in Reference [2], was extended to apply to a broad range of liner types. This method included the effect of local gradients along the liner surface, and was particularly appropriate for situations with flow over the liner and grazing incidence acoustic fields. In order to utilize time domain computational methods to solve for the propfan acoustic field, corresponding liner boundary conditions were developed for time domain solutions rather than frequency domain solutions.
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.
Uddin, Mohammed J; Khan, Waqar A; Ismail, Ahmed I
2012-01-01
Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement. PMID:23166688
Uddin, Mohammed J.; Khan, Waqar A.; Ismail, Ahmed I.
2012-01-01
Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement. PMID:23166688
High Energy Boundary Conditions for a Cartesian Mesh Euler Solver
NASA Technical Reports Server (NTRS)
Pandya, Shishir; Murman, Scott; Aftosmis, Michael
2003-01-01
Inlets and exhaust nozzles are common place in the world of flight. Yet, many aerodynamic simulation packages do not provide a method of modelling such high energy boundaries in the flow field. For the purposes of aerodynamic simulation, inlets and exhausts are often fared over and it is assumed that the flow differences resulting from this assumption are minimal. While this is an adequate assumption for the prediction of lift, the lack of a plume behind the aircraft creates an evacuated base region thus effecting both drag and pitching moment values. In addition, the flow in the base region is often mis-predicted resulting in incorrect base drag. In order to accurately predict these quantities, a method for specifying inlet and exhaust conditions needs to be available in aerodynamic simulation packages. A method for a first approximation of a plume without accounting for chemical reactions is added to the Cartesian mesh based aerodynamic simulation package CART3D. The method consists of 3 steps. In the first step, a components approach where each triangle is assigned a component number is used. Here, a method for marking the inlet or exhaust plane triangles as separate components is discussed. In step two, the flow solver is modified to accept a reference state for the components marked inlet or exhaust. In the third step, the flow solver uses these separated components and the reference state to compute the correct flow condition at that triangle. The present method is implemented in the CART3D package which consists of a set of tools for generating a Cartesian volume mesh from a set of component triangulations. The Euler equations are solved on the resulting unstructured Cartesian mesh. The present methods is implemented in this package and its usefulness is demonstrated with two validation cases. A generic missile body is also presented to show the usefulness of the method on a real world geometry.
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.
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.
NASA Astrophysics Data System (ADS)
Träuble, Markus; Kirchner, Carolina Nunes; Wittstock, Gunther
2007-12-01
The use of the boundary element method (BEM) in simulating steady-state experiments of scanning electrochemical microscopy in feedback mode and in generation-collection mode using complex three dimensional geometries has been shown in previous papers. In the context of generation-collection mode experiments, catalytic reaction mechanisms of immobilized enzymes are of great interest. Due to the catalytic reaction behaviour, which can be described by nonlinear Michaelis-Menten kinetics, the modelling of such systems results in solving a diffusion equation with nonlinear boundary conditions. In this article it is described how such nonlinear reaction mechanisms can be treated with the BEM.
NASA Astrophysics Data System (ADS)
Jung, Narina; Seo, Hae Won; Yoo, Chun Sang
2015-12-01
Two-dimensional (2-D) characteristic boundary conditions (CBC) based on the characteristic analysis are formulated for the lattice Boltzmann methods (LBM). In this approach, the classical locally-one dimensional inviscid (LODI) relations are improved by recovering multi-dimensional effects on flows at open boundaries. The 2-D CBC are extended to a general subsonic flow configuration in the LBM and the effects of the transverse terms are clarified. From the vortex convection and vortex shedding problems, it is verified that the improved CBC shows better performance in accuracy compared to the conventional CBC approaches.
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 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
Flux change in viscous laminar flow under oscillating boundary condition
NASA Astrophysics Data System (ADS)
Ueda, R.; Mikada, H.; Goto, T.; Takekawa, J.
2012-12-01
The behavior of interstitial fluid is one of major interest in earth sciences in terms of the exploitation of water resources, the initiation of earthquakes, enhanced oil recovery (EOR), etc. Seismic waves are often known to increase the flux of interstitial fluid but the relationship between the flux and propagating seismic waves have not been well investigated in the past, although seismic stimulation has been applied in the oil industry for enhanced oil recovery (EOR). Many observations indicated that seismic waves could stimulate the oil production due to lowering of apparent viscosity coefficient, to the coalescence and/or the dispersion of droplets of a phase in multiphase fluids. However, the detailed mechanism of seismic stimulation has not been fully understood, either. In this study, We attempt to understand the mechanism of the flux change in viscous laminar flow under oscillating boundary condition for the simulation of interstitial flow. Here, we analyze a monophase flow in a pore throat. We first assume a Hagen-Poiseuille flow of incompressible fluid through a pore-throat in a porous medium. We adopt the Lattice Boltzmann method (LBM) in which the motion of fluid is simulated through the variation of velocity distribution function representing the distribution of discrete particle velocities. We use an improved incompressible LBKG model (d2q9i) proposed in Zou et. al. (1995) to accurately accommodate the boundary conditions of pressure and velocity in the Hagen-Poiseuille flow. We also use an half-way bounce back boundary condition as the velocity boundary condition. Also, we assume a uniform pressure (density) difference between inlet and outlet flow, and the density difference could initiate the flow in our simulation. The oscillating boundary condition is given by the body force acting on fluid particles. In this simulation, we found that the flux change is negligible under small amplitude of oscillation in both horizontal and vertical directions
Nondestructive evaluation of ceramic candle filter with various boundary conditions
Chen, H.L.; Kiriakidis, A.C.
2005-06-01
Nondestructive evaluation (NDE) using a dynamic characterization technique was conducted to study ceramic candle filters. Ceramic candle filters are hollow cylindrical structures made of porous ceramic materials used to protect gas turbine in coal-fired power plants. Deterioration and failure of ceramic filters occurs after being exposed to high-temperature and high-pressure operational environment over a period of time. This paper focuses on the development of an NDE method that can predict the in-situ structural stiffness of the candle filters while still being attached to the plenum. A combination of laboratory testing, theoretical analysis, and finite element method (FEM) simulations are presented. The candle filters were tested using a laser vibrometer/accelerometer setup with variable boundary restraints. A variable end-restraint Timoshenko beam equation was derived to determine the dynamic response of the candle filters with simulated in-situ boundary conditions. Results from the FEM simulation were verified with the analysis to determine the stiffness degradation of the candle filters as well as the boundary conditions. Results from this study show that the vibration characteristics can be used effectively to evaluate both the structural stiffness and the in-situ boundary restraints of the ceramic candle filters during field inspections.
The unified method: II. NLS on the half-line with t-periodic boundary conditions
NASA Astrophysics Data System (ADS)
Lenells, J.; Fokas, A. S.
2012-05-01
Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-line can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this general method to this particular class of problems yields the solution in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the complex k-plane (the Fourier plane), which has a jump matrix with explicit (x, t)-dependence involving four scalar functions of k, called spectral functions. Two of these functions depend on the initial data, whereas the other two depend on all boundary values. The most difficult step of the new method is the characterization of the latter two spectral functions in terms of the given initial and boundary data, i.e. the elimination of the unknown boundary values. For certain boundary conditions, called linearizable, this can be achieved by simply using algebraic manipulations. Here, we first present an effective characterization of the spectral functions in terms of the given initial and boundary data for the general case of non-linearizable boundary conditions. This characterization is based on the analysis of the so-called global relation and on the introduction of the so-called Gelfand-Levitan-Marchenko representations of the eigenfunctions defining the spectral functions. We then concentrate on the physically significant case of t-periodic Dirichlet boundary data. After presenting certain heuristic arguments which suggest that the Neumann boundary values become periodic as t → ∞, we show that for the case of the NLS with a sine-wave as Dirichlet data, the asymptotics of the Neumann boundary values can be computed explicitly at least up to third order in a perturbative expansion and indeed at least up to this order are asymptotically periodic.
New boundary conditions for AdS3
NASA Astrophysics Data System (ADS)
Compère, Geoffrey; Song, Wei; Strominger, Andrew
2013-05-01
New chiral boundary conditions are found for quantum gravity with matter on AdS3. The associated asymptotic symmetry group is generated by a single right-moving U(1) Kac-Moody-Virasoro algebra with {c_R}={3ℓ}/2G . The Kac-Moody zero mode generates global left-moving translations and equals, for a BTZ black hole, the sum of the total mass and spin. The level is positive about the global vacuum and negative in the black hole sector, corresponding to ergosphere formation. Realizations arising in Chern-Simons gravity and string theory are analyzed. The new boundary conditions are shown to naturally arise for warped AdS3 in the limit that the warp parameter is taken to zero.
Bond chaos in spin glasses revealed through thermal boundary conditions
NASA Astrophysics Data System (ADS)
Wang, Wenlong; Machta, Jonathan; Katzgraber, Helmut G.
2016-06-01
Spin glasses have competing interactions that lead to a rough energy landscape which is highly susceptible to small perturbations. These chaotic effects strongly affect numerical simulations and, as such, gaining a deeper understanding of chaos in spin glasses is of much importance. The use of thermal boundary conditions is an effective approach to study chaotic phenomena. Here we generalize population annealing Monte Carlo, combined with thermal boundary conditions, to study bond chaos due to small perturbations in the spin-spin couplings of the three-dimensional Edwards-Anderson Ising spin glass. We show that bond and temperature-induced chaos share the same scaling exponents and that bond chaos is stronger than temperature chaos.
A Boundary Condition for Simulation of Flow Over Porous Surfaces
NASA Technical Reports Server (NTRS)
Frink, Neal T.; Bonhaus, Daryl L.; Vatsa, Veer N.; Bauer, Steven X. S.; Tinetti, Ana F.
2001-01-01
A new boundary condition is presented.for simulating the flow over passively porous surfaces. The model builds on the prior work of R.H. Bush to eliminate the need for constructing grid within an underlying plenum, thereby simplifying the numerical modeling of passively porous flow control systems and reducing computation cost. Code experts.for two structured-grid.flow solvers, TLNS3D and CFL3D. and one unstructured solver, USM3Dns, collaborated with an experimental porosity expert to develop the model and implement it into their respective codes. Results presented,for the three codes on a slender forebody with circumferential porosity and a wing with leading-edge porosity demonstrate a good agreement with experimental data and a remarkable ability to predict the aggregate aerodynamic effects of surface porosity with a simple boundary condition.
Revisiting Johnson and Jackson boundary conditions for granular flows
Li, Tingwen; Benyahia, Sofiane
2012-07-01
In this article, we revisit Johnson and Jackson boundary conditions for granular flows. The oblique collision between a particle and a flat wall is analyzed by adopting the classic rigid-body theory and a more realistic semianalytical model. Based on the kinetic granular theory, the input parameter for the partial-slip boundary conditions, specularity coefficient, which is not measurable in experiments, is then interpreted as a function of the particle-wall restitution coefficient, the frictional coefficient, and the normalized slip velocity at the wall. An analytical expression for the specularity coefficient is suggested for a flat, frictional surface with a low frictional coefficient. The procedure for determining the specularity coefficient for a more general problem is outlined, and a working approximation is provided.
The high-order statistics of APG turbulent boundary layers
NASA Astrophysics Data System (ADS)
Maciel, Yvan; Gungor, Ayse G.; Simens, Mark P.; Soria, Julio
2013-11-01
One and two-point statistics are presented from a new direct numerical simulation of an adverse pressure gradient boundary layer, at Reθ = 250 - 2175 , in which the transition to turbulence is triggered by a trip wire which is modeled using the immersed boundary method. Mean velocity results in the attached turbulent region do not show log law profiles. Departure from the law of the wall occurs throughout the inner region. The production and Reynolds stress peaks move to roughly the middle of the boundary layer. The profiles of the uv correlation factor reveal that de-correlation between u and v takes place throughout the boundary layer, but especially near the wall, as the mean velocity defect increases. The non-dimensional stress ratios and quadrant analysis of uv indicate changes to the turbulence structure. The structure parameter is low, similar to equilibrium APG flows and mixing layers in the present flow and seems to be decreasing as the mean velocity defect increases. The statistics of the upper half of the APG flow show resemblance with results for a mixing layer. Funded in part by ITU, NSERC of Canada, ARC Discovery Grant, and Multiflow program of the ERC.
Entropy of bosonic open string and boundary conditions
NASA Astrophysics Data System (ADS)
Abdalla, M. C. B.; Graça, E. L.; Vancea, I. V.
2002-05-01
The entropy of the states associated to the solutions of the equations of motion of the bosonic open string with combinations of Neumann and Dirichlet boundary conditions is given. Also, the entropy of the string in the states Ai>=αi-10> and φa>=αa- 10> that describe the massless fields on the world-volume of the /Dp-brane is computed.
Stability analysis of intermediate boundary conditions in approximate factorization schemes
NASA Technical Reports Server (NTRS)
South, J. C., Jr.; Hafez, M. M.; Gottlieb, D.
1986-01-01
The paper discusses the role of the intermediate boundary condition in the AF2 scheme used by Holst for simulation of the transonic full potential equation. It is shown that the treatment suggested by Holst led to a restriction on the time step and ways to overcome this restriction are suggested. The discussion is based on the theory developed by Gustafsson, Kreiss, and Sundstrom and also on the von Neumann method.
Probabilistic flood hazard mapping: effects of uncertain boundary conditions
NASA Astrophysics Data System (ADS)
Domeneghetti, A.; Vorogushyn, S.; Castellarin, A.; Merz, B.; Brath, A.
2013-08-01
Comprehensive flood risk assessment studies should quantify the global uncertainty in flood hazard estimation, for instance by mapping inundation extents together with their confidence intervals. This appears of particular importance in the case of flood hazard assessments along dike-protected reaches, where the possibility of occurrence of dike failures may considerably enhance the uncertainty. We present a methodology to derive probabilistic flood maps in dike-protected flood prone areas, where several sources of uncertainty are taken into account. In particular, this paper focuses on a 50 km reach of River Po (Italy) and three major sources of uncertainty in hydraulic modelling and flood mapping: uncertainties in the (i) upstream and (ii) downstream boundary conditions, and (iii) uncertainties in dike failures. Uncertainties in the definition of upstream boundary conditions (i.e. design-hydrographs) are assessed through a copula-based bivariate analysis of flood peaks and volumes. Uncertainties in the definition of downstream boundary conditions are characterised by uncertainty in the rating curve with confidence intervals which reflect discharge measurement and interpolation errors. The effects of uncertainties in boundary conditions and randomness of dike failures are assessed by means of the Inundation Hazard Assessment Model (IHAM), a recently proposed hybrid probabilistic-deterministic model that considers three different dike failure mechanisms: overtopping, piping and micro-instability due to seepage. The results of the study show that the IHAM-based analysis enables probabilistic flood hazard mapping and provides decision-makers with a fundamental piece of information for devising and implementing flood risk mitigation strategies in the presence of various sources of uncertainty.
Some results for the primitive equations with physical boundary conditions
NASA Astrophysics Data System (ADS)
Evans, Lawrence Christopher; Gastler, Robert
2013-12-01
In this paper, we consider the (simplified) 3-dimensional primitive equations with physical boundary conditions. We show that the equations with constant forcing have a bounded absorbing ball in the H 1-norm and that a solution to the unforced equations has its H 1-norm decay to 0. From this, we argue that there exists an invariant measure (on H 1) for the equations under random kick-forcing.
Slarti: A boundary condition editor for a coupled climate model
NASA Astrophysics Data System (ADS)
Mickelson, S. A.; Jacob, R. L.; Pierrehumbert, R.
2006-12-01
One of the largest barriers to making climate models more flexible is the difficulty in creating new boundary conditions, especially for "deep time" paleoclimate cases where continents are in different positions. Climate models consist of several mutually-interacting component models and the boundary conditions must be consistent between them. We have developed a program called Slarti which uses a Graphical User Interface and a set of consistency rules to aid researchers in creating new, consistent, boundary condition files for the Fast Ocean Atmosphere Model (FOAM). Users can start from existing mask, topography, or bathymetry data or can build a "world" entirely from scratch (e.g. a single island continent). Once a case has been started, users can modify mask, vegetation, bathymetry, topography, and river flow fields by drawing new data through a "paint" interface. Users activate a synchronization button which goes through the fields to eliminate inconsistencies. When the changes are complete and save is selected, Slarti creates all the necessary files for an initial run of FOAM. The data is edited at the highest resolution (the ocean-land surface in FOAM) and then interpolated to the atmosphere resolution. Slarti was implemented in Java to maintain portability across platforms. We also relied heavily on Java Swing components to create the interface. This allowed us to create an object-oriented interface that could be used on many different systems. Since Slarti allows users to visualize their changes, they are able to see areas that may cause problems when the model is ran. Some examples would be lakes from the river flow field and narrow trenches within the bathymetry. Through different checks and options available through its interface, Slarti makes the process of creating new boundary conditions for FOAM easier and faster while reducing the chance for user errors.
The linking number in systems with Periodic Boundary Conditions
NASA Astrophysics Data System (ADS)
Panagiotou, E.
2015-11-01
Periodic Boundary Conditions (PBC) are often used for the simulation of complex physical systems. Using the Gauss linking number, we define the periodic linking number as a measure of entanglement for two oriented curves in a system employing PBC. In the case of closed chains in PBC, the periodic linking number is an integer topological invariant that depends on a finite number of components in the periodic system. For open chains, the periodic linking number is an infinite series that accounts for all the topological interactions in the periodic system. In this paper we give a rigorous proof that the periodic linking number is defined for the infinite system, i.e., that it converges for one, two, and three PBC models. It gives a real number that varies continuously with the configuration and gives a global measure of the geometric complexity of the system of chains. Similarly, for a single oriented chain, we define the periodic self-linking number and prove that it also is defined for open chains. In addition, we define the cell periodic linking and self-linking numbers giving localizations of the periodic linking numbers. These can be used to give good estimates of the periodic linking numbers in infinite systems. We also define the local periodic linking number associated to chains in the immediate cell neighborhood of a chain in order to study local linking measures in contrast to the global linking measured by the periodic linking numbers. Finally, we study and compare these measures when applied to a PBC model of polyethylene melts.
Artificial Boundary Conditions for Computation of Oscillating External Flows
NASA Technical Reports Server (NTRS)
Tsynkov, S. V.
1996-01-01
In this paper, we propose a new technique for the numerical treatment of external flow problems with oscillatory behavior of the solution in time. Specifically, we consider the case of unbounded compressible viscous plane flow past a finite body (airfoil). Oscillations of the flow in time may be caused by the time-periodic injection of fluid into the boundary layer, which in accordance with experimental data, may essentially increase the performance of the airfoil. To conduct the actual computations, we have to somehow restrict the original unbounded domain, that is, to introduce an artificial (external) boundary and to further consider only a finite computational domain. Consequently, we will need to formulate some artificial boundary conditions (ABC's) at the introduced external boundary. The ABC's we are aiming to obtain must meet a fundamental requirement. One should be able to uniquely complement the solution calculated inside the finite computational domain to its infinite exterior so that the original problem is solved within the desired accuracy. Our construction of such ABC's for oscillating flows is based on an essential assumption: the Navier-Stokes equations can be linearized in the far field against the free-stream back- ground. To actually compute the ABC's, we represent the far-field solution as a Fourier series in time and then apply the Difference Potentials Method (DPM) of V. S. Ryaben'kii. This paper contains a general theoretical description of the algorithm for setting the DPM-based ABC's for time-periodic external flows. Based on our experience in implementing analogous ABC's for steady-state problems (a simpler case), we expect that these boundary conditions will become an effective tool for constructing robust numerical methods to calculate oscillatory flows.
Shear rupture under constant normal stiffness boundary conditions
NASA Astrophysics Data System (ADS)
Bewick, R. P.; Kaiser, P. K.; Bawden, W. F.
2014-11-01
A grain based Distinct Element Method and its embedded Grain Based Method are used to simulate the fracturing processes leading to shear rupture zone creation in a calibrated massive (non-jointed) brittle rock specimen deformed in direct shear under constant normal stiffness boundary conditions. Under these boundary conditions, shear rupture zone creation relative to the shear stress versus applied horizontal displacement (load-displacement) curve occurs pre-peak, before the maximum peak shear strength is reached. This is found to be the result of a normal stress feedback process caused by the imposed shear displacement which couples increases in normal stress, due to rupture zone dilation, with shear stress, producing a complex normal-shear stress-path that reaches and then follows the rock's yield (strength) envelope. While the yield envelope is followed, the shear strength increases further and shear stress oscillations (repeated stress drops followed by re-strengthening periods) in the load-displacement curves occur due to fracture creation as the rupture zone geometry smoothens. Once the maximum peak strength is reached (after a series of shear stress oscillations) the largest stress drops occur as the ultimate or residual shear strength is approached. The simulation results provide insight into the fracturing process during rupture zone creation and improve the understanding of the shear stress versus applied horizontal displacement response, as well as the stick-slip behaviour of shear rupture zones that are being created under constant normal stiffness boundary conditions.
Surface flow boundary conditions in modeling land subsidence due to fluid withdrawal.
Baú, Domenico; Ferronato, Massimiliano; Gambolati, Giuseppe; Teatini, Pietro
2004-01-01
Land subsidence due to subsurface fluid (water, gas, oil) withdrawal is often predicted by either finite element or finite difference numerical models based on coupled poroelastic theory, where the soil is represented as a semi-infinite medium bounded by the traction-free (ground) surface. One of the variables playing a most important role on the final outcome is the flow condition used on the traction-free boundary, which may be assumed as either permeable or impermeable. Although occasionally justified, the assumption of no-flow surface seems to be in general rather unrealistic. A permeable boundary where the fluid pressure is fixed to the external atmospheric pressure appears to be more appropriate. This paper addresses the response, in terms of land subsidence, obtained with a coupled poroelastic finite element model that simulates a distributed pumping from a horizontal aquifer confined between two relatively impervious layers, and takes either a permeable boundary surface, i.e., constant hydraulic potential, or an impermeable boundary, i.e., a zero Neumann flow condition. The analysis reveals that land subsidence is rather sensitive to the flow condition implemented on the traction-free boundary. In general, the no-flow condition leads to an overestimate of the predicted ground surface settlement, which could even be 1 order of magnitude larger than that obtained with the permeable boundary. PMID:15318774
Permeable wall boundary conditions for transonic airfoil design
NASA Astrophysics Data System (ADS)
Leonard, O.; van den Braembussche, R.
This paper describes a method for the design of airfoils with prescribed Mach number or static pressure distribution along both the suction and pressure sides. The method consists of an iterative procedure, in which the final geometry is obtained through successive modifications of an existing shape. Each modification is computed by solving the Euler equations using permeable wall boundary conditions, in which the required Mach number distribution can be imposed on the airfoil wall. Since the classical slip condition is no longer imposed, the resulting flow is not tangent to the wall. A new geometry is created using this normal velocity component and a transpiration method.
Solitons induced by boundary conditions from the Boussinesq equation
NASA Technical Reports Server (NTRS)
Chou, Ru Ling; Chu, C. K.
1990-01-01
The behavior of solitons induced by boundary excitation is investigated at various time-dependent conditions and different unperturbed water depths, using the Korteweg-de Vries (KdV) equation. Then, solitons induced from Boussinesq equations under similar conditions were studied, making it possible to remove the restriction in the KdV equation and to treat soliton head-on collisions (as well as overtaking collisions) and reflections. It is found that the results obtained from the KdV and the Boussinesq equations are in good agreement.
High Energy Boundary Conditions for a Cartesian Mesh Euler Solver
NASA Technical Reports Server (NTRS)
Pandya, Shishir A.; Murman, Scott M.; Aftosmis, Michael J.
2004-01-01
Inlets and exhaust nozzles are often omitted or fared over in aerodynamic simulations of aircraft due to the complexities involving in the modeling of engine details such as complex geometry and flow physics. However, the assumption is often improper as inlet or plume flows have a substantial effect on vehicle aerodynamics. A tool for specifying inlet and exhaust plume conditions through the use of high-energy boundary conditions in an established inviscid flow solver is presented. The effects of the plume on the flow fields near the inlet and plume are discussed.
New Existence Conditions for Order Complementarity Problems
NASA Astrophysics Data System (ADS)
Németh, S. Z.
2009-09-01
Complementarity problems are mathematical models of problems in economics, engineering and physics. A special class of complementarity problems are the order complementarity problems [2]. Order complementarity problems can be applied in lubrication theory [6] and economics [1]. The notion of exceptional family of elements for general order complementarity problems in Banach spaces will be introduced. It will be shown that for general order complementarity problems defined by completely continuous fields the problem has either a solution or an exceptional family of elements (for other notions of exceptional family of elements see [1, 2, 3, 4] and the related references therein). This solves a conjecture of [2] about the existence of exceptional family of elements for order complementarity problems. The proof can be done by using the Leray-Schauder alternative [5]. An application to integral operators will be given.
On the nonlinear Schrodinger equation with nonzero boundary conditions
NASA Astrophysics Data System (ADS)
Fagerstrom, Emily
integral, provided the initial condition satisfies further conditions. Modulational instability (focusing NLS with symmetric nonzero boundary conditions at infinity.) The focusing NLS equation is considered with potentials that are "box-like" piecewise constant functions. Several results are obtained. In particular, it is shown that there are conditions on the parameters of the potential for which there are no discrete eigenvalues. Thus there is a class of potentials for which the corresponding solutions of the NLS equation have no solitons. Hence, solitons cannot be the medium for the modulational instability. This contradicts a recent conjecture by Zakharov. On the other hand, it is shown for a different class of potentials the scattering problem always has a discrete eigenvalue along the imaginary axis. Thus, there exist arbitrarily small perturbations of the constant potential for which solitons exist, so no area theorem is possible. The existence, number and location of discrete eigenvalues in other situations are studied numerically. Finally, the small-deviation limit of the IST is computed and compared with the direct linearization of the NLS equation around a constant background. From this it is shown that there is an interval of the continuous spectrum on which the eigenvalue is imaginary and the scattering parameter is imaginary. The Jost eigenfunctions corresponding to this interval are the nonlinear analogue of the unstable Fourier modes. Defocusing NLS equation with asymmetric boundary conditions at infinity. The defocusing NLS equation with asymmetric boundary conditions is considered. To do so, first the case of symmetric boundary conditions is revisited. While the IST for this case has been formulated in the literature, it is usually done through the use of a uniformization variable. This was done because the eigenvalues of the scattering problem have branching; the uniformization variable allows one to move from a 2-sheeted Riemann surface to the complex
Positivity and Almost Positivity of Biharmonic Green's Functions under Dirichlet Boundary Conditions
NASA Astrophysics Data System (ADS)
Grunau, Hans-Christoph; Robert, Frédéric
2010-03-01
In general, for higher order elliptic equations and boundary value problems like the biharmonic equation and the linear clamped plate boundary value problem, neither a maximum principle nor a comparison principle or—equivalently—a positivity preserving property is available. The problem is rather involved since the clamped boundary conditions prevent the boundary value problem from being reasonably written as a system of second order boundary value problems. It is shown that, on the other hand, for bounded smooth domains {Ω subsetmathbb{R}^n} , the negative part of the corresponding Green’s function is “small” when compared with its singular positive part, provided {n≥q 3} . Moreover, the biharmonic Green’s function in balls {Bsubsetmathbb{R}^n} under Dirichlet (that is, clamped) boundary conditions is known explicitly and is positive. It has been known for some time that positivity is preserved under small regular perturbations of the domain, if n = 2. In the present paper, such a stability result is proved for {n≥q 3}.
NASA Astrophysics Data System (ADS)
Sasaki, Kensuke; Suzuki, Yukihisa
A Mur type analytical absorbing boundary condition (A-ABC), which is based on the one-dimensional one-way wave equation, is proposed for multidimensional wave analysis by introducing the directional splitting technique. This new absorbing boundary condition is expansion of the first-order Mur. The absorbing ability, required memory, and calculation speed of the Mur type A-ABC are evaluated by comparison with those of conventional ABCs. The result indicated that absorbing ability of the proposed ABC is higher than the first-order Mur and lower than the second-order Mur at large incident angle. While, our proposed ABC has advantage in both required memory and calculation speed by comparison with the second-order Mur. Thus, effectivity of the proposed Mur type A-ABC is shown.
Equilibration and generalized Gibbs ensemble for hard wall boundary conditions
NASA Astrophysics Data System (ADS)
Goldstein, Garry; Andrei, Natan
2015-10-01
In this work we present an analysis of a quench for the repulsive Lieb-Liniger gas confined to a large box with hard wall boundary conditions. We study the time average of local correlation functions and show that both the quench action approach and the generalized Gibbs ensemble formalism are applicable for the long-time average of local correlation functions. We find that the time average of the system corresponds to an eigenstate of the Lieb-Liniger Hamiltonian and that this eigenstate is related to an eigenstate of a Lieb-Liniger Hamiltonian with periodic boundary conditions on an interval of twice the length and with twice as many particles (a doubled system). We further show that local operators with support far away from the boundaries of the hard wall have the same expectation values with respect to this eigenstate as corresponding operators for the doubled system. We present an example of a quench where the gas is initially confined in several moving traps and then released into a bigger container, an approximate description of the Newton's cradle experiment. We calculate the time average of various correlation functions for long times after the quench.
Electrostatics of solvated systems in periodic boundary conditions
NASA Astrophysics Data System (ADS)
Andreussi, Oliviero; Marzari, Nicola
2014-12-01
Continuum solvation methods can provide an accurate and inexpensive embedding of quantum simulations in liquid or complex dielectric environments. Notwithstanding a long history and manifold applications to isolated systems in open boundary conditions, their extension to materials simulations, typically entailing periodic boundary conditions, is very recent, and special care is needed to address correctly the electrostatic terms. We discuss here how periodic boundary corrections developed for systems in vacuum should be modified to take into account solvent effects, using as a general framework the self-consistent continuum solvation model developed within plane-wave density-functional theory [O. Andreussi et al., J. Chem. Phys. 136, 064102 (2012), 10.1063/1.3676407]. A comprehensive discussion of real- and reciprocal-space corrective approaches is presented, together with an assessment of their ability to remove electrostatic interactions between periodic replicas. Numerical results for zero- and two-dimensional charged systems highlight the effectiveness of the different suggestions, and underline the importance of a proper treatment of electrostatic interactions in first-principles studies of charged systems in solution.
Boundary condition handling approaches for the model reduction of a vehicle frame
NASA Astrophysics Data System (ADS)
Xie, Qingxi; Zhang, Nong; Zhang, Bangji; Ji, Jinchen
2016-06-01
In order to apply model reduction technique to improve the computational efficiency for the large-scale FEM model of a vehicle, this paper presents the handling approaches for three widely-used boundary conditions, namely fixed boundary condition (FBC), prescribed motion (PSM) and coupling (COUP), respectively. It is found that iterated improved reduction system (IIRS) reduction method tends to generate better reduction approximation. Guyan method is not sensitive to the sequence of reduction and constraint under FBC, and can thus provide flexibility in handling different boundary conditions for the same system. As for PSM, 'constraint first' is recommended no matter which reduction method is used, and then separate reduction models can be coupled to form a new model with relative small dofs. By selecting appropriate master dofs for model reduction, the coupled model based on reduced models could produce same results as the original full one.
Compatibility between shape equation and boundary conditions of lipid membranes with free edges.
Tu, Z C
2010-02-28
Only some special open surfaces satisfying the shape equation of lipid membranes can be compatible with the boundary conditions. As a result of this compatibility, the first integral of the shape equation should vanish for axisymmetric lipid membranes, from which two theorems of nonexistence are verified: (i) there is no axisymmetric open membrane being a part of torus satisfying the shape equation; (ii) there is no axisymmetric open membrane being a part of a biconcave discodal surface satisfying the shape equation. Additionally, the shape equation is reduced to a second-order differential equation while the boundary conditions are reduced to two equations due to this compatibility. Numerical solutions to the reduced shape equation and boundary conditions agree well with the experimental data [A. Saitoh et al., Proc. Natl. Acad. Sci. U.S.A. 95, 1026 (1998)]. PMID:20192294
A Formulation of Asymptotic and Exact Boundary Conditions Using Local Operators
NASA Technical Reports Server (NTRS)
Hagstrom, T.; Hariharan, S. I.
1998-01-01
In this paper we describe a systematic approach for constructing asymptotic boundary conditions for isotropic wave-like equations using local operators. The conditions take a recursive form with increasing order of accuracy. In three dimensions the recursion terminates and the resulting conditions are exact for solutions which are described by finite combinations of angular spherical harmonics. First, we develop the expansion for the two-dimensional wave equation and construct a sequence of easily implementable boundary conditions. We show that in three dimensions and analogous conditions are again easily implementable in addition to being exact. Also, we provide extensions of these ideas to hyperbolic systems. Namely, Maxwell's equations for TM waves are used to demonstrate the construction. Finally, we provide numerical examples to demonstrate the effectiveness of these conditions for a model problem governed by the wave equation.
Boundary conditions towards realistic simulation of jet engine noise
NASA Astrophysics Data System (ADS)
Dhamankar, Nitin S.
Strict noise regulations at major airports and increasing environmental concerns have made prediction and attenuation of jet noise an active research topic. Large eddy simulation coupled with computational aeroacoustics has the potential to be a significant research tool for this problem. With the emergence of petascale computer clusters, it is now computationally feasible to include the nozzle geometry in jet noise simulations. In high Reynolds number experiments on jet noise, the turbulent boundary layer on the inner surface of the nozzle separates into a turbulent free shear layer. Inclusion of a nozzle with turbulent inlet conditions is necessary to simulate this phenomenon realistically. This will allow a reasonable comparison of numerically computed noise levels with the experimental results. Two viscous wall boundary conditions are implemented for modeling the nozzle walls. A characteristic-based approach is compared with a computationally cheaper, extrapolation-based formulation. In viscous flow over a circular cylinder under two different regimes, excellent agreement is observed between the results of the two approaches. The results agree reasonably well with reference experimental and numerical results. Both the boundary conditions are thus found to be appropriate, the extrapolation-based formulation having an edge with its low cost. This is followed with the crucial step of generation of a turbulent boundary layer inside the nozzle. A digital filter-based turbulent inflow condition, extended in a new way to non-uniform curvilinear grids is implemented to achieve this. A zero pressure gradient flat plate turbulent boundary layer is simulated at a high Reynolds number to show that the method is capable of producing sustained turbulence. The length of the adjustment region necessary for synthetic inlet turbulence to recover from modeling errors is estimated. A low Reynolds number jet simulation including a round nozzle geometry is performed and the method
Functions with constant Laplacian satisfying homogeneous Robin boundary conditions
NASA Astrophysics Data System (ADS)
Keady, Grant; McNabb, Alex
1993-01-01
The authors study properties of real-valued functions u defined over {Omega}, a simply-connected domain in RN for which the Laplacian of u is constant in {Omega}, and which satisfy, on the boundary of {Omega}, the Robin boundary condition u+{beta}({partial}u/{partial}n)=0. Here n is the outward normal and {beta}[≥]0. When N=2 and {beta}=0, this is the classical St Venant torsion problem, but the concern in this paper is with N[≥]2 and {beta}[≥]0. Results concerning the magnitude um and location zm of the maximum value of u, and estimates for the functional S{beta}={int}{Omega}u, and the maxima pm and qm of |{nabla}u| and |{partial}u/{partial}n|, respectively, are established using comparison theorems and variational arguments.
Unified semi-analytical wall boundary conditions applied to 2-D incompressible SPH
NASA Astrophysics Data System (ADS)
Leroy, A.; Violeau, D.; Ferrand, M.; Kassiotis, C.
2014-03-01
This work aims at improving the 2-D incompressible SPH model (ISPH) by adapting it to the unified semi-analytical wall boundary conditions proposed by Ferrand et al. [10]. The ISPH algorithm considered is as proposed by Lind et al. [25], based on the projection method with a divergence-free velocity field and using a stabilising procedure based on particle shifting. However, we consider an extension of this model to Reynolds-Averaged Navier-Stokes equations based on the k-ɛ turbulent closure model, as done in [10]. The discrete SPH operators are modified by the new description of the wall boundary conditions. In particular, a boundary term appears in the Laplacian operator, which makes it possible to accurately impose a von Neumann pressure wall boundary condition that corresponds to impermeability. The shifting and free-surface detection algorithms have also been adapted to the new boundary conditions. Moreover, a new way to compute the wall renormalisation factor in the frame of the unified semi-analytical boundary conditions is proposed in order to decrease the computational time. We present several verifications to the present approach, including a lid-driven cavity, a water column collapsing on a wedge and a periodic schematic fish-pass. Our results are compared to Finite Volumes methods, using Volume of Fluids in the case of free-surface flows. We briefly investigate the convergence of the method and prove its ability to model complex free-surface and turbulent flows. The results are generally improved when compared to a weakly compressible SPH model with the same boundary conditions, especially in terms of pressure prediction.
Three dimensional dynamics of rotating structures under mixed boundary conditions
NASA Astrophysics Data System (ADS)
Bediz, Bekir; Romero, L. A.; Ozdoganlar, O. Burak
2015-12-01
This paper presents the spectral-Tchebychev (ST) technique for solution of three dimensional (3D) dynamics of rotating structures. In particular, structures that exhibit coupled dynamic response require a 3D modeling approach to capture their dynamic behavior. Rotational motions further complicate this behavior, inducing coriolis, centrifugal softening, and (nonlinear) stress-stiffening effects. Therefore, a 3D solution approach is needed to accurately capture the rotational dynamics. The presented 3D-ST technique provides a fast-converging and precise solution approach for rotational dynamics of structures with complex geometries and mixed boundary conditions. Specifically, unlike finite elements techniques, the presented technique uses a series expansion approach considering distributed-parameter system equations: The integral boundary value problem for rotating structures is discretized using the spectral-Tchebychev approach. To simplify the domain of the structures, cross-sectional and rotational transformations are applied to problems with curved cross-section and pretwisted geometry. The nonlinear terms included in the integral boundary value problem are linearized around an equilibrium solution using the quasi-static method. As a result, mass, damping, and stiffness matrices, as well as a forcing vector, are obtained for a given rotating structure. Several case studies are then performed to demonstrate the application and effectiveness of the 3D-ST solution. For each problem, the natural frequencies and modes shapes from the 3D-ST solution are compared to those from the literature (when available) and to those from a commercial finite elements software. The case studies include rotating/spinning parallelepipeds under free and mixed boundary conditions, and a cantilevered pretwisted beam (i.e., rotating blade) with an airfoil geometry rotating on a hub. It is seen that the natural frequencies and mode shapes from the 3D-ST technique differ from those from the
The dielectric boundary condition for the embedded curved boundary (ECB) method
Hewwitt, D. W., LLNL
1998-01-26
A new version of ECB has been completed that allows nonuniform grid spacing and a new dieledric boundary condition. ECB was developed to retain the simplicity and speed of an orthogonal mesh while capturing much of the fidelity of adaptive, unstructured finite element meshes. Codes based on orthogonal meshes are easy to work with and lead to well-posed elliptic and parabolic problems that are comparatively easy to solve. Generally, othogonal mesh representations lead to banded matrices while unstructured representations lead to more complicated sparse matrices. Recent advances in adapting banded linear systems to massively parallel computers reinforce our opinion that iterative field solutions utilizing banded matrix methods will continue to be competitive. Unfortunately, the underlying ``stair-step`` boundary representation in simple orthogonal mesh (and recent Adaptive Mesh Refinement) applications is inadequate. With ECB, the curved boundary is represented by piece-wise-linear representations of curved internal boundaries embedded into the orthogonal mesh- we build better, but not more, coefficients in the vicinity of these boundaries-and we use the surplus free energy on more ambitious physics models. ECB structures are constructed out of the superposition of analytically prescribed building blocks. In 2-D, we presently use a POLY4 (linear boundaries defined by 4 end points), an ANNULUS, (center, inner & outer radii, starting & stopping angle), a ROUND (starting point & angle, stopping point & angle, fillet radius). A link-list AIRFOIL has also been constructed. In the ECB scheme, we first find each intercept of the structure boundary with an I or J grid line is assigned an index K. We store the actual z,y value at the intercept, and the slope of the boundary at that intercept, in arrays whose index K is associated with the corresponding mesh point just inside the structure. In 2-D, a point just outside a structure may have up to 4 intercepts associated with it
Towards Multiphase Periodic Boundary Conditions with Flow Rate Constraint
NASA Astrophysics Data System (ADS)
Sawko, Robert; Thompson, Chris P.
2011-09-01
This paper presents the development of a solver for a two-phase, stratified flow with periodic boundary conditions. Governing equations are supplemented with a specification of constant mass fluxes for each phase. The method allows an estimate steady state phase fraction and pressure drop in the streamwise direction. The analytical solution for two-phase laminar flow is presented and serves as a validation of the numerical technique. For turbulent conditions, Reynolds-Averaged Navier-Stokes equations are employed and closed with a two-equation model. Experimental data is taken as a reference for the purpose of validation. In both flow conditions the method delivers accurate results although in the case of turbulent flow it requires the specification of interfacial viscosity showing that a direct generalisation of two-equation model is unsatisfactory. Further research avenues are outlined.
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.
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
Reflecting boundary conditions for graded p-n junctions
NASA Technical Reports Server (NTRS)
Schacham, S. E.
1990-01-01
In a graded junction, the formalism for handling reflecting boundary conditions must be modified. Since a significant drift term is present, zero recombination velocity at the surface does not imply a zero excess carrier gradient but rather zero overall flux. A model for analyzing p-n junctions fabricated by implantation or diffusion is presented, assuming the dominant recombination mechanism in the graded region is Auger. The model enables optimization of diode design. By proper selection of parameters, mainly by reducing surface concentration or by increasing the steepness of the dopant profile, it is possible to drastically reduce the saturation current generated by the graded region.
Proceedings for the ICASE Workshop on Heterogeneous Boundary Conditions
NASA Technical Reports Server (NTRS)
Perkins, A. Louise; Scroggs, Jeffrey S.
1991-01-01
Domain Decomposition is a complex problem with many interesting aspects. The choice of decomposition can be made based on many different criteria, and the choice of interface of internal boundary conditions are numerous. The various regions under study may have different dynamical balances, indicating that different physical processes are dominating the flow in these regions. This conference was called in recognition of the need to more clearly define the nature of these complex problems. This proceedings is a collection of the presentations and the discussion groups.
General rule for boundary conditions from the action principle
NASA Astrophysics Data System (ADS)
Steiner, Roee
2016-03-01
We construct models where initial and boundary conditions can be found from the fundamental rules of physics, without the need to assume them, they will be derived from the action principle. Those constraints are established from physical viewpoint, and it is not in the form of Lagrange multipliers. We show some examples from the past and some new examples that can be useful, where constraint can be obtained from the action principle. Those actions represent physical models. We show that it is possible to use our rule to get those constraints directly.
Reconnection properties in collisionless plasma with open boundary conditions
Sun, H. E.; Ma, Z. W.; Huang, J.
2014-07-15
Collisionless magnetic reconnection in a Harris current sheet with different initial thicknesses is investigated using a 21/2 -D Darwin particle-in-cell simulation with the magnetosonic open boundary condition. It is found that the thicknesses of the ion dissipation region and the reconnection current sheet, when the reconnection rate E{sub r} reaches its first peak, are independent of the initial thickness of the current sheet; while the peak reconnection rate depends on it. The peak reconnection rate increases with decrease of the current sheet thickness as E{sub r}∼a{sup −1/2}, where a is the initial current sheet half-thickness.
Bound states on the lattice with partially twisted boundary conditions
NASA Astrophysics Data System (ADS)
Agadjanov, D.; Guo, F.-K.; Ríos, G.; Rusetsky, A.
2015-01-01
We propose a method to study the nature of exotic hadrons by determining the wave function renormalization constant Z from lattice simulations. It is shown that, instead of studying the volume-dependence of the spectrum, one may investigate the dependence of the spectrum on the twisting angle, imposing twisted boundary conditions on the fermion fields on the lattice. In certain cases, e.g., the case of the DK bound state which is addressed in detail, it is demonstrated that the partial twisting is equivalent to the full twisting up to exponentially small corrections.
Hawking radiation, covariant boundary conditions, and vacuum states
Banerjee, Rabin; Kulkarni, Shailesh
2009-04-15
The basic characteristics of the covariant chiral current
Hawking radiation, effective actions and covariant boundary conditions
NASA Astrophysics Data System (ADS)
Banerjee, Rabin; Kulkarni, Shailesh
2008-01-01
From an appropriate expression for the effective action, the Hawking radiation from charged black holes is derived, using only covariant boundary conditions at the event horizon. The connection of our approach with the Unruh vacuum and the recent analysis [S.P. Robinson, F. Wilczek, Phys. Rev. Lett. 95 (2005) 011303, arxiv:gr-qc/0502074; S. Iso, H. Umetsu, F. Wilczek, Phys. Rev. Lett. 96 (2006) 151302, arxiv:hep-th/0602146; R. Banerjee, S. Kulkarni, arxiv:arXiv: 0707.2449 [hep-th
Analytical solutions with Generalized Impedance Boundary Conditions (GIBC)
NASA Technical Reports Server (NTRS)
Syed, H. H.; Volakis, John L.
1991-01-01
Rigorous uniform geometrical theory of diffraction (UTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. In particular, ray solutions are obtained which remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. These involve new transition functions in place of the usual Fock-type integrals, characteristics to the impedance cylinder. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. The diffraction coefficients for the convex cylinder are obtained via a generalization of the corresponding ones for the circular cylinder.
Implementation of a Blowing Boundary Condition in the LAURA Code
NASA Technical Reports Server (NTRS)
Thompson, Richard a.; Gnoffo, Peter A.
2008-01-01
Preliminary steps toward modeling a coupled ablation problem using a finite-volume Navier-Stokes code (LAURA) are presented in this paper. Implementation of a surface boundary condition with mass transfer (blowing) is described followed by verification and validation through comparisons with analytic results and experimental data. Application of the code to a carbon-nosetip ablation problem is demonstrated and the results are compared with previously published data. It is concluded that the code and coupled procedure are suitable to support further ablation analyses and studies.
A Kinetic 13-Moment Boundary Conditions Method for Particle Simulations of Viscous Rarefied Flows
NASA Astrophysics Data System (ADS)
Averkin, Sergey; Gatsonis, Nikolaos
2015-11-01
The kinetic 13-moment (Navier-Stokes-Fourrier) boundary condition method is developed for direct simulation Monte Carlo (DSMC) simulations of rarefied gas flows. The particles are injected into the computational domain from the inlet and outlet following the first-order Chapman-Enskog distribution function. The unknown parameters of the Chapman-Enskog distribution function are reconstructed from the full 13-moment (Navier-Stokes-Fourier) equations discretized on the boundaries with the wave amplitudes calculated by the local one dimensional inviscid (LODI) formulation used in compressible (continuous) flow computations. The kinetic-moment boundary conditions are implemented in an unstructured 3D DSMC (U3DSMC) code and are supplemented with a neighboring-cell sampling approach and a time-average smoothing techniques to speed up convergence and reduce fluctuations. Simulations of a pressure-driven viscous subsonic flow in a circular tube are used for verification and validation of the boundary conditions. In addition, the present method is compared to the previously developed kinetic-moment boundary conditions derived from the five-moment (Euler) equations. AFOSR-FA9550-14-1-0366 Computational Mathematics Program.
NASA Astrophysics Data System (ADS)
Li, Jing; Zeng, Zhaofa; Huang, Ling; Liu, Fengshan
2012-12-01
When applying the finite difference time domain (FDTD) method in Ground Penetrating Radar (GPR) simulation, the absorbing boundary conditions (ABC) are used to mitigate undesired reflection that can arise at the model's truncation boundaries. The classical PML boundary can make spurious reflection for the waves, such as reaching to the PML interface with near-grazing angles, low frequency waves or evanescent waves. The non-split complex frequency shifted PML which base on recursive integration (CFS-RIPML) has a good absorption effect for these interference waves. Meanwhile, the recursive integration, which does not need split field component, can overcome the shortcoming of CFS technique that needs more intermediate variable and large memory. In addition, the high-order FDTD can improve calculation accuracy and reduce the error caused by numerical dispersion effectively. In this paper, we derive the 3D high-order FDTD method with CFS-RIPML boundary and apply it in GPR simulation. The results show that the CFS-RIPML has significantly better absorption effect and lower reflections error than UPML and PML boundary. Compared with the two-order, the high-order FDTD can improve calculation accuracy effectively with the same grid size. Combination with CFS-RIPML boundary and high-order FDTD can improve the reliability and calculation accuracy of GPR and other geophysics numerical simulation.
Magnetospheric conditions near the equatorial footpoints of proton isotropy boundaries
NASA Astrophysics Data System (ADS)
Sergeev, V. A.; Chernyaev, I. A.; Angelopoulos, V.; Ganushkina, N. Y.
2015-12-01
Data from a cluster of three THEMIS (Time History of Events and Macroscale Interactions during Substorms) spacecraft during February-March 2009 frequently provide an opportunity to construct local data-adaptive magnetospheric models, which are suitable for the accurate mapping along the magnetic field lines at distances of 6-9 Re in the nightside magnetosphere. This allows us to map the isotropy boundaries (IBs) of 30 and 80 keV protons observed by low-altitude NOAA POES (Polar Orbiting Environmental Satellites) to the equatorial magnetosphere (to find the projected isotropy boundary, PIB) and study the magnetospheric conditions, particularly to evaluate the ratio KIB (Rc/rc; the magnetic field curvature radius to the particle gyroradius) in the neutral sheet at that point. Special care is taken to control the factors which influence the accuracy of the adaptive models and mapping. Data indicate that better accuracy of an adaptive model is achieved when the PIB distance from the closest spacecraft is as small as 1-2 Re. For this group of most accurate predictions, the spread of KIB values is still large (from 4 to 32), with the median value KIB ~13 being larger than the critical value Kcr ~ 8 expected at the inner boundary of nonadiabatic angular scattering in the current sheet. It appears that two different mechanisms may contribute to form the isotropy boundary. The group with K ~ [4,12] is most likely formed by current sheet scattering, whereas the group having KIB ~ [12,32] could be formed by the resonant scattering of low-energy protons by the electromagnetic ion-cyclotron (EMIC) waves. The energy dependence of the upper K limit and close proximity of the latter event to the plasmapause locations support this conclusion. We also discuss other reasons why the K ~ 8 criterion for isotropization may fail to work, as well as a possible relationship between the two scattering mechanisms.
Riemann solvers and boundary conditions for two-dimensional shallow water simulations
NASA Astrophysics Data System (ADS)
Guinot, Vincent
2003-04-01
Most existing algorithms for two-dimensional shallow water simulations treat multi-dimensional waves using wave splitting or time splitting. This often results in anisotropy of the computed flow. Both wave splitting and time splitting are based on a local decomposition of the multi-dimensional problem into one-dimensional, orthogonal problems. Therefore, these algorithms handle boundary conditions in a very similar way to classical one-dimensional algorithms. This should be expected to trigger a dependence of the number of boundary conditions on the direction of the flow at the boundaries. However, most computational codes based on alternate directions do not exhibit such sensitivity, which seems to contradict the theory of existence and uniqueness of the solution. The present paper addresses these issues. A Riemann solver is presented that aims to convert two-dimensional Riemann problems into a one-dimensional equivalent Riemann problem (ERP) at the interfaces between the computational cells. The ERP is derived by applying the theory of bicharacteristics at each end of the interface and by performing a linear averaging along the interface. The proposed approach is tested against the traditional one-dimensional approach on the classical circular dambreak problem. The results show that the proposed solver allows the isotropy of the solution to be better preserved. Use of the two-dimensional solver with a first-order scheme may give better results than use of a second-order scheme with a one-dimensional solver. The theory of bicharacteristics is also used to discuss the issue of boundary conditions. It is shown that, when the flow is subcritical, the number of boundary conditions affects the accuracy of the solution, but not its existence and uniqueness. When only one boundary condition is to be prescribed, it should not be the velocity in the direction parallel to the boundary. When two boundary conditions are to be prescribed, at least one of them should involve
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.
Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces
NASA Astrophysics Data System (ADS)
Mantile, Andrea; Posilicano, Andrea; Sini, Mourad
2016-07-01
The theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of a second-order elliptic differential operator on Rn with linear boundary conditions on (a relatively open part of) a compact hypersurface. Our approach allows to obtain Kreĭn-like resolvent formulae where the reference operator coincides with the "free" operator with domain H2 (Rn); this provides an useful tool for the scattering problem from a hypersurface. Concrete examples of this construction are developed in connection with the standard boundary conditions, Dirichlet, Neumann, Robin, δ and δ‧-type, assigned either on a (n - 1) dimensional compact boundary Γ = ∂ Ω or on a relatively open part Σ ⊂ Γ. Schatten-von Neumann estimates for the difference of the powers of resolvents of the free and the perturbed operators are also proven; these give existence and completeness of the wave operators of the associated scattering systems.
Tear film dynamics on an eye-shaped domain I: pressure boundary conditions.
Maki, Kara L; Braun, Richard J; Henshaw, William D; King-Smith, P Ewen
2010-09-01
We study the relaxation of a model for the human tear film after a blink on a stationary eye-shaped domain corresponding to a fully open eye using lubrication theory and explore the effects of viscosity, surface tension, gravity and boundary conditions that specify the pressure. The governing non-linear partial differential equation is solved on an overset grid by a method of lines using a finite-difference discretization in space and an adaptive second-order backward-difference formula solver in time. Our 2D simulations are calculated in the Overture computational framework. The computed flows show sensitivity to both our choices between two different pressure boundary conditions and the presence of gravity; this is particularly true around the boundary. The simulations recover features seen in 1D simulations and capture some experimental observations including hydraulic connectivity around the lid margins. PMID:20064825
Role of the basin boundary conditions in gravity wave turbulence
NASA Astrophysics Data System (ADS)
Berhanu, Michael; Deike, Luc; Miquel, Benjamin; Gutierrez, Pablo; Jamin, Timothee; Semin, Benoit; Falcon, Eric; Bonnefoy, Felicien
2015-11-01
Gravity wave turbulence is studied in a large wave basin where irregular waves are generated unidirectionally. The role of the basin boundary conditions (absorbing or reflecting) are investigated. To that purpose, an absorbing sloping beach opposite to the wavemaker can be replaced by a reflecting vertical wall. The wave field properties depend strongly on these boundary conditions. Unidirectional waves propagate before to be damped by the beach whereas a more multidirectional wave field is observed with the wall. In both cases, the wave spectrum scales as a frequency-power law with an exponent that increases continuously with the forcing amplitude up to a value close to -4. We have also studied freely decaying gravity wave turbulence in the closed basin. No self-similar decay of the spectrum is observed, whereas its Fourier modes decay first as a time power law due to nonlinear mechanisms, and then exponentially due to linear viscous damping. We estimate the linear, nonlinear and dissipative time scales to test the time scale separation. Using the mean energy flux from the initial decay of wave energy, the Kolmogorov-Zakharov constant of the weak turbulence theory is evaluated experimentally for the first time.
Complex Wall Boundary Conditions for Modeling Combustion in Catalytic Channels
NASA Astrophysics Data System (ADS)
Zhu, Huayang; Jackson, Gregory
2000-11-01
Monolith catalytic reactors for exothermic oxidation are being used in automobile exhaust clean-up and ultra-low emissions combustion systems. The reactors present a unique coupling between mass, heat, and momentum transport in a channel flow configuration. The use of porous catalytic coatings along the channel wall presents a complex boundary condition when modeled with the two-dimensional channel flow. This current work presents a 2-D transient model for predicting the performance of catalytic combustion systems for methane oxidation on Pd catalysts. The model solves the 2-D compressible transport equations for momentum, species, and energy, which are solved with a porous washcoat model for the wall boundary conditions. A time-splitting algorithm is used to separate the stiff chemical reactions from the convective/diffusive equations for the channel flow. A detailed surface chemistry mechanism is incorporated for the catalytic wall model and is used to predict transient ignition and steady-state conversion of CH4-air flows in the catalytic reactor.
A whisker sensor: role of geometry and boundary conditions
NASA Astrophysics Data System (ADS)
Hans, Hendrik; Valdivia Y Alvarado, Pablo; Thekoodan, Dilip; Jianmin, Miao; Triantafyllou, Michael
2011-11-01
Harbor seal whiskers are currently being studied for their role in sensing and tracking of the fluid structures left in wakes. Seal whiskers are exposed to incoming flows and are subject to self-induced vibrations. The whisker's unusual geometry is thought to reduce these self-induced disturbances and facilitate a stable reference for wake sensing. An experimental platform was designed to measure flow-induced displacements and vibrations at the base of whisker-like models. Four different whisker-like models (scale: 3x) were towed at different speeds down a towing tank and base displacements in the direction of motion and in the perpendicular axis were measured. Each model incorporated a particular geometrical feature found in harbor seal whiskers. Three different visco-elastic supports were used to mimic various boundary conditions at the base of the whisker models. The effects of geometrical features and boundary conditions on measured base vibrations at three relevant Reynolds numbers are discussed. The material properties of a model's base influence its sensitivity. When compared to a circular cylinder model, whisker models show almost no sign of VIV.
Boundary conditions on the vapor liquid interface at strong condensation
NASA Astrophysics Data System (ADS)
Kryukov, A. P.; Levashov, V. Yu.
2016-07-01
The problem of the formulation of boundary conditions on the vapor-liquid interface is considered. The different approaches to this problem and their difficulties are discussed. Usually, a quasi-equilibrium scheme is used. At sufficiently large deviations from thermodynamic equilibrium, a molecular kinetics approach should be used for the description of the vapor flow at condensation. The formulation of the boundary conditions at the vapor liquid interface to solve the Boltzmann kinetic equation for the distribution of molecules by velocity is a sophisticated problem. It appears that molecular dynamics simulation (MDS) can be used to provide this solution at the interface. The specific problems occur in the realization of MDS on large time and space scales. Some of these problems, and a hierarchy of continuum, kinetic and molecular dynamic time scales, are discussed in the paper. A description of strong condensation at the kinetic level is presented for the steady one-dimensional problem. A formula is provided for the calculation of the limiting condensation coefficient. It is shown that as the condensation coefficient approaches the limiting value, the vapor pressure rises significantly. The results of the corresponding calculations for the Mach number and temperature at different vapor flows are demonstrated. As a result of the application of the molecular kinetics method and molecular dynamics simulation to the problem of the determination of argon condensation coefficients in the range of temperatures of vapor and liquid ratio 1.0-4.0, it is concluded that the condensation coefficient is close to unity.
NASA Astrophysics Data System (ADS)
Thoraval, C.; Richards, M. A.
1997-10-01
The authors address several of the most straightforward problems inherent in geoid modelling, namely the issues of viscosity structure resolution, uncertainties in appropriate boundary conditions, and differences among mantle heterogeneity models. A robust feature of all models is a lower-mantle viscosity at least a factor of 30 greater than that of the upper mantle, but there is little resolution with regard to finer details such as lithospheric or uppermost mantle ("low-viscosity zone") viscosity. Ironically, free-slip boundary conditions result in the best fits to the geoid in all cases, but all boundary conditions exhibit predictable trade-offs with the uppermost-mantle viscosity. Models with a single viscosity layer representing the lower mantle yield similar dynamic topography estimates of the order of 700-1000 m in amplitude, regardless of the finer details of upper-mantle viscosity structure, boundary conditions or input heterogeneity models. Comparing mantle heterogeneity models based on two independent seismological determinations (Harvard and Berkeley models) and on the history of subduction, the authors find that these models are virtually indistinguishable regarding inferences of mantle viscosity structure and amplitude of dynamic topography, and in terms of the effects of different boundary conditions. Uncertainties concerning which type of boundary condition is appropriate are much more important than which mantle heterogeneity model is chosen. Given other uncertainties in modelling the geoid, particularly the strong effects due to lateral viscosity variations for intermediate (<10,000 km) wavelengths, the authors conclude that the class of dynamic geoid models explored so far cannot reliably elucidate the details of upper-mantle viscosity structure.
Boundary conditions for arbitrarily shaped and tightly focused laser pulses in electromagnetic codes
NASA Astrophysics Data System (ADS)
Thiele, Illia; Skupin, Stefan; Nuter, Rachel
2016-09-01
Investigation of laser matter interaction with electromagnetic codes requires to implement sources for the electromagnetic fields. A way to do so is to prescribe the fields at the numerical box boundaries in order to achieve the desired fields inside the numerical box. Here we show that the often used paraxial approximation can lead to unexpected field profiles with strong impact on the laser matter interaction results. We propose an efficient numerical algorithm to compute the required laser boundary conditions consistent with the Maxwell's equations for arbitrarily shaped, tightly focused laser pulses.
NASA Astrophysics Data System (ADS)
Li, Like; AuYeung, Nick; Mei, Renwei; Klausner, James F.
2016-08-01
We present a systematic study on the effects of tangential-type boundary condition discontinuities on the accuracy of the lattice Boltzmann equation (LBE) method for Dirichlet and Neumann problems in heat and mass transfer modeling. The second-order accurate boundary condition treatments for continuous Dirichlet and Neumann problems are directly implemented for the corresponding discontinuous boundary conditions. Results from three numerical tests, including both straight and curved boundaries, are presented to show the accuracy and order of convergence of the LBE computations. Detailed error assessments are conducted for the interior temperature or concentration (denoted as a scalar ϕ) and the interior derivatives of ϕ for both types of boundary conditions, for the boundary flux in the Dirichlet problem and for the boundary ϕ values in the Neumann problem. When the discontinuity point on the straight boundary is placed at the center of the unit lattice in the Dirichlet problem, it yields only first-order accuracy for the interior distribution of ϕ, first-order accuracy for the boundary flux, and zeroth-order accuracy for the interior derivatives compared with the second-order accuracy of all quantities of interest for continuous boundary conditions. On the lattice scale, the LBE solution for the interior derivatives near the singularity is largely independent of the resolution and correspondingly the local distribution of the absolute errors is almost invariant with the changing resolution. For Neumann problems, when the discontinuity is placed at the lattice center, second-order accuracy is preserved for the interior distribution of ϕ; and a "superlinear" convergence order of 1.5 for the boundary ϕ values and first-order accuracy for the interior derivatives are obtained. For straight boundaries with the discontinuity point arbitrarily placed within the lattice and curved boundaries, the boundary flux becomes zeroth-order accurate for Dirichlet problems
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
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.
Theory of a curved planar waveguide with Robin boundary conditions.
Olendski, O; Mikhailovska, L
2010-03-01
A model of a thin straight strip with a uniformly curved section and with boundary requirements zeroing at the edges a linear superposition of the wave function and its normal derivative (Robin boundary condition) is analyzed theoretically within the framework of the linear Schrödinger equation and is applied to the study of the processes in the bent magnetic multilayers, superconducting films and metallic ferrite-filled waveguides. In particular, subband thresholds of the straight and curved parts of the film are calculated and analyzed as a function of the Robin parameter 1/Lambda , with Lambda being an extrapolation length entering Robin boundary condition. For the arbitrary Robin coefficients which are equal on the opposite interfaces of the strip and for all bend parameters the lowest-mode energy of the continuously curved duct is always smaller than its straight counterpart. Accordingly, the bound state below the fundamental propagation threshold of the straight arms always exists as a result of the bend. In terms of the superconductivity language it means an increased critical temperature of the curved film compared to its straight counterpart. Localized-level dependence on the parameters of the curve is investigated with its energy decreasing with increasing bend angle and decreasing bend radius. Conditions of the bound-state existence for the different Robin parameters on the opposite edges are analyzed too; in particular, it is shown that the bound state below the first transverse threshold of the straight arm always exists if the inner extrapolation length is not larger than the outer one. In the opposite case there is a range of the bend parameters where the curved film cannot trap the wave and form the localized mode; for example, for the fixed bend radius the bound state emerges from the continuum at some nonzero bend angle that depends on the difference of the two lengths Lambda at the opposite interfaces. Various transport properties of the film
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
NASA Astrophysics Data System (ADS)
da Silva, José B.; Leite, Marcelo M.
2012-04-01
We introduce a renormalized one-particle irreducible, 1PI, vertex part scalar field theory setting in momentum space to computing the critical exponents ν and η, at least at two-loop order, for a layered parallel plate geometry separated by a distance L, with periodic as well as antiperiodic boundary conditions on the plates. We utilize massive and massless fields in order to extract the exponents in independent ultraviolet and infrared scaling analysis, respectively, which are required in a complete description of the scaling regions for finite size systems. We prove that fixed points and other critical amounts either in the ultraviolet or in the infrared regime dependent on the plates boundary condition are a general feature of normalization conditions. We introduce a new description of typical crossover regimes occurring in finite size systems. Avoiding these crossovers, the three regions of finite size scaling present for each of these boundary conditions are shown to be indistinguishable in the results of the exponents in periodic and antiperiodic conditions, which coincide with those from the (bulk) infinite system.
NASA Astrophysics Data System (ADS)
Cai, Jian; Modest, Michael F.
2016-01-01
In simulations of periodic or symmetric geometries, computational domains are reduced by imaginary boundaries that present the symmetry conditions. In Photon Monte Carlo methods, this is achieved by imposing specular reflective boundary conditions for the radiative intensity. In this work, a similar specular reflective boundary condition is developed for Discrete Ordinate Methods. The effectiveness of the new boundary condition is demonstrated by multiple numerical examples including plane symmetry and axisymmetry.
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.
Zhi-Gang Feng
2012-05-31
The simulation of particulate flows for industrial applications often requires the use of two-fluid models, where the solid particles are considered as a separate continuous phase. One of the underlining uncertainties in the use of the two-fluid models in multiphase computations comes from the boundary condition of the solid phase. Typically, the gas or liquid fluid boundary condition at a solid wall is the so called no-slip condition, which has been widely accepted to be valid for single-phase fluid dynamics provided that the Knudsen number is low. However, the boundary condition for the solid phase is not well understood. The no-slip condition at a solid boundary is not a valid assumption for the solid phase. Instead, several researchers advocate a slip condition as a more appropriate boundary condition. However, the question on the selection of an exact slip length or a slip velocity coefficient is still unanswered. Experimental or numerical simulation data are needed in order to determinate the slip boundary condition that is applicable to a two-fluid model. The goal of this project is to improve the performance and accuracy of the boundary conditions used in two-fluid models such as the MFIX code, which is frequently used in multiphase flow simulations. The specific objectives of the project are to use first principles embedded in a validated Direct Numerical Simulation particulate flow numerical program, which uses the Immersed Boundary method (DNS-IB) and the Direct Forcing scheme in order to establish, modify and validate needed energy and momentum boundary conditions for the MFIX code. To achieve these objectives, we have developed a highly efficient DNS code and conducted numerical simulations to investigate the particle-wall and particle-particle interactions in particulate flows. Most of our research findings have been reported in major conferences and archived journals, which are listed in Section 7 of this report. In this report, we will present a
Fluid-solid interaction in arteries incorporating the autoregulation concept in boundary conditions.
Afkari, Damon; Gabaldón, Felipe
2016-07-01
In pre-surgery decisions in hospital emergency cases, fast and reliable results of the solid and fluid mechanics problems are of great interest to clinicians. In the current investigation, an iterative process based on a pressure-type boundary condition is proposed in order to reduce the computational costs of blood flow simulations in arteries, without losing control of the important clinical parameters. The incorporation of cardiovascular autoregulation, together with the well-known impedance boundary condition, forms the basis of the proposed methodology. With autoregulation, the instabilities associated with conventional pressure-type or impedance boundary conditions are avoided without an excessive increase in computational costs. The general behaviour of pulsatile blood flow in arteries, which is important from the clinical point of view, is well reproduced through this new methodology. In addition, the interaction between the blood and the arterial walls occurs via a modified weak coupling, which makes the simulation more stable and computationally efficient. Based on in vitro experiments, the hyperelastic behaviour of the wall is characterised and modelled. The applications and benefits of the proposed pressure-type boundary condition are shown in a model of an idealised aortic arch with and without an ascending aorta dissection, which is a common cardiovascular disorder. PMID:26404580
Denniston, Colin; Robbins, Mark O
2006-12-01
Molecular dynamics simulations are used to explore the flow behavior and diffusion of miscible fluids near solid surfaces. The solid produces deviations from bulk fluid behavior that decay over a distance of the order of the fluid correlation length. Atomistic results are mapped onto two types of continuum model: Mesoscopic models that follow this decay and conventional sharp interface boundary conditions for the stress and velocity. The atomistic results, and mesoscopic models derived from them, are consistent with the conventional Marangoni stress boundary condition. However, there are deviations from the conventional Navier boundary condition that states that the slip velocity between wall and fluid is proportional to the strain rate. A general slip boundary condition is derived from the mesoscopic model that contains additional terms associated with the Marangoni stress and diffusion, and is shown to describe the atomistic simulations. The additional terms lead to strong flows when there is a concentration gradient. The potential for using this effect to make a nanomotor or pump is evaluated. PMID:17166010
Unsteady Squeezing Flow of Carbon Nanotubes with Convective Boundary Conditions
Hayat, Tasawar; Muhammad, Khursheed; Farooq, Muhammad; Alsaedi, Ahmad
2016-01-01
Unsteady flow of nanofluids squeezed between two parallel plates is discussed in the presence of viscous dissipation. Heat transfer phenomenon is disclosed via convective boundary conditions. Carbon nanotubes (single-wall and multi-wall) are used as nanoparticles which are homogeneously distributed in the base fluid (water). A system of non-linear differential equations for the flow is obtained by utilizing similarity transformations through the conservation laws. Influence of various emerging parameters on the velocity and temperature profiles are sketched graphically and discussed comprehensively. Analyses of skin fraction coefficient and Nusselt number are also elaborated numerically. It is found out that velocity is smaller for squeezing parameter in the case of multi-wall carbon nanotubes when compared with single-wall carbon nanotubes. PMID:27149208
Equilibrium iron isotope fractionation at core-mantle boundary conditions.
Polyakov, Veniamin B
2009-02-13
The equilibrium iron isotope fractionation between lower mantle minerals and metallic iron at core-mantle boundary conditions can be evaluated from the high-pressure 57Fe partial vibrational density of states determined by synchrotron inelastic nuclear resonant x-ray scattering spectroscopy using a diamond anvil. Ferropericlase [(Mg,Fe)O] and (Fe,Mg)SiO3- post-perovskite are enriched in heavy iron isotopes relative to metallic iron at ultrahigh pressures, as opposed to the equilibrium iron isotope fractionation between these compounds at low pressure. The enrichment of Earth and Moon basalts in heavy iron isotopes relative to those from Mars and asteroid Vesta can be explained by the equilibrium iron isotope fractionation during the segregation of Earth's core and the assumption that Earth was already differentiated before the Moon-forming "giant impact." PMID:19213913
Unsteady Squeezing Flow of Carbon Nanotubes with Convective Boundary Conditions.
Hayat, Tasawar; Muhammad, Khursheed; Farooq, Muhammad; Alsaedi, Ahmad
2016-01-01
Unsteady flow of nanofluids squeezed between two parallel plates is discussed in the presence of viscous dissipation. Heat transfer phenomenon is disclosed via convective boundary conditions. Carbon nanotubes (single-wall and multi-wall) are used as nanoparticles which are homogeneously distributed in the base fluid (water). A system of non-linear differential equations for the flow is obtained by utilizing similarity transformations through the conservation laws. Influence of various emerging parameters on the velocity and temperature profiles are sketched graphically and discussed comprehensively. Analyses of skin fraction coefficient and Nusselt number are also elaborated numerically. It is found out that velocity is smaller for squeezing parameter in the case of multi-wall carbon nanotubes when compared with single-wall carbon nanotubes. PMID:27149208
Dynamic behaviour of thin composite plates for different boundary conditions
Sprintu, Iuliana E-mail: rotaruconstantin@yahoo.com; Rotaru, Constantin E-mail: rotaruconstantin@yahoo.com
2014-12-10
In the context of composite materials technology, which is increasingly present in industry, this article covers a topic of great interest and theoretical and practical importance. Given the complex design of fiber-reinforced materials and their heterogeneous nature, mathematical modeling of the mechanical response under different external stresses is very difficult to address in the absence of simplifying assumptions. In most structural applications, composite structures can be idealized as beams, plates, or shells. The analysis is reduced from a three-dimensional elasticity problem to a oneor two-dimensional problem, based on certain simplifying assumptions that can be made because the structure is thin. This paper aims to validate a mathematical model illustrating how thin rectangular orthotropic plates respond to the actual load. Thus, from the theory of thin plates, new analytical solutions are proposed corresponding to orthotropic rectangular plates having different boundary conditions. The proposed analytical solutions are considered both for solving equation orthotropic rectangular plates and for modal analysis.
On combined source solutions for bodies with impedance boundary conditions
NASA Astrophysics Data System (ADS)
Rogers, J. R.
1985-04-01
Studies conducted by Rogers (1984, 1983) regarding impedance boundary condition (IBC) integral equations have been mainly concerned with the spurious interior resonance problem associated with electromagnetic solutions exterior to a closed surface. Specifically, exterior radiation and scattering solutions of the IBC electric and magnetic field integral equations (EFIE and MFI) have nonunique solutions at the interior resonant frequencies of a perfectly conducting cavity having the same shape as the impedance target. In the present investigation, examples are presented of numerical solutions to the IBC combined source integral equation for scattering from impedance spheres. The presented results demonstrate that the IBC combined source integral equation (CSIE) is effective in eliminating the spurious solutions which occur in the electric and magnetic field integral equations.
Fluid flow in nanopores: Accurate boundary conditions for carbon nanotubes
NASA Astrophysics Data System (ADS)
Sokhan, Vladimir P.; Nicholson, David; Quirke, Nicholas
2002-11-01
Steady-state Poiseuille flow of a simple fluid in carbon nanopores under a gravitylike force is simulated using a realistic empirical many-body potential model for carbon. Building on our previous study of slit carbon nanopores we show that fluid flow in a nanotube is also characterized by a large slip length. By analyzing temporal profiles of the velocity components of particles colliding with the wall we obtain values of the Maxwell coefficient defining the fraction of molecules thermalized by the wall and, for the first time, propose slip boundary conditions for smooth continuum surfaces such that they are equivalent in adsorption, diffusion, and fluid flow properties to fully dynamic atomistic models.
Boundary conditions for star matter and other periodic fermionic systems
NASA Astrophysics Data System (ADS)
Gulminelli, F.; Furuta, T.; Juillet, O.; Leclercq, C.
2011-12-01
Bulk fermionic matter, as can be notably found in supernova matter and neutrons stars, is subject to correlations of infinite range due to the antisymmetrization of the N-body wave function, which cannot be explicitly accounted for in a practical simulation. This problem is usually addressed in condensed matter physics by means of the so-called twist averaged boundary condition method. A different ansatz based on the localized Wannier representation has been proposed in the context of antisymmetrized molecular dynamics. In this paper we work out the formal relation between the two approaches. We show that, while the two coincide when working with exact eigenstates of the N-body Hamiltonian, differences appear in the case of variational approaches, which are currently used for the description of stellar matter. Some model applications with fermionic molecular dynamics are shown.
Charged dopants in semiconductor nanowires under partially periodic boundary conditions
NASA Astrophysics Data System (ADS)
Chan, Tzu-Liang; Zhang, S. B.; Chelikowsky, James R.
2011-06-01
We develop a one-dimensional, periodic real-space formalism for examining the electronic structure of charged nanowires from first principles. The formalism removes spurious electrostatic interactions between charged unit cells by appropriately specifying a boundary condition for the Kohn-Sham equation. The resultant total energy of the charged system remains finite, and a Madelung-type correction is unnecessary. We demonstrate our scheme by examining the ionization energy of P-doped Si<110> nanowires. We find that there is an effective repulsion between charged P dopants along the nanowire owing to the repulsive interaction of the induced surface charge between adjacent periodic cells. This repulsive interaction decays exponentially with unit cell size instead of a power law behavior assumed in typical charged calculations.
Gas cushion model and hydrodynamic boundary conditions for superhydrophobic textures
NASA Astrophysics Data System (ADS)
Nizkaya, Tatiana V.; Asmolov, Evgeny S.; Vinogradova, Olga I.
2014-10-01
Superhydrophobic Cassie textures with trapped gas bubbles reduce drag, by generating large effective slip, which is important for a variety of applications that involve a manipulation of liquids at the small scale. Here we discuss how the dissipation in the gas phase of textures modifies their friction properties. We propose an operator method, which allows us to map the flow in the gas subphase to a local slip boundary condition at the liquid-gas interface. The determined uniquely local slip length depends on the viscosity contrast and underlying topography, and can be immediately used to evaluate an effective slip of the texture. Besides superlubricating Cassie surfaces, our approach is valid for rough surfaces impregnated by a low-viscosity "lubricant," and even for Wenzel textures, where a liquid follows the surface relief. These results provide a framework for the rational design of textured surfaces for numerous applications.
Simulating flight boundary conditions for orbiter payload modal survey
NASA Technical Reports Server (NTRS)
Chung, Y. T.; Sernaker, M. L.; Peebles, J. H.
1993-01-01
An approach to simulate the characteristics of the payload/orbiter interfaces for the payload modal survey was developed. The flexure designed for this approach is required to provide adequate stiffness separation in the free and constrained interface degrees of freedom to closely resemble the flight boundary condition. Payloads will behave linearly and demonstrate similar modal effective mass distribution and load path as the flight if the flexure fixture is used for the payload modal survey. The potential non-linearities caused by the trunnion slippage during the conventional fixed base modal survey may be eliminated. Consequently, the effort to correlate the test and analysis models can be significantly reduced. An example is given to illustrate the selection and the sensitivity of the flexure stiffness. The advantages of using flexure fixtures for the modal survey and for the analytical model verification are also demonstrated.
NASA Astrophysics Data System (ADS)
Ramesh, G. K.; Gireesha, B. J.; Gorla, Rama Subba Reddy
2015-08-01
The steady two-dimensional boundary layer flow of a viscous dusty fluid over a stretching sheet with the bottom surface of the sheet heated by convection from a hot fluid is considered. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, before being solved numerically by a Runge-Kutta-Fehlberg fourth-fifth order method (RKF45 Method) with the help of MAPLE. The effects of convective Biot number, fluid particle interaction parameter, and Prandtl number on the heat transfer characteristics are discussed. It is found that the temperature of both fluid and dust phase increases with increasing Biot number. A comparative study between the previous published and present results in a limiting sense is found in an excellent agreement.
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
Deniz, Furkan Nur; Alagoz, Baris Baykant; Tan, Nusret; Atherton, Derek P
2016-05-01
This paper introduces an integer order approximation method for numerical implementation of fractional order derivative/integrator operators in control systems. The proposed method is based on fitting the stability boundary locus (SBL) of fractional order derivative/integrator operators and SBL of integer order transfer functions. SBL defines a boundary in the parametric design plane of controller, which separates stable and unstable regions of a feedback control system and SBL analysis is mainly employed to graphically indicate the choice of controller parameters which result in stable operation of the feedback systems. This study reveals that the SBL curves of fractional order operators can be matched with integer order models in a limited frequency range. SBL fitting method provides straightforward solutions to obtain an integer order model approximation of fractional order operators and systems according to matching points from SBL of fractional order systems in desired frequency ranges. Thus, the proposed method can effectively deal with stability preservation problems of approximate models. Illustrative examples are given to show performance of the proposed method and results are compared with the well-known approximation methods developed for fractional order systems. The integer-order approximate modeling of fractional order PID controllers is also illustrated for control applications. PMID:26876378
Casimir force in the rotor model with twisted boundary conditions.
Bergknoff, Jonathan; Dantchev, Daniel; Rudnick, Joseph
2011-10-01
We investigate the three-dimensional lattice XY model with nearest neighbor interaction. The vector order parameter of this system lies on the vertices of a cubic lattice, which is embedded in a system with a film geometry. The orientations of the vectors are fixed at the two opposite sides of the film. The angle between the vectors at the two boundaries is α where 0≤α≤π. We make use of the mean field approximation to study the mean length and orientation of the vector order parameter throughout the film--and the Casimir force it generates--as a function of the temperature T, the angle α, and the thickness L of the system. Among the results of that calculation are a Casimir force that depends in a continuous way on both the parameter α and the temperature and that can be attractive or repulsive. In particular, by varying α and/or T one controls both the sign and the magnitude of the Casimir force in a reversible way. Furthermore, for the case α=π, we discover an additional phase transition occurring only in the finite system associated with the variation of the orientations of the vectors. PMID:22181114
33 CFR 177.04 - Order of unsafe condition.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 33 Navigation and Navigable Waters 2 2012-07-01 2012-07-01 false Order of unsafe condition. 177.04 Section 177.04 Navigation and Navigable Waters COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) BOATING SAFETY CORRECTION OF ESPECIALLY HAZARDOUS CONDITIONS § 177.04 Order of unsafe condition. (a) The Commandant has redelegated to...
33 CFR 177.04 - Order of unsafe condition.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 33 Navigation and Navigable Waters 2 2014-07-01 2014-07-01 false Order of unsafe condition. 177.04 Section 177.04 Navigation and Navigable Waters COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) BOATING SAFETY CORRECTION OF ESPECIALLY HAZARDOUS CONDITIONS § 177.04 Order of unsafe condition. (a) The Commandant has redelegated to...
A spherical shell numerical dynamo benchmark with pseudo-vacuum magnetic boundary conditions
NASA Astrophysics Data System (ADS)
Jackson, A.; Sheyko, A.; Marti, P.; Tilgner, A.; Cébron, D.; Vantieghem, S.; Simitev, R.; Busse, F.; Zhan, X.; Schubert, G.; Takehiro, S.; Sasaki, Y.; Hayashi, Y.-Y.; Ribeiro, A.; Nore, C.; Guermond, J.-L.
2014-02-01
It is frequently considered that many planetary magnetic fields originate as a result of convection within planetary cores. Buoyancy forces responsible for driving the convection generate a fluid flow that is able to induce magnetic fields; numerous sophisticated computer codes are able to simulate the dynamic behaviour of such systems. This paper reports the results of a community activity aimed at comparing numerical results of several different types of computer codes that are capable of solving the equations of momentum transfer, magnetic field generation and heat transfer in the setting of a spherical shell, namely a sphere containing an inner core. The electrically conducting fluid is incompressible and rapidly rotating and the forcing of the flow is thermal convection under the Boussinesq approximation. We follow the original specifications and results reported in Harder & Hansen to construct a specific benchmark in which the boundaries of the fluid are taken to be impenetrable, non-slip and isothermal, with the added boundary condition for the magnetic field B that the field must be entirely radial there; this type of boundary condition for B is frequently referred to as `pseudo-vacuum'. This latter condition should be compared with the more frequently used insulating boundary condition. This benchmark is so-defined in order that computer codes based on local methods, such as finite element, finite volume or finite differences, can handle the boundary condition with ease. The defined benchmark, governed by specific choices of the Roberts, magnetic Rossby, Rayleigh and Ekman numbers, possesses a simple solution that is steady in an azimuthally drifting frame of reference, thus allowing easy comparison among results. Results from a variety of types of code are reported, including codes that are fully spectral (based on spherical harmonic expansions in angular coordinates and polynomial expansions in radius), mixed spectral and finite difference, finite volume
NASA Astrophysics Data System (ADS)
Janssen, R. H. H.; Vilà-Guerau de Arellano, J.; Ganzeveld, L. N.; Kabat, P.; Jimenez, J. L.; Farmer, D. K.; van Heerwaarden, C. C.; Mammarella, I.
2012-08-01
We study the combined effects of land surface conditions, atmospheric boundary layer dynamics and chemistry on the diurnal evolution of biogenic secondary organic aerosol in the atmospheric boundary layer, using a model that contains the essentials of all these components. First, we evaluate the model for a case study in Hyytiälä, Finland, and find that it is able to satisfactorily reproduce the observed dynamics and gas-phase chemistry. We show that the exchange of organic aerosol between the free troposphere and the boundary layer (entrainment) must be taken into account in order to explain the observed diurnal cycle in organic aerosol (OA) concentration. An examination of the budgets of organic aerosol and terpene concentrations show that the former is dominated by entrainment, while the latter is mainly driven by emission and chemical transformation. We systematically investigate the role of the land surface, which governs both the surface energy balance partitioning and terpene emissions, and the large-scale atmospheric process of vertical subsidence. Entrainment is especially important for the dilution of organic aerosol concentrations under conditions of dry soils and low terpene emissions. Subsidence suppresses boundary layer growth while enhancing entrainment. Therefore, it influences the relationship between organic aerosol and terpene concentrations. Our findings indicate that the diurnal evolution of secondary organic aerosols (SOA) in the boundary layer is the result of coupled effects of the land surface, dynamics of the atmospheric boundary layer, chemistry, and free troposphere conditions. This has potentially some consequences for the design of both field campaigns and large-scale modeling studies.
NASA Technical Reports Server (NTRS)
Fisher, Travis C.; Carpenter, Mark H.; Yamaleev, Nail K.; Frankel, Steven H.
2009-01-01
A general strategy exists for constructing Energy Stable Weighted Essentially Non Oscillatory (ESWENO) finite difference schemes up to eighth-order on periodic domains. These ESWENO schemes satisfy an energy norm stability proof for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, boundary closures are developed for the fourth-order ESWENO scheme that maintain wherever possible the WENO stencil biasing properties, while satisfying the summation-by-parts (SBP) operator convention, thereby ensuring stability in an L2 norm. Second-order, and third-order boundary closures are developed that achieve stability in diagonal and block norms, respectively. The global accuracy for the second-order closures is three, and for the third-order closures is four. A novel set of non-uniform flux interpolation points is necessary near the boundaries to simultaneously achieve 1) accuracy, 2) the SBP convention, and 3) WENO stencil biasing mechanics.
Boundary conditions on faster-than-light transportation systems
NASA Technical Reports Server (NTRS)
Bennett, Gary L.; Knowles, H. B.
1993-01-01
In order to be consistent with current physical theories, any proposal of a faster-than light (FTL) transportation system must satisfy several critical conditions. It must predict the mass, space, and time dimensional changes predicted by relativity physics when velocity falls below the speed of light. It must also not violate causality, and remain consistent with quantum physics in the limit of microscopic systems. It is also essential that the proposal conserve energy.
A note on the nonlocal boundary value problem for a third order partial differential equation
NASA Astrophysics Data System (ADS)
Belakroum, Kheireddine; Ashyralyev, Allaberen; Guezane-Lakoud, Assia
2016-08-01
The nonlocal boundary-value problem for a third order partial differential equation d/3u (t ) d t3 +A d/u (t ) d t =f (t ), 0
A fourth-order box method for solving the boundary layer equations
NASA Technical Reports Server (NTRS)
Wornom, S. F.
1977-01-01
A fourth order box method for calculating high accuracy numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations is presented. The method is the natural extension of the second order Keller Box scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary layer equations. Numerical results for high accuracy test cases show the method to be significantly faster than other higher order and second order methods.
NASA Technical Reports Server (NTRS)
Iyer, Venkit
1990-01-01
A solution method, fourth-order accurate in the body-normal direction and second-order accurate in the stream surface directions, to solve the compressible 3-D boundary layer equations is presented. The transformation used, the discretization details, and the solution procedure are described. Ten validation cases of varying complexity are presented and results of calculation given. The results range from subsonic flow to supersonic flow and involve 2-D or 3-D geometries. Applications to laminar flow past wing and fuselage-type bodies are discussed. An interface procedure is used to solve the surface Euler equations with the inviscid flow pressure field as the input to assure accurate boundary conditions at the boundary layer edge. Complete details of the computer program used and information necessary to run each of the test cases are given in the Appendix.
New Bondi-type outgoing boundary condition for the Einstein equations with cosmological constant
NASA Astrophysics Data System (ADS)
He, Xiaokai; Cao, Zhoujian
2015-07-01
In the middle of last century, Bondi and his coworkers proposed an outgoing boundary condition for the Einstein equations. Recently, more and more observations imply that the Einstein equations should include a nonzero cosmological constant. A spacetime with a positive cosmological constant approaches to a de Sitter space asymptotically. Bondi's original boundary condition is not valid for these asymptotically de Sitter spacetimes. But the traditional conformally flat boundary condition excludes the gravitational radiation for the asymptotically de Sitter spacetimes. In this work, a new Bondi-type outgoing boundary condition based on Bondi-Sachs coordinates is considered. With this new boundary condition, the gravitational wave behavior for the asymptotically de Sitter spacetime is similar to the one for the asymptotically Minkowski spacetime. The traditional conformally flat boundary condition falls into a special subclass of the new boundary condition.
Reconstructing geographical boundary conditions for palaeoclimate modelling during the Cenozoic
NASA Astrophysics Data System (ADS)
Baatsen, Michiel; van Hinsbergen, Douwe J. J.; von der Heydt, Anna S.; Dijkstra, Henk A.; Sluijs, Appy; Abels, Hemmo A.; Bijl, Peter K.
2016-08-01
Studies on the palaeoclimate and palaeoceanography using numerical model simulations may be considerably dependent on the implemented geographical reconstruction. Because building the palaeogeographic datasets for these models is often a time-consuming and elaborate exercise, palaeoclimate models frequently use reconstructions in which the latest state-of-the-art plate tectonic reconstructions, palaeotopography and -bathymetry, or vegetation have not yet been incorporated. In this paper, we therefore provide a new method to efficiently generate a global geographical reconstruction for the middle-late Eocene. The generalised procedure is also reusable to create reconstructions for other time slices within the Cenozoic, suitable for palaeoclimate modelling. We use a plate-tectonic model to make global masks containing the distribution of land, continental shelves, shallow basins and deep ocean. The use of depth-age relationships for oceanic crust together with adjusted present-day topography gives a first estimate of the global geography at a chosen time frame. This estimate subsequently needs manual editing of areas where existing geological data indicate that the altimetry has changed significantly over time. Certain generic changes (e.g. lowering mountain ranges) can be made relatively easily by defining a set of masks while other features may require a more specific treatment. Since the discussion regarding many of these regions is still ongoing, it is crucial to make it easy for changes to be incorporated without having to redo the entire procedure. In this manner, a complete reconstruction can be made that suffices as a boundary condition for numerical models with a limited effort. This facilitates the interaction between experts in geology and palaeoclimate modelling, keeping reconstructions up to date and improving the consistency between different studies. Moreover, it facilitates model inter-comparison studies and sensitivity tests regarding certain
Shroud boundary condition characterization experiments at the Radiant Heat Facility.
Suo-Anttila, Jill Marie; Nakos, James Thomas; Gill, Walter
2004-10-01
A series of experiments was performed to better characterize the boundary conditions from an inconel heat source ('shroud') painted with Pyromark black paint. Quantifying uncertainties in this type of experimental setup is crucial to providing information for comparisons with code predictions. The characterization of this boundary condition has applications in many scenarios related to fire simulation experiments performed at Sandia National Laboratories Radiant Heat Facility (RHF). Four phases of experiments were performed. Phase 1 results showed that a nominal 1000 C shroud temperature is repeatable to about 2 C. Repeatability of temperatures at individual points on the shroud show that temperatures do not vary more than 10 C from experiment to experiment. This variation results in a 6% difference in heat flux to a target 4 inches away. IR camera images showed the shroud was not at a uniform temperature, although the control temperature was constant to about {+-}2 C during a test. These images showed that a circular shaped, flat shroud with its edges supported by an insulated plate has a temperature distribution with higher temperatures at the edges and lower temperatures in the center. Differences between the center and edge temperatures were up to 75 C. Phase 3 results showed that thermocouple (TC) bias errors are affected by coupling with the surrounding environment. The magnitude of TC error depends on the environment facing the TC. Phase 4 results were used to estimate correction factors for specific applications (40 and 63-mil diameter, ungrounded junction, mineral insulated, metal-sheathed TCs facing a cold surface). Correction factors of about 3.0-4.5% are recommended for 40 mil diameter TCs and 5.5-7.0% for 63 mil diameter TCs. When mounted on the cold side of the shroud, TCs read lower than the 'true' shroud temperature, and the TC reads high when on the hot side. An alternate method uses the average of a cold side and hot side TC of the same size to
Mennemann, Jan-Frederik Jüngel, Ansgar
2014-10-15
Discrete transparent boundary conditions (DTBC) and the Perfectly Matched Layers (PML) method for the realization of open boundary conditions in quantum device simulations are compared, based on the stationary and time-dependent Schrödinger equation. The comparison includes scattering state, wave packet, and transient scattering state simulations in one and two space dimensions. The Schrödinger equation is discretized by a second-order Crank–Nicolson method in case of DTBC. For the discretization with PML, symmetric second-, fourth-, and sixth-order spatial approximations as well as Crank–Nicolson and classical Runge–Kutta time-integration methods are employed. In two space dimensions, a ring-shaped quantum waveguide device is simulated in the stationary and transient regime. As an application, a simulation of the Aharonov–Bohm effect in this device is performed, showing the excitation of bound states localized in the ring region. The numerical experiments show that the results obtained from PML are comparable to those obtained using DTBC, while keeping the high numerical efficiency and flexibility as well as the ease of implementation of the former method. -- Highlights: •In-depth comparison between discrete transparent boundary conditions (DTBC) and PML. •First 2-D transient scattering state simulations using DTBC. •First 2-D transient scattering state simulations of the Aharonov–Bohm effect.
NASA Astrophysics Data System (ADS)
Muthukumaran, Packirisamy; Stiharu, Ion G.; Bhat, Rama B.
2003-10-01
This paper presents and applies the concept of micro-boundary conditioning to the design synthesis of microsystems in order to quantify the influence of inherent limitations of the fabrication process and the operating conditions on both static and dynamic behavior of microsystems. The predicted results on the static and dynamic behavior of a capacitive MEMS device, fabricated through MUMPs process, under the influence of the fabrication limitation and operating environment are presented along with the test results. The comparison between the predicted and experimental results shows a good agreement.
Boundary Behavior of the Ginzburg-Landau Order Parameter in the Surface Superconductivity Regime
NASA Astrophysics Data System (ADS)
Correggi, Michele; Rougerie, Nicolas
2016-01-01
We study the 2D Ginzburg--Landau theory for a type-II superconductor in an applied magnetic field varying between the second and third critical value. In this regime the order parameter minimizing the GL energy is concentrated along the boundary of the sample and is well approximated to leading order (in L 2 norm) by a simplified 1D profile in the direction perpendicular to the boundary. Motivated by a conjecture of Xing-Bin Pan, we address the question of whether this approximation can hold uniformly in the boundary region. We prove that this is indeed the case as a corollary of a refined, second order energy expansion including contributions due to the curvature of the sample. Local variations of the GL order parameter are controlled by the second order term of this energy expansion, which allows us to prove the desired uniformity of the surface superconductivity layer.
Eigenmode Analysis of Boundary Conditions for One-Dimensional Preconditioned Euler Equations
NASA Technical Reports Server (NTRS)
Darmofal, David L.
1998-01-01
An analysis of the effect of local preconditioning on boundary conditions for the subsonic, one-dimensional Euler equations is presented. Decay rates for the eigenmodes of the initial boundary value problem are determined for different boundary conditions. Riemann invariant boundary conditions based on the unpreconditioned Euler equations are shown to be reflective with preconditioning, and, at low Mach numbers, disturbances do not decay. Other boundary conditions are investigated which are non-reflective with preconditioning and numerical results are presented confirming the analysis.
Higher-order conditioning and the retrosplenial cortex.
Todd, Travis P; Huszár, Roman; DeAngeli, Nicole E; Bucci, David J
2016-09-01
The retrosplenial cortex (RSC) is known to contribute to contextual and spatial learning and memory. This is consistent with its well-established connectivity; the RSC is located at the interface of visuo-spatial association areas and the parahippocampal-hippocampal memory system. However, the RSC also contributes to learning and memory for discrete cues. For example, both permanent lesions and temporary inactivation of the RSC have been shown to impair sensory preconditioning, a form of higher-order conditioning. The purpose of the present experiment was to examine the role of the RSC in a closely related higher-order conditioning paradigm: second-order conditioning. Sham and RSC lesioned rats received first-order conditioning in which one visual stimulus (V1) was paired with footshock and one visual stimulus (V2) was not. Following first-order conditioning, one auditory stimulus (A1) was then paired with V1 and a second auditory stimulus (A2) was paired with V2. Although lesions of the RSC impaired the first-order discrimination, they had no impact on the acquisition of second-order conditioning. Thus, the RSC does not appear necessary for acquisition/expression of second-order fear conditioning. The role of the RSC in higher-order conditioning, as well as a possible dissociation from the hippocampus, is discussed. PMID:27208598
Boundary conditions for gas flow problems from anisotropic scattering kernels
NASA Astrophysics Data System (ADS)
To, Quy-Dong; Vu, Van-Huyen; Lauriat, Guy; Léonard, Céline
2015-10-01
The paper presents an interface model for gas flowing through a channel constituted of anisotropic wall surfaces. Using anisotropic scattering kernels and Chapman Enskog phase density, the boundary conditions (BCs) for velocity, temperature, and discontinuities including velocity slip and temperature jump at the wall are obtained. Two scattering kernels, Dadzie and Méolans (DM) kernel, and generalized anisotropic Cercignani-Lampis (ACL) are examined in the present paper, yielding simple BCs at the wall fluid interface. With these two kernels, we rigorously recover the analytical expression for orientation dependent slip shown in our previous works [Pham et al., Phys. Rev. E 86, 051201 (2012) and To et al., J. Heat Transfer 137, 091002 (2015)] which is in good agreement with molecular dynamics simulation results. More important, our models include both thermal transpiration effect and new equations for the temperature jump. While the same expression depending on the two tangential accommodation coefficients is obtained for slip velocity, the DM and ACL temperature equations are significantly different. The derived BC equations associated with these two kernels are of interest for the gas simulations since they are able to capture the direction dependent slip behavior of anisotropic interfaces.
Outflow Boundary Conditions for Blood Flow in Arterial Trees
Du, Tao; Hu, Dan; Cai, David
2015-01-01
In the modeling of the pulse wave in the systemic arterial tree, it is necessary to truncate small arterial crowns representing the networks of small arteries and arterioles. Appropriate boundary conditions at the truncation points are required to represent wave reflection effects of the truncated arterial crowns. In this work, we provide a systematic method to extract parameters of the three-element Windkessel model from the impedance of a truncated arterial tree or from experimental measurements of the blood pressure and flow rate at the inlet of the truncated arterial crown. In addition, we propose an improved three-element Windkessel model with a complex capacitance to accurately capture the fundamental-frequency time lag of the reflection wave with respect to the incident wave. Through our numerical simulations of blood flow in a single artery and in a large arterial tree, together with the analysis of the modeling error of the pulse wave in large arteries, we show that both a small truncation radius and the complex capacitance in the improved Windkessel model play an important role in reducing the modeling error, defined as the difference in dynamics induced by the structured tree model and the Windkessel models. PMID:26000782
On stochastic inlet boundary condition for unsteady simulations
NASA Astrophysics Data System (ADS)
Niedoba, P.; Jícha, M.; Čermák, L.
2014-03-01
The paper deals with the stochastic generation of synthesized turbulence, which may be used for a generating of an inlet boundary condition for unsteady simulations, e.g. Direct Numerical Simulation (DNS) or Large Eddy Simulation (LES). Assumptions for the generated turbulence are isotropy and homogeneity. The described method produces a stochastic turbulent velocity field using the synthesis of a finite sum of random Fourier modes. The calculation of individual Fourier modes is based on known energy spectrum of turbulent flow, and some turbulent quantities, e.g. turbulent kinetic energy and turbulent dissipation rate. A division of wave number range of the energy spectrum determines directly the number of Fourier modes, and has a direct impact on accuracy and speed of this calculation. Therefore, this work will examine the influence of the number of Fourier modes on a conservation of the first and second statistical moments of turbulent velocity components, which are prespecified. It is important to ensure a sufficient size of a computational domain, and a sufficient number of cells for meaningful comparative results. Dimensionless parameters characterizing the resolution and size of the computational domain according to a turbulent length scale will be introduced for this purpose. Subsequently, the sufficient values of this parameters will be shown for individual numbers of Fourier modes.
Effect of electromagnetic boundary condition on dynamo actions
NASA Astrophysics Data System (ADS)
Xu, MingTian
2015-04-01
In this paper, based on the mean field dynamo theory, the influence of the electromagnetic boundary condition on the dynamo actions driven by the small scale turbulent flows in a cylindrical vessel is investigated by the integral equation approach. The numerical results show that the increase of the electrical conductivity or magnetic permeability of the walls of the cylindrical vessel can reduce the critical magnetic Reynolds number. Furthermore, the critical magnetic Reynolds number is more sensitive to the varying electrical conductivity of the end wall or magnetic permeability of the side wall. For the anisotropic dynamo which is the mean field model of the Karlsruhe experiment, when the relative electrical conductivity of the side wall or the relative magnetic permeability of the end wall is less than some critical value, the m=1 ( m is the azimuthal wave number) magnetic mode is the dominant mode, otherwise the m=0 mode predominates the excited magnetic field. Therefore, by changing the material of the walls of the cylindrical vessel, one can select the magnetic mode excited by the anisotropic dynamo.
Analytical model of infiltration under constant-concentration boundary conditions
NASA Astrophysics Data System (ADS)
Triadis, D.; Broadbridge, P.
2010-03-01
Known integrable models for 1D flow in unsaturated soil have a rescaled soil water diffusivity that is either constant or proportional to C(C - 1)/(C - Θ)2, where Θ is the degree of saturation and C > 1 is constant. With a wider more realistic range of hydraulic conductivity functions than has been used in this context before, a formal series solution is developed for infiltration, subject to constant-concentration boundary conditions. A readily programmed iteration algorithm, applicable for any value of C, is used to construct many coefficients of the infiltration series without requiring any numerical integration. In particular, for either C - 1 small or 1/C small, several infiltration series coefficients are constructed as formal power series in C - 1 or in 1/C, for which we construct a number of terms explicitly. In the limit as the diffusivity approaches a delta function, the infiltration coefficients are obtained in simpler closed form. All but the sorptivity depend on the form of the conductivity function.
Generalized Radiation Boundary Conditions in Gyrotron Oscillator Modeling
NASA Astrophysics Data System (ADS)
Alberti, S.; Tran, T. M.; Brunner, S.; Braunmueller, F.; Genoud, J.; Hogge, J.-Ph.; Tran, M. Q.
2015-11-01
A numerical procedure to implement a frequency-independent generalized non-reflecting radiation boundary conditions, GNRBC, based on the Laplace Transform, is described in details and tested successfully on a simple 2 frequency test problem. In the case of non-stationary regimes occurring in gyrotron oscillators, it is shown that the reflection at frequencies significantly separated from the carrier frequency can be effectively suppressed by this method. A detailed analysis shows that this numerical approach can be consistently used only for models in which there is no assumed separation of time scales between the RF field envelope time-evolution and the electron time of flight across the interaction region. The GNRBC has been implemented in a nonlinear time-dependent self-consistent monomode model, TWANGpic, in which there is no time scale separation since the RF field envelope is updated at each integration time step of the electron motion. The illustration of the effectiveness of the GNRBC is made with TWANGpic on a gyrotron for which extensive theoretical and experimental results have been performed.
Boundary Conditions for Aeolian Activity in North American Dune Fields
NASA Astrophysics Data System (ADS)
Halfen, A. F.; Lancaster, N.; Wolfe, S.
2014-12-01
Geomorphic and chronological data for dune fields are evaluated for three contrasting areas of North America: 1) the Prairie-Parkland-Boreal ecozones of the northern Great Plains in Canada; 2) the Central Great Plains of the USA; and 3) the deserts of southwestern USA and northern Mexico. Luminescence and radiocarbon ages for periods of dune accumulation and stability are compared with palaeoenvironment proxies to provide an assessment of the boundary conditions of dune system response to changes in sediment supply, availability, and mobility. Dune fields in the northern Great Plains were formed from sediment originating from glaciofluvial or glaciolacustrine sediments deposited during deglaciation 16-11 ka. Subsequent aeolian deposition occurred in Parkland and Prairie dune fields as a result of mid-Holocene (8-5 ka) and late-Holocene (< 3.5 ka) activity related to drought conditions that reworked pre-existing aeolian sands. In the Central Great Plains, dune fields are closely linked to fluvial sediment sources. Sediment supply was high during deglaciation of the Rocky Mountains and resulted in widespread dune construction 16-10 ka. Multiple periods of Holocene reactivation are recorded and reflect increased sediment availability during drought episodes. Dune fields in the southwestern deserts experienced periods of construction as a result of enhanced supply of sediment from fluvial and lacustrine sources during the period 11.8-8 ka and at multiple intervals during the late Holocene. Despite spatial and temporal gaps in chronometric data as a result of sampling biases, the record from North American dune fields indicates the strong influence of sediment supply on dune construction, with changes in sediment availability as a result of drought episodes resulting in dune field reactivation and reworking of pre-existing sediment.
Inflow/outflow boundary conditions and global dynamics of spatial mixing layers
NASA Technical Reports Server (NTRS)
Buell, J. C.; Huerre, P.
1988-01-01
The numerical simulation of incompressible spatially-developing shear flows poses a special challenge to computational fluid dynamicists. The Navier-Stokes equations are elliptic and boundary equations need to be specified at the inflow and outflow boundaries in order to compute the fluid properties within the region of interest. It is, however, difficult to choose inflow and outflow conditions corresponding to a given experimental situation. Furthermore the effects that changes in the boundary conditions or in the size of the computational domain may induce on the global dynamics of the flow are presently unknown. These issues are examined in light of recent developments in hydrodynamic stability theory. The particular flow considered is the spatial mixing layer but it was expected that similar phenomena were bound to occur in other cases such as channel flow, the boundary layer, etc. A short summary of local/global and absolute/convective instability concepts is given. The results of numerical simulations are presented which strongly suggest that global resonances may be triggered in domains of finite streamwise extent although the evolution of the perturbation vorticity field is everywhere locally convective. A relationship between finite domains and pressure sources which might help in devising a scheme to eliminate these difficulties is discussed.
Global boundary conditions for a Dirac operator on the solid torus
Klimek, Slawomir; McBride, Matt
2011-06-15
We study a Dirac operator subject to Atiayh-Patodi-Singer-like boundary conditions on the solid torus and shows that the corresponding boundary value problem is elliptic in the sense that the Dirac operator has a compact parametrix.
Further development and testing of a second-order bulk boundary layer model. Master's thesis
Krasner, R.D.
1993-05-03
A one-layer bulk boundary layer model is developed. The model predicts the mixed layer values of the potential temperature, mixing ratio, and u- and v-momentum. The model also predicts the depth of the boundary layer and the vertically integrated turbulence kinetic energy (TKE). The TKE is determined using a second-order closure that relates the rate of dissipation to the TKE. The fractional area covered by rising motion sigma and the entrainment rate (E) are diagnostically determined. The model is used to study the clear convective boundary layer (CBL) using data from the Wangara, Australia boundary layer experiment. The Wangara data is also used as an observation base to validate model results. A further study is accomplished by simulating the planetary boundary layer (PBL) over an ocean surface. This study is designed to find the steady-state solutions of the prognostic variable.
Effect of Insolation Boundary Conditions on Type B Package Internal Temperatures
Hovingh, J; Shah, VL
2002-05-30
The prescription of the initial conditions and the final conditions for a thermal accident for Type B packages are different for differing regulations. This paper presents an analytical method for estimating the effect of the boundary conditions on post-fire peak internal package temperatures. Results are given for several boundary conditions for a Type B drum-type package.
A Discrete Analysis of Non-reflecting Boundary Conditions for Discontinuous Galerkin Method
NASA Technical Reports Server (NTRS)
Hu, Fang Q.; Atkins, Harold L.
2003-01-01
We present a discrete analysis of non-reflecting boundary conditions for the discontinuous Galerkin method. The boundary conditions considered in this paper include the recently proposed Perfectly Matched Layer absorbing boundary condition for the linearized Euler equation and two non-reflecting boundary conditions based on the characteristic decomposition of the flux on the boundary. The analyses for the three boundary conditions are carried out in a unifled way. In each case, eigensolutions of the discrete system are obtained and applied to compute the numerical reflection coefficients of a specified out-going wave. The dependencies of the reflections at the boundary on the out-going wave angle and frequency as well as the mesh sizes arc? studied. Comparisons with direct numerical simulation results are also presented.
NASA Astrophysics Data System (ADS)
Biswas, Debabrata; Singh, Gaurav; Kumar, Raghwendra
2015-09-01
Numerical solution of the Poisson equation in metallic enclosures, open at one or more ends, is important in many practical situations, such as high power microwave or photo-cathode devices. It requires imposition of a suitable boundary condition at the open end. In this paper, methods for solving the Poisson equation are investigated for various charge densities and aspect ratios of the open ends. It is found that a mixture of second order and third order local asymptotic boundary conditions is best suited for large aspect ratios, while a proposed non-local matching method, based on the solution of the Laplace equation, scores well when the aspect ratio is near unity for all charge density variations, including ones where the centre of charge is close to an open end or the charge density is non-localized. The two methods complement each other and can be used in electrostatic calculations where the computational domain needs to be terminated at the open boundaries of the metallic enclosure.
Biswas, Debabrata; Singh, Gaurav; Kumar, Raghwendra
2015-09-15
Numerical solution of the Poisson equation in metallic enclosures, open at one or more ends, is important in many practical situations, such as high power microwave or photo-cathode devices. It requires imposition of a suitable boundary condition at the open end. In this paper, methods for solving the Poisson equation are investigated for various charge densities and aspect ratios of the open ends. It is found that a mixture of second order and third order local asymptotic boundary conditions is best suited for large aspect ratios, while a proposed non-local matching method, based on the solution of the Laplace equation, scores well when the aspect ratio is near unity for all charge density variations, including ones where the centre of charge is close to an open end or the charge density is non-localized. The two methods complement each other and can be used in electrostatic calculations where the computational domain needs to be terminated at the open boundaries of the metallic enclosure.
NASA Technical Reports Server (NTRS)
Davis, J. E.; Medan, R. T.
1977-01-01
This segment of the POTFAN system is used to generate right hand sides (boundary conditions) of the system of equations associated with the flow field under consideration. These specified flow boundary conditions are encountered in the oblique derivative boundary value problem (boundary value problem of the third kind) and contain the Neumann boundary condition as a special case. Arbitrary angle of attack and/or sideslip and/or rotation rates may be specified, as well as an arbitrary, nonuniform external flow field and the influence of prescribed singularity distributions.
Second-Order Conditioning during a Compound Extinction Treatment
ERIC Educational Resources Information Center
Pineno, Oskar; Zilski, Jessica M.; Schachtman, Todd R.
2007-01-01
Two conditioned taste aversion experiments with rats were conducted to establish if a target taste that had received a prior pairing with illness could be subject to second-order conditioning during extinction treatment in compound with a flavor that also received prior conditioning. In these experiments, the occurrence of second-order…
On the convergence of a fourth-order method for a class of singular boundary value problems
NASA Astrophysics Data System (ADS)
Pandey, R. K.; Singh, Arvind K.
2009-02-01
In the present paper we extend the fourth order method developed by Chawla et al. [M.M. Chawla, R. Subramanian, H.L. Sathi, A fourth order method for a singular two-point boundary value problem, BIT 28 (1988) 88-97] to a class of singular boundary value problems where p(x)=xb0q(x), b0>=0 is a non-negative function. The order of accuracy of the method is established under quite general conditions on f(x,y) and is also verified by one example. The oxygen diffusion problem in a spherical cell and a nonlinear heat conduction model of a human head are presented as illustrative examples. For these examples, the results are in good agreement with existing ones.
Second-order Knudsen-layer analysis for the generalized slip-flow theory: Boundary curvature effects
NASA Astrophysics Data System (ADS)
Hattori, Masanari; Takata, Shigeru
2015-11-01
A systematic asymptotic analysis of the Boltzmann equation shows that the overall behavior of a gas can be described by fluid-dynamic-type equations with the appropriate slip/jump boundary condition when the Knudsen number is small [the generalized slip-flow theory; see Y. Sone, Molecular Gas Dynamics (Birkhäuser, Boston, 2007)]. Near the boundary, a non-fluid-like correction (the Knudsen-layer correction) to the overall solution is required. Although the theory itself has been established up to the second order of the Knudsen number expansion, the data of the correction have been lacking for a long time for the original Boltzmann equation. Recently, we have obtained the required data, except for the effects of boundary curvature, assuming the hard-sphere molecules and the diffuse reflection boundary condition. In the present work, the effects of boundary curvature have been clarified in details, thereby completing the required numerical data. A local singularity appears at the level of the velocity distribution function. We have developed the numerical method that handles such a singularity safely. The present work is supported in part by KAKENHI from JSPS (Nos. 23360083 and 13J01011).
Lyard, F.; Genco, M.L.
1994-10-01
A bidimensional, spectral in time, quasi-linearised hydrodynamic ocean tide model has been developed at the Institut de Mecanique de Grenoble. This model is derived from the classical shallow water equations by removing the velocity unknowns in the continuity equation, that leads to an elliptic, second-order differential equation where tide denivellation remains the only unknown quantity. The problem is solved in its variational formulation and the finite elements method is used to discretise the equations in the spatial domain with a Lagrange-P2 approximation. Bottom topography has to be known at the integration points of the elements. In the case of the large oceanic basins, a specific method, called the bathymetry optimisation method, is needed to correctly take into account the bottom topography inside the model. The accuracy of the model`s solutions is also strongly dependent on the quality of the open boundary conditions because of the elliptic characteristics of the problem. The optimisation method for open boundary conditions relies on the use of the in situ data available in the modelled domain. The aim of this paper is to present the basis of these optimisations of bathymetry and open boundary conditions. An illustration of the related improvements is presented on the North Atlantic Basin. 36 refs., 10 figs., 5 tabs.
Investigating TIME-GCM Atmospheric Tides for Different Lower Boundary Conditions
NASA Astrophysics Data System (ADS)
Haeusler, K.; Hagan, M. E.; Lu, G.; Forbes, J. M.; Zhang, X.; Doornbos, E.
2013-12-01
It has been recently established that atmospheric tides generated in the lower atmosphere significantly influence the geospace environment. In order to extend our knowledge of the various coupling mechanisms between the different atmospheric layers, we rely on model simulations. Currently there exist two versions of the Global Scale Wave Model (GSWM), i.e. GSWM02 and GSWM09, which are used as a lower boundary (ca. 30 km) condition for the Thermosphere-Ionosphere-Mesosphere-Electrodynamics General Circulation Model (TIME-GCM) and account for the upward propagating atmospheric tides that are generated in the troposphere and lower stratosphere. In this paper we explore the various TIME-GCM upper atmospheric tidal responses for different lower boundary conditions and compare the model diagnostics with tidal results from satellite missions such as TIMED, CHAMP, and GOCE. We also quantify the differences between results associated with GSWM02 and GSWM09 forcing and results of TIMEGCM simulations using Modern-Era Retrospective Analysis for Research and Application (MERRA) data as a lower boundary condition.
NASA Astrophysics Data System (ADS)
Boutaghane, A.; Bouhadef, K.; Valensi, F.; Pellerin, S.; Benkedda, Y.
2011-04-01
This paper presents results of theoretical and experimental investigation of the welding arc in Gas Tungsten Arc Welding (GTAW) and Gas Metal Arc Welding (GMAW) processes. A theoretical model consisting in simultaneous resolution of the set of conservation equations for mass, momentum, energy and current, Ohm's law and Maxwell equation is used to predict temperatures and current density distribution in argon welding arcs. A current density profile had to be assumed over the surface of the cathode as a boundary condition in order to make the theoretical calculations possible. In stationary GTAW process, this assumption leads to fair agreement with experimental results reported in literature with maximum arc temperatures of ~21 000 K. In contrast to the GTAW process, in GMAW process, the electrode is consumable and non-thermionic, and a realistic boundary condition of the current density is lacking. For establishing this crucial boundary condition which is the current density in the anode melting electrode, an original method is setup to enable the current density to be determined experimentally. High-speed camera (3000 images/s) is used to get geometrical dimensions of the welding wire used as anode. The total area of the melting anode covered by the arc plasma being determined, the current density at the anode surface can be calculated. For a 330 A arc, the current density at the melting anode surface is found to be of 5 × 107 A m-2 for a 1.2 mm diameter welding electrode.
NASA Astrophysics Data System (ADS)
Zhang, Tiangang; Koshizuka, Seiichi; Murotani, Kohei; Shibata, Kazuya; Ishii, Eiji; Ishikawa, Masanori
2016-02-01
The boundary conditions represented by polygons in moving particle semi-implicit (MPS) method (Koshizuka and Oka, Nuclear Science and Engineering, 1996) have been widely used in the industry simulations since it can simply simulate complex geometry with high efficiency. However, the inaccurate particle number density near non-planar wall boundaries dramatically affects the accuracy of simulations. In this paper, we propose an initial boundary particle arrangement technique coupled with the wall weight function method (Zhang et al. Transaction of JSCES, 2015) to improve the particle number density near slopes and curved surfaces with boundary conditions represented by polygons in three dimensions. Two uniform grids are utilized in the proposed technique. The grid points in the first uniform grid are used to construct boundary particles, and the second uniform grid stores the same information as in the work by Zhang et al. The wall weight functions of the grid points in the second uniform grid are calculated by newly constructed boundary particles. The wall weight functions of the fluid particles are interpolated from the values stored on the grid points in the second uniform grid. Because boundary particles are located on the polygons, complex geometries can be accurately represented. The proposed method can dramatically improve the particle number density and maintain the high efficiency. The performance of the previously proposed wall weight function (Zhang et al.) with the boundary particle arrangement technique is verified in comparison with the wall weight function without boundary particle arrangement by investigating two example geometries. The simulations of a water tank with a wedge and a complex geometry show the general applicability of the boundary particle arrangement technique to complex geometries and demonstrate its improvement of the wall weight function near the slopes and curved surfaces.
NASA Astrophysics Data System (ADS)
Groh, Jannis; Vanderborght, Jan; Pütz, Thomas; Vereecken, Harry
2014-05-01
The SOILCan lysimeter network is a large scale climate feedback experiment and is embedded in the four long term observatories of TERENO (TERestrial ENvironmental Observatories). The focus of the SOILCan-project is to observe the impact of climate change on water and matter budgets in different grass- and arable-land lysimeters. The monitoring infrastructure was established across a rainfall and temperature transect along which lysimeters were transported from wetter to drier conditions. The lysimeters in SOILCan have a controlled bottom boundary condition using a rack of suction candles that enables upward and downward flow of water. This pressure head at the bottom is controlled by measured soil water potentials in undisturbed soil in the close vicinity of the bottom of the lysimeter. For transported lysimeters this controlling approach no longer works as the surrounding soil profile and both its upper climatic boundary conditions and lower boundary conditions related to its hydrogeological setting differ from the place where the lysimeter was taken from. In order to evaluate these artefacts and to derive a suited approach to control the lower boundary of transported lysimeters, water balance simulations were run. We analyzed three different approaches to impose bottom boundary conditions for transported lysimeters. A 'zeroth-order' approach is to define the bottom boundary at the bottom of the lysimeter and use the pressure heads measured at the location from which the soil lysimeter was taken. However, this approach is prone to artefacts since these bottom boundary conditions are determined by the climate at the site where the lysimeter was taken from. A 'first-order' approach is to define a bottom boundary condition at a certain hydrogeological boundary that can be defined deeper in the soil profile such as a seepage face or a groundwater table. However, for shallow groundwater tables, this approach may also lead to artefacts since the depth of the groundwater
NASA Astrophysics Data System (ADS)
Steich, David James
1995-01-01
The Finite Difference Time Domain (FDTD) method is a simple yet powerful method for numerically solving electromagnetic wave phenomenon on computers. The FDTD technique discretizes Maxwell's equations with finite difference equations. These finite difference equations, which approximate local field behavior, are applied to large spatial lattices allowing calculation of a vast array of electromagnetical phenomenon. The greatest strengths of the FDTD method are in its simplicity, efficiency, and diversity. FDTD is capable of modeling the scattering and coupling to lossy dielectrics, lossy magnetics, anisotropic media, dispersive media, and nonlinear materials for general geometric shapes. Wideband frequency information can be obtained using FDTD for both near and far field observation points in a single computational run. However, along with all of its benefits, the FDTD algorithm has some deficiencies. For most problems of interest, poor accuracy at geometry interfaces of differing media and at outer problem space boundarys where the spatial lattice must be truncated are the two largest error sources of the FDTD algorithm. Although most accuracy issues can be circumvented by expending large amounts of computer memory and cpu time, using excessive computer resources is not always possible and is never appealing. The purpose of this thesis is to generalize, analyze, and test various mainstream local Outer Radiating Boundary Conditions (ORBCs) for the FDTD method applied to Maxwell's equations in order to help gain a better understanding of present ORBC limitations. A common mathematical model is presented for the boundary conditions. Boundary conditions shown to fit the model include Mur, Superabsorption, Liao, Higdon, and Lindman ORBCs of varying orders. Simple operators are defined and then used to generate the final discretized equations for each of the boundary conditions, automatically, without requiring complicated high order equations. The procedure also allows
Phase-modulated solitary waves controlled by a boundary condition at the bottom.
Mukherjee, Abhik; Janaki, M S
2014-06-01
A forced Korteweg-de Vries (KdV) equation is derived to describe weakly nonlinear, shallow-water surface wave propagation over nontrivial bottom boundary condition. We show that different functional forms of bottom boundary conditions self-consistently produce different forced KdV equations as the evolution equations for the free surface. Solitary wave solutions have been analytically obtained where phase gets modulated controlled by bottom boundary condition, whereas amplitude remains constant. PMID:25019847
Implementation of C* Boundary Conditions in the Hybrid Monte Carlo Algorithm
NASA Astrophysics Data System (ADS)
Carmona, José Manuel; D'elia, Massimo; Di Giacomo, Adriano; Lucini, Biagio
In the study of QCD dynamics, C* boundary conditions are physically relevant in certain cases. In this paper, we study the implementation of these boundary conditions in the lattice formulation of full QCD with staggered fermions. In particular, we show that the usual even-odd partition trick to avoid the redoubling of the fermion matrix is still valid in this case. We give an explicit implementation of these boundary conditions for the Hybrid Monte Carlo algorithm.
Analysis of boundary conditions for SSME subsonic internal viscous flow analysis
NASA Technical Reports Server (NTRS)
Baker, A. J.
1986-01-01
A study was completed of mathematically proper boundary conditions for unique numerical solution of internal, viscous, subsonic flows in the space shuttle main engine. The study has concentrated on well posed considerations, with emphasis on computational efficiency and numerically stable boundary condition statements. The method of implementing the established boundary conditions is applicable to a wide variety of finite difference and finite element codes, as demonstrated.
Revisit boundary conditions for the self-adjoint angular flux formulation
Wang, Yaqi; Gleicher, Frederick N.
2015-03-01
We revisit the boundary conditions for SAAF. We derived the equivalent parity variational form ready for coding up. The more rigorous approach of evaluating odd parity should be solving the odd parity equation coupled with the even parity. We proposed a symmetric reflecting boundary condition although neither positive definiteness nor even-odd decoupling is achieved. A simple numerical test verifies the validity of these boundary conditions.
A generalized bag-like boundary condition for fields with arbitrary spin
NASA Astrophysics Data System (ADS)
Stokes, Adam; Bennett, Robert
2015-07-01
Boundary conditions (BCs) for the Maxwell and Dirac fields at material surfaces are widely-used and physically well-motivated, but do not appear to have been generalized to deal with higher spin fields. As a result there is no clear prescription as to which BCs should be selected in order to obtain physically-relevant results pertaining to confined higher spin fields. This lack of understanding is significant given that boundary-dependent phenomena are ubiquitous across physics, a prominent example being the Casimir effect. Here, we use the two-spinor calculus formalism to present a unified treatment of BCs routinely employed in the treatment of spin-1/2 and spin-1 fields. We then use this unification to obtain a BC that can be applied to massless fields of any spin, including the spin-2 graviton, and its supersymmetric partner the spin-3/2 gravitino.
Conditions at the downstream boundary for simulations of viscous incompressible flow
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas
1990-01-01
The proper specification of boundary conditions at artificial boundaries for the simulation of time-dependent fluid flows has long been a matter of controversy. A general theory of asymptotic boundary conditions for dissipative waves is applied to the design of simple, accurate conditions at downstream boundary for incompressible flows. For Reynolds numbers far enough below the critical value for linear stability, a scaling is introduced which greatly simplifies the construction of the asymptotic conditions. Numerical experiments with the nonlinear dynamics of vortical disturbances to plane Poiseuille flow are presented which illustrate the accuracy of our approach. The consequences of directly applying the scalings to the equations are also considered.
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.
f(T) Gravity from Holographic Ricci Dark Energy Model with New Boundary Conditions
NASA Astrophysics Data System (ADS)
Huang, Peng; Huang, Yong-Chang; Yuan, Fang-Fang
2013-11-01
Commonly used boundary conditions in reconstructing f(T) gravity from holographic Ricci dark energy (RDE) model are found to cause some problem, we therefore propose new boundary conditions in this paper. By reconstructing f(T) gravity from the RDE with these new boundary conditions, we show that the new ones are better than the present commonly used ones since they can give the physically expected information, which is lost when the commonly used ones are taken in the reconstruction, of the resulting f(T) theory. Thus, the new boundary conditions proposed here are more suitable for the reconstruction of f(T) gravity.
Entanglement and area law with a fractal boundary in a topologically ordered phase
Hamma, Alioscia; Lidar, Daniel A.; Severini, Simone
2010-01-15
Quantum systems with short-range interactions are known to respect an area law for the entanglement entropy: The von Neumann entropy S associated to a bipartition scales with the boundary p between the two parts. Here we study the case in which the boundary is a fractal. We consider the topologically ordered phase of the toric code with a magnetic field. When the field vanishes it is possible to analytically compute the entanglement entropy for both regular and fractal bipartitions (A,B) of the system and this yields an upper bound for the entire topological phase. When the A-B boundary is regular we have S/p=1 for large p. When the boundary is a fractal of the Hausdorff dimension D, we show that the entanglement between the two parts scales as S/p=gamma<=1/D, and gamma depends on the fractal considered.
Analysis of a Time Implicit Scheme for the Oseen Model Driven by Nonlinear Slip Boundary Conditions
NASA Astrophysics Data System (ADS)
Djoko, J. K.; Lubuma, J. M.
2016-04-01
This work is concerned with the time discrete analysis of the Oseen system of equations driven by nonlinear slip boundary conditions of friction type. We study the existence of solutions of the time discrete model and derive several a priori estimates needed to recover the solution of the continuous problem by means of weak compactness. Moreover, for the difference between the exact and approximate solutions, we obtain the rate of convergence of order one with respect to the time step without imposing extra regularity on the weak solution.
An analytical method of free vibration for laminated plates including various boundary conditions
NASA Astrophysics Data System (ADS)
Xia, Chuanyou; Wen, Lizhou
1991-10-01
It is shown that, by introducing the displacement function Phi(x, y, t), the system of original differential equations developed by Whitney and Pagano (1970) for the first-order shear deformation theory of symmetric cross-ply laminated plates can be transformed into a single differential equation of the displacement function. On the basis of this differential equation an exact solution is given to the problem of free vibration of symmetric cross-ply laminated plates including various boundary conditions. It is shown that the natural frequencies obtained by the present analytical method are lower than those of results obtained using approximate methods.
A new conformal absorbing boundary condition for finite element meshes and parallelization of FEMATS
NASA Technical Reports Server (NTRS)
Chatterjee, A.; Volakis, J. L.; Nguyen, J.; Nurnberger, M.; Ross, D.
1993-01-01
Some of the progress toward the development and parallelization of an improved version of the finite element code FEMATS is described. This is a finite element code for computing the scattering by arbitrarily shaped three dimensional surfaces composite scatterers. The following tasks were worked on during the report period: (1) new absorbing boundary conditions (ABC's) for truncating the finite element mesh; (2) mixed mesh termination schemes; (3) hierarchical elements and multigridding; (4) parallelization; and (5) various modeling enhancements (antenna feeds, anisotropy, and higher order GIBC).
Computation of the high temperature Coulomb density matrix in periodic boundary conditions
NASA Astrophysics Data System (ADS)
Militzer, B.
2016-07-01
The high temperature many-body density matrix is fundamental to path integral computation. The pair approximation, where the interaction part is written as a product of pair density matrices, is commonly used and is accurate to order τ2, where τ is the step size in the imaginary time. Here we present a method for systems with Coulomb interactions in periodic boundary conditions that consistently treats the all interactions with the same level of accuracy. It is shown that this leads to a more accurate high temperature solution of the Bloch equation. The method is applied to many-body simulation and tests for the isolated hydrogen atom and molecule are presented.
NASA Astrophysics Data System (ADS)
Zhao, Peng; Jia, Junguo; Xu, Mengmeng
2013-06-01
In this article, the well posedness of the Cauchy problem associated to transport equations with singular cross-sections (i.e., unbounded collision frequencies and unbounded collision operators) on Lp spaces with periodic boundary conditions is discussed, and some compactness (or weak compactness) of the first order remainder term of the Dyson-Phillips expansion for a large class of singular collision operators is proved on Lp(1 < p < ∞) (or L1) spaces. Thus, this allows us to evaluate the essential type of the transport semigroup from which the asymptotic behavior and the well posedness of the solution is derived. Consequently, the stability of the essential spectrum is concluded.
Evaporation from soils subjected to natural boundary conditions at the land-atmospheric interface
NASA Astrophysics Data System (ADS)
Smits, K.; Illngasekare, T.; Ngo, V.; Cihan, A.
2012-04-01
Bare soil evaporation is a key process for water exchange between the land and the atmosphere and an important component of the water balance in semiarid and arid regions. However, there is no agreement on the best methodology to determine evaporation under different boundary conditions at the land surface. This becomes critical in developing models that couples land to the atmosphere. Because it is difficult to measure evaporation from soil, with the exception of using lysimeters, numerous formulations have been proposed to establish a relationship between the rate of evaporation and soil moisture and/or soil temperature and thermal properties. Different formulations vary in how they partition available energy. A need exists to systematically compare existing methods to experimental data under highly controlled conditions not achievable in the field. The goal of this work is to perform controlled experiments under transient conditions of soil moisture, temperature and wind at the land/atmospheric interface to test different conceptual and mathematical formulations for the soil surface boundary conditions to develop appropriate numerical models to be used in simulations. In this study, to better understand the coupled water-vapor-heat flow processes in the shallow subsurface near the land surface, we modified a previously developed theory by Smits et al. [2011] that allows non-equilibrium liquid/gas phase change with gas phase vapor diffusion to better account for dry soil conditions. The model did not implement fitting parameters such as a vapor enhancement factor that is commonly introduced into the vapor diffusion coefficient as an arbitrary multiplication factor. In order to experimentally test the numerical formulations/code, we performed a two-dimensional physical model experiment under varying boundary conditions using test sand for which the hydraulic and thermal properties were well characterized. Precision data under well-controlled transient heat and
A suitable boundary condition for bounded plasma simulation without sheath resolution
Parker, S.E.; Procassini, R.J.; Birdsall, C.K. ); Cohen, B.I. )
1993-01-01
We have developed a technique that allows for a sheath boundary layer without having to resolve the inherently small space and time scales of the sheath region. We refer to this technique as the logical sheath boundary condition. This boundary condition, when incorporated into a direct-implicit particle code, permits large space- and time-scale simulations of bounded systems, which would otherwise be impractical on current supercomputers. The lack of resolution of the collector sheath potential drop obtained from conventional implicit simulations at moderate values of [omega][sub pe][Delta]t and [Delta]z/[lambda][sup De] provides the motivation for the development of the logical sheath boundary condition. The algorithm for use of the logical sheath boundary condition in a particle simulation is presented. Results from simulations which use the logical sheath boundary condition are shown to compare reasonably well with those from an analytic theory and simulations in which the sheath is resolved.
NASA Astrophysics Data System (ADS)
Borjan, Z.
2016-09-01
We consider critical Casimir force in the Ising strips with boundary conditions defined by standard normal and ordinary surface universality classes containing also the internal grain boundary. Using exact variational approach of Mikheev and Fisher we have elaborated on behaviors of Casimir amplitudes Δ++(g) , ΔOO(g) and Δ+O(g) , corresponding to normal-normal, ordinary-ordinary and mixed normal-ordinary boundary conditions, respectively, with g as a strength of the grain boundary. Closed analytic results describe Casimir amplitudes Δ++(g) and ΔOO(g) as continuous functions of the grain boundary's strength g, changing the character of the Casimir force from repulsive to attractive and vice versa for certain domains of g. Present results reveal a new type of symmetry between Casimir amplitudes Δ++(g) and ΔOO(g) . Unexpectedly simple constant result for the Casimir amplitude Δ+O(g) = π/12 we have comprehensively interpreted in terms of equilibrium states of the present Ising strip as a complex interacting system comprising two sub-systems. Short-distance expansions of energy density profiles in the vicinity of the grain boundary reveal new distant-wall correction amplitudes that we examined in detail. Analogy of present considerations with earlier more usual short-distance expansions near one of the (N), (O) and (SB) boundaries, as well as close to surfaces with variable boundary conditions refers to the set of scaling dimensions appearing in the present calculations but also to the discovery of the de Gennes-Fisher distant wall correction amplitudes.
Incorporation of a boundary condition to numerical solution of POISSON's equation
Caspi, S.; Helm, M.; Laslett, L.J.
1988-10-01
Two-dimensional and axially-symmetric problems in electrostatics, magnetostatics or potential fluid flow frequently are solved numerically by means of relaxation techniques -- employing, for example, the finite-difference program POISSON. In many such problems, the ''sources'' (charges or currents, vorticity, and regions of permeable material) lie exclusively within a finite closed boundary curve and the relaxation process, in principle, then can be confined to the region interior to such a boundary -- provided that a suitable boundary condition is imposed on the solution at the boundary. This paper is a review and illustration of a computational method that uses a boundary condition of such a nature as to avoid the inaccuracies and more extensive meshes present when, alternatively, a simple Dirichlet or Neumann boundary condition is specified on a somewhat more remote outer boundary. 2 refs., 5 figs., 1 tab.
NASA Astrophysics Data System (ADS)
Goodman, Michael L.
1990-10-01
The Mie series solution for the scattered field of a sphere with an anisotropic impedance boundary condition (IBC) is derived along with the corresponding scattering cross section. Conditions on the impedance that ensure a unique solution for the scattered field are derived. The anisotropic IBC is derived for a material with an anisotropic electric permittivity and a large anisotropic conductivity. For the special case of an isotropic IBC, a method is presented for testing whether any given impedance leads to a unique solution for the scattered field, and it is shown that, for every incident wave frequency and mode number l, there are exactly two values of the impedance for which the scattered field is not unique.
Molecular insights into the boundary conditions in the Stokes-Einstein relation
NASA Astrophysics Data System (ADS)
Ishii, Yoshiki; Ohtori, Norikazu
2016-05-01
In order to mimic the Brownian particle in liquid, molecular dynamics calculations of dilute solutions of spherical fullerene molecules with various sizes in liquid Ar were performed. To establish the scaling equation for self-diffusion coefficient, D , of the fullerenes, the dependence of D was examined on the mass ratio of solute to solvent and on the energy-parameter ratio used in the Lennard-Jones potentials. The dependence on the energy-parameter ratio remains up to C540, whereas D rapidly becomes independent of the mass ratio with increasing mass of the solute. The product of the scaling equations obtained for the D of the solute and for shear viscosity, ηsv, for the solvent gives a relation which replaces the Stokes-Einstein relation based on the hydrodynamics. The present expression does not need both the boundary conditions and the hydrodynamic particle size, but instead the energy-parameter ratio, packing fraction of solvent, and bare size of solute. From the viewpoint of the tackiness at the boundary, the cage correlation function around the diffusing particle was examined; it was found that the decay time of the function depends mainly on the the energy-parameter ratio. Therefore, the energy-parameter ratio accounts for the main part of both the boundary conditions and the hydrodynamic particle size in the Stokes equation, which have so far been ill-defined in any molecular theories.
Molecular insights into the boundary conditions in the Stokes-Einstein relation.
Ishii, Yoshiki; Ohtori, Norikazu
2016-05-01
In order to mimic the Brownian particle in liquid, molecular dynamics calculations of dilute solutions of spherical fullerene molecules with various sizes in liquid Ar were performed. To establish the scaling equation for self-diffusion coefficient, D, of the fullerenes, the dependence of D was examined on the mass ratio of solute to solvent and on the energy-parameter ratio used in the Lennard-Jones potentials. The dependence on the energy-parameter ratio remains up to C_{540}, whereas D rapidly becomes independent of the mass ratio with increasing mass of the solute. The product of the scaling equations obtained for the D of the solute and for shear viscosity, η_{sv}, for the solvent gives a relation which replaces the Stokes-Einstein relation based on the hydrodynamics. The present expression does not need both the boundary conditions and the hydrodynamic particle size, but instead the energy-parameter ratio, packing fraction of solvent, and bare size of solute. From the viewpoint of the tackiness at the boundary, the cage correlation function around the diffusing particle was examined; it was found that the decay time of the function depends mainly on the the energy-parameter ratio. Therefore, the energy-parameter ratio accounts for the main part of both the boundary conditions and the hydrodynamic particle size in the Stokes equation, which have so far been ill-defined in any molecular theories. PMID:27300813
Forward and Backward Second-Order Pavlovian Conditioning in Honeybees
ERIC Educational Resources Information Center
Hussaini, Syed Abid; Komischke, Bernhard; Menzel, Randolf; Lachnit, Harald
2007-01-01
Second-order conditioning (SOC) is the association of a neutral stimulus with another stimulus that had previously been combined with an unconditioned stimulus (US). We used classical conditioning of the proboscis extension response (PER) in honeybees ("Apis mellifera") with odors (CS) and sugar (US). Previous SOC experiments in bees were…
Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2014-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
NASA Astrophysics Data System (ADS)
Esmaili Sikarudi, M. A.; Nikseresht, A. H.
2016-01-01
Smoothed particle hydrodynamics is a robust Lagrangian particle method which is widely used in various applications, from astrophysics to hydrodynamics and heat conduction. It has intrinsic capabilities for simulating large deformation, composites, multiphysics events, and multiphase fluid flows. It is vital to use reliable boundary conditions when boundary value problems like heat conduction or Poisson equation for incompressible flows are solved. Since smoothed particle hydrodynamics is not a boundary fitted grids method, implementation of boundary conditions can be problematic. Many methods have been proposed for enhancing the accuracy of implementation of boundary conditions. In the present study a new approach for facilitating the implementation of Robin and Neumann boundary conditions is proposed and proven to give accurate results. Also there is no need to use complicated preprocessing as in virtual particle method. The new method is compared to an equivalent one dimensional moving least square scheme and it is shown that the present method is less sensitive to particle disorder.
Experimental verification of free-space singular boundary conditions in an invisibility cloak
NASA Astrophysics Data System (ADS)
Wu, Qiannan; Gao, Fei; Song, Zhengyong; Lin, Xiao; Zhang, Youming; Chen, Huanyang; Zhang, Baile
2016-04-01
A major issue in invisibility cloaking, which caused intense mathematical discussions in the past few years but still remains physically elusive, is the plausible singular boundary conditions associated with the singular metamaterials at the inner boundary of an invisibility cloak. The perfect cloaking phenomenon, as originally proposed by Pendry et al for electromagnetic waves, cannot be treated as physical before a realistic inner boundary of a cloak is demonstrated. Although a recent demonstration has been done in a waveguide environment, the exotic singular boundary conditions should apply to a general environment as in free space. Here we fabricate a metamaterial surface that exhibits the singular boundary conditions and demonstrate its performance in free space. Particularly, the phase information of waves reflected from this metamaterial surface is explicitly measured, confirming the singular responses of boundary conditions for an invisibility cloak.
NASA Technical Reports Server (NTRS)
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2015-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
NASA Astrophysics Data System (ADS)
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2015-07-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
Green's function of a heat problem with a periodic boundary condition
NASA Astrophysics Data System (ADS)
Erzhanov, Nurzhan E.
2016-08-01
In the paper, a nonlocal initial-boundary value problem for a non-homogeneous one-dimensional heat equation is considered. The domain under consideration is a rectangle. The classical initial condition with respect to t is put. A nonlocal periodic boundary condition by a spatial variable x is put. It is well-known that a solution of problem can be constructed in the form of convergent orthonormal series according to eigenfunctions of a spectral problem for an operator of multiple differentiation with periodic boundary conditions. Therefore Green's function can be also written in the form of an infinite series with respect to trigonometric functions (Fourier series). For classical first and second initial-boundary value problems there also exists a second representation of the Green's function by Jacobi function. In this paper we find the representation of the Green's function of the nonlocal initial-boundary value problem with periodic boundary conditions in the form of series according to exponents.
Thermal stability of static coronal loops: Part 1: Effects of boundary conditions
NASA Technical Reports Server (NTRS)
Antiochos, S. K.; Shoub, E. C.; An, C. H.; Emslie, A. G.
1985-01-01
The linear stability of static coronal-loop models undergoing thermal perturbations was investigated. The effect of conditions at the loop base on the stability properties of the models was considered in detail. The question of appropriate boundary conditions at the loop base was considered and it was concluded that the most physical assumptions are that the temperature and density (or pressure) perturbations vanish there. However, if the base is taken to be sufficiently deep in the chromosphere, either several chromospheric scale heights or several coronal loop lengths in depth, then the effect of the boundary conditions on loop stability becomes negligible so that all physically acceptable conditions are equally appropriate. For example, one could as well assume that the velocity vanishes at the base. The growth rates and eigenmodes of static models in which gravity is neglected and in which the coronal heating is a relatively simple function, either constant per-unit mass or per-unit volume were calculated. It was found that all such models are unstable with a growth rate of the order of the coronal cooling time. The physical implications of these results for the solar corona and transition region are discussed.
Third-order accurate entropy-stable schemes for initial-boundary-value conservation laws
NASA Astrophysics Data System (ADS)
Svärd, Magnus
2012-08-01
We consider initial-boundary-value conservation laws with the objective to obtain high-order approximations. We study two different approaches to obtain third-order accuracy, local entropy stability and a global bound on the entropy. The results are applicable to, for example the Euler equations of gas dynamics, for which we present numerical results demonstrating the robustness and accuracy of the scheme.
Higher-order accurate Osher schemes with application to compressible boundary layer stability
NASA Technical Reports Server (NTRS)
Vandervegt, J. J. W.
1993-01-01
Two fourth order accurate Osher schemes are presented which maintain higher order accuracy on nonuniform grids. They use either a conservative finite difference or finite volume discretization. Both methods are successfully used for direct numerical simulations of flat plate boundary layer instability at different Mach numbers. Results of growth rates of Tollmien-Schlichting waves compare well with direct simulations of incompressible flow and for compressible flow with results obtained by solving the parabolic stability equations.
An adaptive, formally second order accurate version of the immersed boundary method
NASA Astrophysics Data System (ADS)
Griffith, Boyce E.; Hornung, Richard D.; McQueen, David M.; Peskin, Charles S.
2007-04-01
Like many problems in biofluid mechanics, cardiac mechanics can be modeled as the dynamic interaction of a viscous incompressible fluid (the blood) and a (visco-)elastic structure (the muscular walls and the valves of the heart). The immersed boundary method is a mathematical formulation and numerical approach to such problems that was originally introduced to study blood flow through heart valves, and extensions of this work have yielded a three-dimensional model of the heart and great vessels. In the present work, we introduce a new adaptive version of the immersed boundary method. This adaptive scheme employs the same hierarchical structured grid approach (but a different numerical scheme) as the two-dimensional adaptive immersed boundary method of Roma et al. [A multilevel self adaptive version of the immersed boundary method, Ph.D. Thesis, Courant Institute of Mathematical Sciences, New York University, 1996; An adaptive version of the immersed boundary method, J. Comput. Phys. 153 (2) (1999) 509-534] and is based on a formally second order accurate (i.e., second order accurate for problems with sufficiently smooth solutions) version of the immersed boundary method that we have recently described [B.E. Griffith, C.S. Peskin, On the order of accuracy of the immersed boundary method: higher order convergence rates for sufficiently smooth problems, J. Comput. Phys. 208 (1) (2005) 75-105]. Actual second order convergence rates are obtained for both the uniform and adaptive methods by considering the interaction of a viscous incompressible flow and an anisotropic incompressible viscoelastic shell. We also present initial results from the application of this methodology to the three-dimensional simulation of blood flow in the heart and great vessels. The results obtained by the adaptive method show good qualitative agreement with simulation results obtained by earlier non-adaptive versions of the method, but the flow in the vicinity of the model heart valves
General Considerations of the Electrostatic Boundary Conditions in Oxide Heterostructures
Higuchi, Takuya
2011-08-19
When the size of materials is comparable to the characteristic length scale of their physical properties, novel functionalities can emerge. For semiconductors, this is exemplified by the 'superlattice' concept of Esaki and Tsu, where the width of the repeated stacking of different semiconductors is comparable to the 'size' of the electrons, resulting in novel confined states now routinely used in opto-electronics. For metals, a good example is magnetic/non-magnetic multilayer films that are thinner than the spin-scattering length, from which giant magnetoresistance (GMR) emerged, used in the read heads of hard disk drives. For transition metal oxides, a similar research program is currently underway, broadly motivated by the vast array of physical properties that they host. This long-standing notion has been recently invigorated by the development of atomic-scale growth and probe techniques, which enables the study of complex oxide heterostructures approaching the precision idealized in Fig. 1(a). Taking the subset of oxides derived from the perovskite crystal structure, the close lattice match across many transition metal oxides presents the opportunity, in principle, to develop a 'universal' heteroepitaxial materials system. Hand-in-hand with the continual improvements in materials control, an increasingly relevant challenge is to understand the consequences of the electrostatic boundary conditions which arise in these structures. The essence of this issue can be seen in Fig. 1(b), where the charge sequence of the sublayer 'stacks' for various representative perovskites is shown in the ionic limit, in the (001) direction. To truly 'universally' incorporate different properties using different materials components, be it magnetism, ferroelectricity, superconductivity, etc., it is necessary to access and join different charge sequences, labelled here in analogy to the designations 'group IV, III-V, II-VI' for semiconductors. As we will review, interfaces between
NASA Astrophysics Data System (ADS)
Kanguzhin, Baltabek; Tokmagambetov, Niyaz
2016-08-01
In this work, we research a boundary inverse problem of spectral analysis of a differential operator with integral boundary conditions in the functional space L2(0, b) where b < ∞. A uniqueness theorem of the inverse boundary problem in L2(0, b) is proved. Note that a boundary inverse problem of spectral analysis is the problem of recovering boundary conditions of the operator by its spectrum and some additional data.
Hydromagnetic conditions near the core-mantle boundary
NASA Technical Reports Server (NTRS)
Backus, George E.
1995-01-01
The main results of the grant were (1) finishing the manuscript of a proof of completeness of the Poincare modes in an incompressible nonviscous fluid corotating with a rigid ellipsoidal boundary, (2) partial completion of a manuscript describing a definition of helicity that resolved questions in the literature about calculating the helicities of vector fields with complicated topologies, and (3) the beginning of a reexamination of the inverse problem of inferring properties of the geomagnetic field B just outside the core-mantle boundary (CMB) from measurements of elements of B at and above the earth's surface. This last work has led to a simple general formalism for linear and nonlinear inverse problems that appears to include all the inversion schemes so far considered for the uniqueness problem in geomagnetic inversion. The technique suggests some new methods for error estimation that form part of this report.
Compressible Navier Stokes Model with Inflow-Outflow Boundary Conditions
NASA Astrophysics Data System (ADS)
Novo, Sébastien
2005-11-01
In the paper [7], author gives a definition of weak solution to the nonsteady Navier Stokes system of equations which describes compressible and isentropic flows in some bounded region Ω with influx of fluid through a part of the boundary ∂Ω. Here, we present a way for proving existence of such solutions in the same situation as in [7] under the sole hypothesis γ > 3/2 for the adiabatic constant.
On the Boundary Condition Between Two Multiplying Media
DOE R&D Accomplishments Database
Friedman, F. L.; Wigner, E. P.
1944-04-19
The transition region between two parts of a pile which have different compositions is investigated. In the case where the moderator is the same in both parts of the pile, it is found that the diffusion constant times thermal neutron density plus diffusion constant times fast neutron density satisfies the usual pile equations everywhere, right to the boundary. More complicated formulae apply in a more general case.
Trickle-down boundary conditions in aeolian dune-field pattern formation
NASA Astrophysics Data System (ADS)
Ewing, R. C.; Kocurek, G.
2015-12-01
One the one hand, wind-blown dune-field patterns emerge within the overarching boundary conditions of climate, tectonics and eustasy implying the presence of these signals in the aeolian geomorphic and stratigraphic record. On the other hand, dune-field patterns are a poster-child of self-organization, in which autogenic processes give rise to patterned landscapes despite remarkable differences in the geologic setting (i.e., Earth, Mars and Titan). How important are climate, tectonics and eustasy in aeolian dune field pattern formation? Here we develop the hypothesis that, in terms of pattern development, dune fields evolve largely independent of the direct influence of 'system-scale' boundary conditions, such as climate, tectonics and eustasy. Rather, these boundary conditions set the stage for smaller-scale, faster-evolving 'event-scale' boundary conditions. This 'trickle-down' effect, in which system-scale boundary conditions indirectly influence the event scale boundary conditions provides the uniqueness and richness of dune-field patterned landscapes. The trickle-down effect means that the architecture of the stratigraphic record of dune-field pattern formation archives boundary conditions, which are spatially and temporally removed from the overarching geologic setting. In contrast, the presence of an aeolian stratigraphic record itself, reflects changes in system-scale boundary conditions that drive accumulation and preservation of aeolian strata.
Open boundary conditions for ISPH and their application to micro-flow
NASA Astrophysics Data System (ADS)
Hirschler, Manuel; Kunz, Philip; Huber, Manuel; Hahn, Friedemann; Nieken, Ulrich
2016-02-01
Open boundary conditions for incompressible Smoothed Particle Hydrodynamics (ISPH) are rare. For stable simulations with open boundary conditions, one needs to specify all boundary conditions correctly in the pressure force as well as in the linear equation system for pressure calculation. Especially for homogeneous or non-homogeneous Dirichlet boundary conditions for pressure there exist several possibilities but only a few lead to stable results. However, this isn't trivial for open boundary conditions. We introduce a new approach for open boundary conditions for ISPH to enable stable simulations. In contrast to existing models for weakly-compressible SPH, we can specify open pressure boundary conditions because in ISPH, pressure can be calculated independently of the density. The presented approach is based on the mirror particle approach already introduced for solid wall boundary conditions. Here we divide the mirror axis in several segments with time-dependent positions. We validate the presented approach for the example of Poiseuille flow and flow around a cylinder at different Reynolds numbers and show that we get good agreement with references. Then, we demonstrate that the approach can be applied to free surface flows. Finally, we apply the new approach to micro-flow through a random porous medium with a different number of in- and outlets and demonstrate its benefits.
Technology Transfer Automated Retrieval System (TEKTRAN)
Transient unsaturated horizontal column experiments were conducted with a loam soil, under variable boundary conditions, to obtain added insight on anion exclusion processes that impact nitrate transport in soil. The boundary conditions evaluated were column inlet soil water content, initial soil w...
NASA Technical Reports Server (NTRS)
Chiavassa, G.; Liandrat, J.
1996-01-01
We construct compactly supported wavelet bases satisfying homogeneous boundary conditions on the interval (0,1). The maximum features of multiresolution analysis on the line are retained, including polynomial approximation and tree algorithms. The case of H(sub 0)(sup 1)(0, 1)is detailed, and numerical values, required for the implementation, are provided for the Neumann and Dirichlet boundary conditions.
NASA Astrophysics Data System (ADS)
Olson, Nathan M.
2015-11-01
The bounce-back boundary condition in the lattice Boltzmann method distorts curved or inclined boundaries by forcing them to conform to a rectangular grid. This paper proposes a modification that reduces the effect of this discretization on the fluid flow. The modification takes the form of the addition of a type of node that is neither solid nor fluid, called the "sticky node". Sticky nodes are used in all cells that contain both fluid and solid. They are treated like fluid nodes with modified viscosity, body force, and velocity calculation. The method is applied to the LBGK model on a D2Q9 grid, and the accuracy of the method is evaluated using several test cases. Decreased discretization artifacts and decreased sensitivity to grid alignment are demonstrated, compared to the standard link bounce-back boundary condition. The method is computationally efficient, local, and demonstrates good numerical stability.
NASA Astrophysics Data System (ADS)
Moalafhi, Ditiro B.; Evans, Jason P.; Sharma, Ashish
2016-01-01
Regional climate modelling studies often begin by downscaling a reanalysis dataset in order to simulate the observed climate, allowing the investigation of regional climate processes and quantification of the errors associated with the regional model. To date choice of reanalysis to perform such downscaling has been made based either on convenience or on performance of the reanalyses within the regional domain for relevant variables such as near-surface air temperature and precipitation. However, the only information passed from the reanalysis to the regional model are the atmospheric temperature, moisture and winds at the location of the boundaries of the regional domain. Here we present a methodology to evaluate reanalyses derived lateral boundary conditions for an example domain over southern Africa using satellite data. This study focusses on atmospheric temperature and moisture which are easily available. Five commonly used global reanalyses (NCEP1, NCEP2, ERA-I, 20CRv2, and MERRA) are evaluated against the Atmospheric Infrared Sounder satellite temperature and relative humidity over boundaries of two domains centred on southern Africa for the years 2003-2012 inclusive. The study reveals that MERRA is the most suitable for climate mean with NCEP1 the next most suitable. For climate variability, ERA-I is the best followed by MERRA. Overall, MERRA is preferred for generating lateral boundary conditions for this domain, followed by ERA-I. While a "better" LBC specification is not the sole precursor to an improved downscaling outcome, any reduction in uncertainty associated with the specification of LBCs is a step in the right direction.
On solvability of some boundary value problems for a biharmonic equation with periodic conditions
NASA Astrophysics Data System (ADS)
Karachik, Valery V.; Massanov, Saparbay K.; Turmetov, Batirkhan Kh.
2016-08-01
In the paper we study questions about solvability of some boundary value problems with periodic conditions for an inhomogeneous biharmonic equation. The exact conditions for solvability of the problems are found.
Yoshida, Hiroaki; Kobayashi, Takayuki; Hayashi, Hidemitsu; Kinjo, Tomoyuki; Washizu, Hitoshi; Fukuzawa, Kenji
2014-07-01
A boundary scheme in the lattice Boltzmann method (LBM) for the convection-diffusion equation, which correctly realizes the internal boundary condition at the interface between two phases with different transport properties, is presented. The difficulty in satisfying the continuity of flux at the interface in a transient analysis, which is inherent in the conventional LBM, is overcome by modifying the collision operator and the streaming process of the LBM. An asymptotic analysis of the scheme is carried out in order to clarify the role played by the adjustable parameters involved in the scheme. As a result, the internal boundary condition is shown to be satisfied with second-order accuracy with respect to the lattice interval, if we assign appropriate values to the adjustable parameters. In addition, two specific problems are numerically analyzed, and comparison with the analytical solutions of the problems numerically validates the proposed scheme. PMID:25122406
Arbitrary Lagrangian-Eulerian approach in reduced order modeling of a flow with a moving boundary
NASA Astrophysics Data System (ADS)
Stankiewicz, W.; Roszak, R.; Morzyński, M.
2013-06-01
Flow-induced deflections of aircraft structures result in oscillations that might turn into such a dangerous phenomena like flutter or buffeting. In this paper the design of an aeroelastic system consisting of Reduced Order Model (ROM) of the flow with a moving boundary is presented. The model is based on Galerkin projection of governing equation onto space spanned by modes obtained from high-fidelity computations. The motion of the boundary and mesh is defined in Arbitrary Lagrangian-Eulerian (ALE) approach and results in additional convective term in Galerkin system. The developed system is demonstrated on the example of a flow around an oscillating wing.
NASA Astrophysics Data System (ADS)
Yang, Zhiguo; Wang, Li-Lian; Rong, Zhijian; Wang, Bo; Zhang, Baile
2016-04-01
In this paper, we present an efficient spectral-element method (SEM) for solving general two-dimensional Helmholtz equations in anisotropic media, with particular applications in accurate simulation of polygonal invisibility cloaks, concentrators and circular rotators arisen from the field of transformation electromagnetics (TE). In practice, we adopt a transparent boundary condition (TBC) characterized by the Dirichlet-to-Neumann (DtN) map to reduce wave propagation in an unbounded domain to a bounded domain. We then introduce a semi-analytic technique to integrate the global TBC with local curvilinear elements seamlessly, which is accomplished by using a novel elemental mapping and analytic formulas for evaluating global Fourier coefficients on spectral-element grids exactly. From the perspective of TE, an invisibility cloak is devised by a singular coordinate transformation of Maxwell's equations that leads to anisotropic materials coating the cloaked region to render any object inside invisible to observers outside. An important issue resides in the imposition of appropriate conditions at the outer boundary of the cloaked region, i.e., cloaking boundary conditions (CBCs), in order to achieve perfect invisibility. Following the spirit of [48], we propose new CBCs for polygonal invisibility cloaks from the essential "pole" conditions related to singular transformations. This allows for the decoupling of the governing equations of inside and outside the cloaked regions. With this efficient spectral-element solver at our disposal, we can study the interesting phenomena when some defects and lossy or dispersive media are placed in the cloaking layer of an ideal polygonal cloak.
NASA Astrophysics Data System (ADS)
Martinez-Carranza, J.; Falaggis, K.; Kozacki, T.; Kujawinska, Malgorzata
2013-05-01
The transport of intensity equation (TIE) describes the relation between the object phase and the intensity distribution in the Fresnel region and can be used as a non-interferometric technique to estimate the phase distribution of an object. A number of techniques have been developed to solve the TIE. In this work we focus on one popular class of Poisson solvers that are based on Fourier and the Multigrid techniques. The aim of this paper is to present an analysis of these types of TIE solvers taking into account the effect of the boundary condition, i.e. the Neumann Boundary Condition (NBC), the Dirichlet Boundary Condition (DBC), and the Periodic Boundary Condition (PBC). This analysis, which depends on the location of an object wave-front in the detector plane, aims to identify the advantages and disadvantage of these kinds of solvers and to provide the rules for choice of the best fitted boundary condition.
Stability of basis property of a periodic problem with nonlocal perturbation of boundary conditions
NASA Astrophysics Data System (ADS)
Imanbaev, Nurlan; Sadybekov, Makhmud
2016-08-01
The present work is the continuation of authors' researchers on stability (instability) of basis property of root vectors of a differential operator with nonlocal perturbation of one of boundary conditions. In this paper a spectral problem for a multiple differentiation operator with an integral perturbation of boundary conditions of one type, which are regular, but not strongly regular, is devoted. For this type of the boundary conditions it is known that the unperturbed problem has an asymptotically simple spectrum, and its system of normalized eigenfunctions creates the Riesz basis. We construct the characteristic determinant of the spectral problem with an integral perturbation of the boundary conditions. It is shown that the Riesz basis property of a system of eigen and adjoint functions is stable with respect to integral perturbations of the boundary condition. In the paper requirements of smoothness to the kernel of the integral perturbation are also reduced (unlike our previous researchers).
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
Exact finite-size corrections for the spanning-tree model under different boundary conditions
NASA Astrophysics Data System (ADS)
Izmailian, N. Sh.; Kenna, R.
2015-02-01
We express the partition functions of the spanning tree on finite square lattices under five different sets of boundary conditions in terms of a principal partition function with twisted-boundary conditions. Based on these expressions, we derive the exact asymptotic expansions of the logarithm of the partition function for each case. We have also established several groups of identities relating spanning-tree partition functions for the different boundary conditions. We also explain an apparent discrepancy between logarithmic correction terms in the free energy for a two-dimensional spanning-tree model with periodic and free-boundary conditions and conformal field theory predictions. We have obtained corner free energy for the spanning tree under free-boundary conditions in full agreement with conformal field theory predictions.
Molecular theory of hydrodynamic boundary conditions in nanofluidics.
Kobryn, Alexander E; Kovalenko, Andriy
2008-10-01
Motivated by the fundamental questions raised by the most recent experimental achievements in nanofluidics, we propose the first-ever derivation and calculation of the hydrodynamic slip length from the first principles of statistical mechanics, namely, a combination of linear response theory and equilibrium molecular theory of solvation. The slip length derived is related to the fluid organization near the solid surface, as governed by the solid-liquid interaction. In the wide range of shear rates and surface-liquid interactions, the slip length is expressed in terms of the Green-Kubo-Nakano relations as a function of the anisotropic inhomogeneous time-correlation function of density fluctuations of the liquid in contact with the surface. The time dependence of the correlation function is factored out by treating it in the hydrodynamic limit. The spatially inhomogeneous two-body correlation function is represented in the Kirkwood-type approximation as a product of the three-dimensional density distributions of interaction sites of the liquid near the surface and the site-site pair correlations of the bulk liquid. The presented treatment generalizes the phenomenological definition of the friction coefficient (as well as the slip length) to a tensor quantity, which reflects an anisotropic nature of an ordered crystalline or nanopatterned surface. This enables theoretical prediction of friction forces acting aslant to the liquid flow direction for such surfaces. We derive generic analytical expressions for the liquid-surface friction coefficient (and slip length) for an arbitrary surface-liquid interaction potential. We further illustrate it by numerical calculations for a laminar flow of nine different molecular liquids, including water, at ambient conditions in contact with the (100) face-centered cubic cell surface of gold, copper, and nickel modeled by using optimized potential for liquid simulation models for liquids and the Steele potential for crystalline
Flow Characteristics and Basal Boundary Condition for Daugaard-Jensen Gletscher, East Greenland
NASA Astrophysics Data System (ADS)
Perry, Thomas; Christoffersen, Poul; Dowdeswell, Julian; Palmer, Steven; Young, Duncan
2014-05-01
The recent acceleration of mass loss from the Greenland Ice Sheet can in part be attributed to the dynamic thinning and acceleration of its tidewater outlet glaciers. Many of these glaciers have been shown to exhibit sensitivity to conditions at their marine termini, where warm ocean currents promote ice front melting and retreat. However, these currents are confined to a northerly extent of 69N, and whilst remarkable change is seen to the south of this latitude, glaciers to the north are considerably more stable in terms of terminus position. Different environmental variables may thus control the flow characteristics of glaciers north of this well-defined geographical boundary. During 2011, high-resolution ice data was collected for Daugaard-Jensen Gletscher (71N) as part of the Greenland Outlet Glacier Geophysics (GrOGG) project. Remote sensing has confirmed its stability but few, if any, have applied an ice flow model to examine its ice dynamics in more detail. Here, the numerical Elmer-ICE model is applied to a new bed DEM in order to analyse flow characteristics and basal boundary conditions for Daugaard-Jensen Gletscher. The bed elevation of the inland part of the catchment was derived from Operation Icebridge and GrOGG ice thickness data, whilst the main glacier trunk was inferred through mass conservation calculations at a resolution of 100 m using TerraSAR-X velocity data. The latter was also used for 3D inverse modelling with Elmer-ICE, to analyse basal boundary conditions such as basal traction, sliding speed, frictional heating, and the basal melt rate. This is critical in accurately reproducing velocities and flow characteristics for the glacier, which is not always successful with a simple parameterisation in pure forward modelling. The new DEM offers considerable improvements in vertical accuracy and horizontal resolution compared to previous bed datasets created at the ice-sheet scale. Preliminary results indicate that two deep channels within the
Self-consistently simulation of RF sheath boundary condition in BOUT + + framework
NASA Astrophysics Data System (ADS)
Gui, Bin; Xu, Xueqiao; Xia, Tianyang
2015-11-01
The effect of the RF sheath boundary condition on the edge-localized modes and the turbulent transport is simulated in this work. The work includes two parts. The first part is to calculate the equilibrium radial electric field with RF sheath boundary condition. It is known the thermal sheath or the rectified RF sheath will modify the potential in the SOL region. The modified potential induces addition shear flow in SOL. In this part, the equilibrium radial electric field across the separatrix is calculated by solving the 2D current continuity equation with sheath boundary condition, drifts and viscosity. The second part is applying the sheath boundary condition on the perturbed variables of the six-field two fluid model in BOUT + + framework. The six-field two-fluid model simulates the ELMs and turbulent transport. The sheath boundary condition is applied in this model and it aims to simulate effect of sheath boundary condition on the turbulent transport. It is found the sheath boundary plays as a sink in the plasma and suppresses the local perturbation. Based on this two work, the effect of RF sheath boundary condition on the ELMs and turbulent transport could be self-consistently simulated. Prepared by LLNL under Contract DE-AC52-07NA27344.
NASA Technical Reports Server (NTRS)
Fisher, Travis C.; Carpenter, Mark H.; Nordstroem, Jan; Yamaleev, Nail K.; Swanson, R. Charles
2011-01-01
Simulations of nonlinear conservation laws that admit discontinuous solutions are typically restricted to discretizations of equations that are explicitly written in divergence form. This restriction is, however, unnecessary. Herein, linear combinations of divergence and product rule forms that have been discretized using diagonal-norm skew-symmetric summation-by-parts (SBP) operators, are shown to satisfy the sufficient conditions of the Lax-Wendroff theorem and thus are appropriate for simulations of discontinuous physical phenomena. Furthermore, special treatments are not required at the points that are near physical boundaries (i.e., discrete conservation is achieved throughout the entire computational domain, including the boundaries). Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and included in E. Narrow-stencil difference operators for linear viscous terms are also derived; these guarantee the conservative form of the combined operator.
A convective-like energy-stable open boundary condition for simulations of incompressible flows
NASA Astrophysics Data System (ADS)
Dong, S.
2015-12-01
We present a new energy-stable open boundary condition, and an associated numerical algorithm, for simulating incompressible flows with outflow/open boundaries. This open boundary condition ensures the energy stability of the system, even when strong vortices or backflows occur at the outflow boundary. Under certain situations it can be reduced to a form that can be analogized to the usual convective boundary condition. One prominent feature of this boundary condition is that it provides a control over the velocity on the outflow/open boundary. This is not available with the other energy-stable open boundary conditions from previous works. Our numerical algorithm treats the proposed open boundary condition based on a rotational velocity-correction type strategy. It gives rise to a Robin-type condition for the discrete pressure and a Robin-type condition for the discrete velocity on the outflow/open boundary, respectively at the pressure and the velocity sub-steps. We present extensive numerical experiments on a canonical wake flow and a jet flow in open domain to test the effectiveness and performance of the method developed herein. Simulation results are compared with the experimental data as well as with other previous simulations to demonstrate the accuracy of the current method. Long-time simulations are performed for a range of Reynolds numbers, at which strong vortices and backflows occur at the outflow/open boundaries. The results show that our method is effective in overcoming the backflow instability, and that it allows for the vortices to discharge from the domain in a fairly natural fashion even at high Reynolds numbers.
Boundary condition thermometry using a thermographic-phosphor-coated thin filament.
Kempema, Nathan J; Long, Marshall B
2016-06-10
Thermographic phosphors (TPs) exhibit a temperature sensitive emission spectrum when excited with ultraviolet radiation. In this study, 14 μm diameter SiC fibers are coated with ZnO or Dy:YAG using a ceramic binder to a total diameter of 70±9 μm. ZnO and Dy:YAG fibers were used to measure fiber temperatures in the range of 294-450 K and 450-1245 K, respectively. The coated fiber provides higher signal levels compared to TP particle seeding and is no more invasive than the commonly used thermocouple. A calibration is performed to relate fiber temperature to the ratio of luminescent signal collected within two different bands of the fiber emission spectrum. Temperature was measured along the inlet of a series of nitrogen diluted ethylene diffusion flames stabilized on the Yale coflow burner to determine suitable thermal boundary conditions for computational modeling. The boundary condition temperatures were derived from a spline fitting of data acquired from the two fiber types in order to obtain fiber temperature sensitivity from 294 to 1245 K. The peak near-burner temperature was found to be higher than ambient conditions and to increase and shift its location radially outward with increased fuel percentage. PMID:27409027
A new multistack radiation boundary condition for FDTD based on self-teleportation of fields
Diaz, Rodolfo E.; Scherbatko, Igor . E-mail: igor_s@asu.edu
2005-02-10
In [Electromagnetics 23 (2003) 187], a technique for injecting perfect plane waves into finite regions of space in FDTD was reported. The essence of the technique, called Field Teleportation, is to invoke the principle of equivalent sources using FDTDs discrete definition of the curl to copy any field propagating in one FDTD domain to a finite region of another domain. In this paper, we apply this technique of Field Teleportation to the original domain itself to create a transparent boundary across which any outward traveling FDTD field produces an exact negative copy of itself. When this copied field is teleported one cell ahead and one cell forward in time it causes significant self-cancelation of the original field. Illustrative experiments in two-dimensions show that a two-layer (10-cell thick) multi-stack Radiation Boundary Condition (RBC) with a simplest Huygens's termination readily yields reflection coefficients of the order of -80 dB up to grazing incidence for all the fields radiated by a harmonic point source ({lambda} = 30 cells) in free space located 20 cells away from the boundary. Similarly low levels of artificial reflection are demonstrated for a case in which the RBC cuts through five different magnetodielectric materials.
NASA Technical Reports Server (NTRS)
Winterstein, R.; Hafez, M.
1993-01-01
A finite volume method is used to calculate compressible inviscid flows over blunt bodies using, in general, unstructured grids. Artificial viscosity forms are derived based on a simplified least squares procedure. The extra second order terms are consistent with the governing equations, hence a systematic treatment of the numerical boundary conditions can be easily implemented. A special treatment of blunt bodies may be required. The discrete equations are linearized and the resulting system is solved by a relaxation method. Preliminary results indicate that the effect of the numerical dissipation is minimal. For subsonic flows over smooth bodies, the solution is practically vorticity-free and the total pressure loss is of the same order as the truncation error. Finally, some extensions of the present method are briefly discussed.
NASA Astrophysics Data System (ADS)
Rosnitskiy, P. B.; Yuldashev, P. V.; Vysokanov, B. A.; Khokhlova, V. A.
2016-03-01
An equivalent source model is developed for setting boundary conditions on the parabolic diffraction equation in order to simulate ultrasound fields radiated by strongly focused medical transducers. The equivalent source is defined in a plane; corresponding boundary conditions for pressure amplitude, aperture, and focal distance are chosen so that the axial solution to the parabolic model in the focal region of the beam matches the solution to the full diffraction model (Rayleigh integral) for a spherically curved uniformly vibrating source. It is shown that the proposed approach to transferring the boundary condition from a spherical surface to a plane makes it possible to match the solutions over an interval of several diffraction maxima around the focus even for focused sources with F-numbers less than unity. This method can be used to accurately simulate nonlinear effects in the fields of strongly focused therapeutic transducers using the parabolic Khokhlov-Zabolotskaya equation.
Implementation and Effects of Low-Altitude Boundary Conditions in Global Magnetosphere Models
NASA Astrophysics Data System (ADS)
Xi, Sheng
The forecast capabilities of global magnetohydrodynamics (MHD) simulations of geospace are sensitive to the particular specification of low-altitude (inner) boundary conditions. The low-altitude boundary conditions imposed in all global simulations (at least six different models are in active use around the world) are artificial in varying degrees. Consequently, they introduce nonphysical artifacts in the MHD solution. The principle objectives of this thesis are to improve the low-altitude boundary conditions in global magnetospheric MHD models in two ways: 1) by developing and employing Poynting flux-conserving boundary conditions and 2) by including the effects of field-aligned potential drops in the magnetosphere-ionosphere interaction in the boundary specification. The proposed boundary conditions have been implemented in the Lyon-Fedder-Mobarry (LFM) global simulation model. LFM simulation results are diagnosed to qualify the resulting improvements in the solution. The results presented in the dissertation illustrate the nonphysical artifacts introduced near the low-altitude boundary by the currently implemented LFM boundary conditions. It is shown that these artifacts are largely eliminated by flux-conserving boundary conditions, which conserve low-frequency (essentially DC) Poynting flux flowing along magnetic field lines. The field-aligned DC Poynting flux just above the boundary is also shown to be very nearly equal to the ionospheric Joule heating, as it should be if electromagnetic energy is conserved. The effects of field-aligned potential drops attributed to anomalous resistive layers that form at low altitude, in the "gap region" between the inner simulation boundary and the ionosphere, have also been included in the effective boundary condition. The model produces much larger potential drops in regions of upward field-aligned current, which are most prevalent on the dusk side, in contrast with those that occur in downward field-aligned currents that
Talbot conditions, Talbot resonators, and first-order systems.
Fernández-Pousa, Carlos R; Flores-Arias, María Teresa; Bao, Carmen; Pérez, María Victoria; Gómez-Reino, Carlos
2003-04-01
A study of first-order Talbot resonators is presented. The general conditions for Talbot effect in ABCD systems are determined. These conditions are applied to the computation of the diffraction overlapping coefficients between array Gaussian emitters in a general first-order Talbot resonator. Relations on the ray-transfer matrix to generate the symmetric and the totally antisymmetric supermodes of the array are derived. These relations generalize the free-space, round-trip lengths of 1/2 and 1/4 of the Talbot distance. A new type of resonator based on a plano-convex gradient-index rod is proposed. PMID:12683489
On the effects of nonlinear boundary conditions in diffusive logistic equations on bounded domains
NASA Astrophysics Data System (ADS)
Cantrell, Robert Stephen; Cosner, Chris
We study a diffusive logistic equation with nonlinear boundary conditions. The equation arises as a model for a population that grows logistically inside a patch and crosses the patch boundary at a rate that depends on the population density. Specifically, the rate at which the population crosses the boundary is assumed to decrease as the density of the population increases. The model is motivated by empirical work on the Glanville fritillary butterfly. We derive local and global bifurcation results which show that the model can have multiple equilibria and in some parameter ranges can support Allee effects. The analysis leads to eigenvalue problems with nonstandard boundary conditions.
Gonzalez-Lopez, Jennifer; Jansen, Karl; Renner, Dru B.; Shindler, Andrea
2013-02-01
The use of chirally rotated boundary conditions provides a formulation of the Schroedinger functional that is compatible with automatic O(a) improvement of Wilson fermions up to O(a) boundary contributions. The elimination of bulk O(a) effects requires the non-perturbative tuning of the critical mass and one additional boundary counterterm. We present the results of such a tuning in a quenched setup for several values of the renormalized gauge coupling, from perturbative to non-perturbative regimes, and for a range of lattice spacings. We also check that the correct boundary conditions and symmetries are restored in the continuum limit.
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.}
Modeling boundary conditions for balanced proliferation in metastatic latency
Taylor, Donald P; Wells, Jakob Z; Savol, Andrej; Chennubhotla, Chakra; Wells, Alan
2013-01-01
Purpose Nearly half of cancer metastases become clinically evident five or more years after primary tumor treatment; thus metastatic cells survived without emerging for extended periods. This dormancy has been explained by at least two countervailing scenarios: cellular quiescence and balanced proliferation; these entail dichotomous mechanistic etiologies. To examine the boundary parameters for balanced proliferation, we performed in silico modeling. Experimental Design To illuminate the balanced proliferation hypothesis, we explored the specific boundary probabilities under which proliferating micrometastases would remain dormant. A two-state Markov chain Monte Carlo model simulated micrometastatic proliferation and death according to stochastic survival probabilities. We varied these probabilities across 100 simulated patients each with 1,000 metastatic deposits and documented whether the micrometastases exceeded one million cells, died out, or remained dormant (survived 1,218 generations). Results The simulations revealed a narrow survival probability window (49.7 – 50.8 percent) that allowed for dormancy across a range of starting cell numbers, and even then for only a small fraction of micrometastases. The majority of micrometastases died out quickly even at survival probabilities that led to rapid emergence of a subset of micrometastases. Within dormant metastases, cell populations depended sensitively on small survival probability increments. Conclusions Metastatic dormancy as explained solely by balanced proliferation is bounded by very tight survival probabilities. Considering the far larger survival variability thought to attend fluxing microenvironments, it is more probable that these micrometastatic nodules undergo at least periods of quiescence rather than exclusively being controlled by balanced proliferation. PMID:23329811
Comparison of Methods for Determining Boundary Layer Edge Conditions for Transition Correlations
NASA Technical Reports Server (NTRS)
Liechty, Derek S.; Berry, Scott A.; Hollis, Brian R.; Horvath, Thomas J.
2003-01-01
Data previously obtained for the X-33 in the NASA Langley Research Center 20-Inch Mach 6 Air Tunnel have been reanalyzed to compare methods for determining boundary layer edge conditions for use in transition correlations. The experimental results were previously obtained utilizing the phosphor thermography technique to monitor the status of the boundary layer downstream of discrete roughness elements via global heat transfer images of the X-33 windward surface. A boundary layer transition correlation was previously developed for this data set using boundary layer edge conditions calculated using an inviscid/integral boundary layer approach. An algorithm was written in the present study to extract boundary layer edge quantities from higher fidelity viscous computational fluid dynamic solutions to develop transition correlations that account for viscous effects on vehicles of arbitrary complexity. The boundary layer transition correlation developed for the X-33 from the viscous solutions are compared to the previous boundary layer transition correlations. It is shown that the boundary layer edge conditions calculated using an inviscid/integral boundary layer approach are significantly different than those extracted from viscous computational fluid dynamic solutions. The present results demonstrate the differences obtained in correlating transition data using different computational methods.
Evaluation of general non-reflecting boundary conditions for industrial CFD applications
NASA Astrophysics Data System (ADS)
Basara, Branislav; Frolov, Sergei; Lidskii, Boris; Posvyanskii, Vladimir
2007-11-01
The importance of having proper boundary conditions for the calculation domain is a known issue in Computational Fluid Dynamics (CFD). In many situations, it is very difficult to define a correct boundary condition. The flow may enter and leave the computational domain at the same time and at the same boundary. In such circumstances, it is important that numerical implementation of boundary conditions enforces certain physical constraints leading to correct results which then ensures a better convergence rate. The aim of this paper is to evaluate recently proposed non-reflecting boundary conditions (Frolov et al., 2001, Advances in Chemical Propulsion) on industrial CFD applications. Derivation of the local non-reflecting boundary conditions at the open boundary is based on finding the solution of linearized Euler equations vanishing at infinity for both incompressible and compressible formulations. This is implemented into the in-house CFD package AVL FIRE and some numerical details will be presented as well. The key applications in this paper are from automotive industry, e.g. an external car aerodynamics, an intake port, etc. The results will show benefits of using effective non-reflecting boundary conditions.
Li, Xiaofan; Nie, Qing
2015-01-01
Many applications in materials involve surface diffusion of elastically stressed solids. Study of singularity formation and long-time behavior of such solid surfaces requires accurate simulations in both space and time. Here we present a high-order boundary integral method for an elastically stressed solid with axi-symmetry due to surface diffusions. In this method, the boundary integrals for isotropic elasticity in axi-symmetric geometry are approximated through modified alternating quadratures along with an extrapolation technique, leading to an arbitrarily high-order quadrature; in addition, a high-order (temporal) integration factor method, based on explicit representation of the mean curvature, is used to reduce the stability constraint on time-step. To apply this method to a periodic (in axial direction) and axi-symmetric elastically stressed cylinder, we also present a fast and accurate summation method for the periodic Green’s functions of isotropic elasticity. Using the high-order boundary integral method, we demonstrate that in absence of elasticity the cylinder surface pinches in finite time at the axis of the symmetry and the universal cone angle of the pinching is found to be consistent with the previous studies based on a self-similar assumption. In the presence of elastic stress, we show that a finite time, geometrical singularity occurs well before the cylindrical solid collapses onto the axis of symmetry, and the angle of the corner singularity on the cylinder surface is also estimated. PMID:26487788
DREAM-3D and the importance of model inputs and boundary conditions
NASA Astrophysics Data System (ADS)
Friedel, Reiner; Tu, Weichao; Cunningham, Gregory; Jorgensen, Anders; Chen, Yue
2015-04-01
Recent work on radiation belt 3D diffusion codes such as the Los Alamos "DREAM-3D" code have demonstrated the ability of such codes to reproduce realistic magnetospheric storm events in the relativistic electron dynamics - as long as sufficient "event-oriented" boundary conditions and code inputs such as wave powers, low energy boundary conditions, background plasma densities, and last closed drift shell (outer boundary) are available. In this talk we will argue that the main limiting factor in our modeling ability is no longer our inability to represent key physical processes that govern the dynamics of the radiation belts (radial, pitch angle and energy diffusion) but rather our limitations in specifying accurate boundary conditions and code inputs. We use here DREAM-3D runs to show the sensitivity of the modeled outcomes to these boundary conditions and inputs, and also discuss alternate "proxy" approaches to obtain the required inputs from other (ground-based) sources.
An implicit-iterative solution of the heat conduction equation with a radiation boundary condition
NASA Technical Reports Server (NTRS)
Williams, S. D.; Curry, D. M.
1977-01-01
For the problem of predicting one-dimensional heat transfer between conducting and radiating mediums by an implicit finite difference method, four different formulations were used to approximate the surface radiation boundary condition while retaining an implicit formulation for the interior temperature nodes. These formulations are an explicit boundary condition, a linearized boundary condition, an iterative boundary condition, and a semi-iterative boundary method. The results of these methods in predicting surface temperature on the space shuttle orbiter thermal protection system model under a variety of heating rates were compared. The iterative technique caused the surface temperature to be bounded at each step. While the linearized and explicit methods were generally more efficient, the iterative and semi-iterative techniques provided a realistic surface temperature response without requiring step size control techniques.
NASA Astrophysics Data System (ADS)
Lee, Sanghyun; Salgado, Abner J.
2016-09-01
We present a stability analysis for two different rotational pressure correction schemes with open and traction boundary conditions. First, we provide a stability analysis for a rotational version of the grad-div stabilized scheme of [A. Bonito, J.-L. Guermond, and S. Lee. Modified pressure-correction projection methods: Open boundary and variable time stepping. In Numerical Mathematics and Advanced Applications - ENUMATH 2013, volume 103 of Lecture Notes in Computational Science and Engineering, pages 623-631. Springer, 2015]. This scheme turns out to be unconditionally stable, provided the stabilization parameter is suitably chosen. We also establish a conditional stability result for the boundary correction scheme presented in [E. Bansch. A finite element pressure correction scheme for the Navier-Stokes equations with traction boundary condition. Comput. Methods Appl. Mech. Engrg., 279:198-211, 2014]. These results are shown by employing the equivalence between stabilized gauge Uzawa methods and rotational pressure correction schemes with traction boundary conditions.
NASA Astrophysics Data System (ADS)
Carrera-Hernández, J. J.; Smerdon, B. D.; Mendoza, C. A.
2012-07-01
SummaryUnsaturated flow modelling is increasingly being used to estimate potential groundwater recharge. A review of previous studies found that unit-gradient and fixed water table lower boundary conditions have been applied to models of both constant and variable vertical grid spacing (discretization). In order to provide a general guidance, this work studies the effect of both discretization and boundary conditions on simulation times and estimated fluxes at the water table, using one-dimensional models of 2, 4, 6, and 12 m comprised of sand, sandy loam, loamy sand, and loam. The study uses climatological data from the Boreal Plain of northern Alberta, Canada. Because of the long-term average water deficit and the thick unconsolidated glacial deposits, unsaturated flow is expected to be vertical, both downward and upward, and inter-annual changes in water storage will be important. Long-term simulations (1919-2007) that comprised both wet and dry cycles, reveal that when a variable vertical discretization at both the top and bottom of the columns (varying from 0.1 to 10 cm) is utilized, a balance between simulation accuracy and running time can be achieved. It is also found that whenever the unsaturated flow modelling approach is used to estimate potential groundwater recharge, a fixed-head lower boundary condition should be selected because it also allows upward flux from the water table during dry periods, a situation that prevails on both sub-humid and semi-arid areas, where accurate groundwater recharge estimates are needed the most. However, it should be kept in mind that the use of a fixed water table is a simple representation of the regional water table, which in reality interacts with the regional groundwater flow and surface water bodies (e.g., lakes and wetlands).
Sharapov, T F
2014-10-31
We consider an elliptic operator in a multidimensional domain with frequently changing boundary conditions in the case when the homogenized operator contains the Dirichlet boundary condition. We prove the uniform resolvent convergence of the perturbed operator to the homogenized operator and obtain estimates for the rate of convergence. A complete asymptotic expansion is constructed for the resolvent when it acts on sufficiently smooth functions. Bibliography: 41 titles.
Exploring the Boundary Conditions of the Redundancy Principle
ERIC Educational Resources Information Center
McCrudden, Matthew T.; Hushman, Carolyn J.; Marley, Scott C.
2014-01-01
This experiment investigated whether study of a scientific text and a visual display that contained redundant text segments would affect memory and transfer. The authors randomly assigned 42 students from a university in the southwestern United States in equal numbers to 1 of 2 conditions: (a) a redundant condition, in which participants studied a…
Order parameter aided phase space exploration under extreme conditions
NASA Astrophysics Data System (ADS)
Samanta, Amit; Hamel, Sebastian; Schwegler, Eric
Efficient exploration of configuration space and identification of metastable structures in condensed phase systems are challenging from both computational as well as algorithmic perspectives. In this talk I will illustrate how we can extend the recently proposed order-parameter aided temperature accelerated sampling schemes to efficiently and systematically explore free energy surfaces, and search for metastable states and reaction pathways within the framework of density functional theory based molecular dynamics. I will illustrate how this sampling scheme can be used to explore the relevant parts of configuration space in prototypical materials, like SiO2 and identify the different metastable structures, transition pathways and phase boundaries. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Second-Order Conditioning of Human Causal Learning
ERIC Educational Resources Information Center
Jara, Elvia; Vila, Javier; Maldonado, Antonio
2006-01-01
This article provides the first demonstration of a reliable second-order conditioning (SOC) effect in human causal learning tasks. It demonstrates the human ability to infer relationships between a cause and an effect that were never paired together during training. Experiments 1a and 1b showed a clear and reliable SOC effect, while Experiments 2a…
Pecuniary Effects, Second-Order Conditions, and the LRAC Curve.
ERIC Educational Resources Information Center
Comolli, Paul M.
2000-01-01
Explores the importance of second-order conditions in the cost-minimization problem confronting the monopsonistic employer of factor inputs. Describes an alternative approach to the presence of pecuniary effects that does not depend on the assumption that firms are monopsonistic in factor markets. (CMK)
Evaluative conditioning depends on higher order encoding processes.
Fiedler, Klaus; Unkelbach, Christian
2011-06-01
Evaluative conditioning (EC) is commonly conceived as stimulus-driven associative learning. Here, we show that internally generated encoding activities mediate EC effects: Neutral conditioned stimuli (CS) faces were paired with positive and negative unconditioned stimuli (US) faces. Depending on the encoding task (Is CS a friend vs. enemy of US?), Experiment 1 yielded either normal EC effects (CS adopting US valence) or a reversal. This pattern was conditional on the degree to which encoding judgements affirmed friend or enemy encoding schemes. Experiments 2a and 2b replicated these findings with more clearly valenced US faces and controlling for demand effects. Experiment 3 demonstrated unconditional encoding effects when participants generated friend or enemy relations between CS and US faces. Explicitly stated friend or enemy relations in Experiment 4 left EC effects unaffected. Together, these findings testify to the importance of higher order cognitive processes in conditioning, much in line with recent evidence on the crucial role of conditioning awareness. PMID:21547766
Finite-volume application of high order ENO schemes to multi-dimensional boundary-value problems
NASA Technical Reports Server (NTRS)
Casper, Jay; Dorrepaal, J. Mark
1990-01-01
The finite volume approach in developing multi-dimensional, high-order accurate essentially non-oscillatory (ENO) schemes is considered. In particular, a two dimensional extension is proposed for the Euler equation of gas dynamics. This requires a spatial reconstruction operator that attains formal high order of accuracy in two dimensions by taking account of cross gradients. Given a set of cell averages in two spatial variables, polynomial interpolation of a two dimensional primitive function is employed in order to extract high-order pointwise values on cell interfaces. These points are appropriately chosen so that correspondingly high-order flux integrals are obtained through each interface by quadrature, at each point having calculated a flux contribution in an upwind fashion. The solution-in-the-small of Riemann's initial value problem (IVP) that is required for this pointwise flux computation is achieved using Roe's approximate Riemann solver. Issues to be considered in this two dimensional extension include the implementation of boundary conditions and application to general curvilinear coordinates. Results of numerical experiments are presented for qualitative and quantitative examination. These results contain the first successful application of ENO schemes to boundary value problems with solid walls.
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.
Unified boundary conditions and Casimir forces for fields with arbitrary spin
NASA Astrophysics Data System (ADS)
Bennett, Robert; Stokes, Adam
The electromagnetic Casimir effect is well-known and has been extensively studied for the last half-century. This attractive force between parallel plates arises from the imposition of boundary conditions upon the fluctuating spin-1 photon field, so a natural further question is wether fields of different spin can cause similar forces when confined in the same way. However, so far it has not been clear what the appropriate boundary conditions for physically-confined spinor fields may be. Here we present work that generalises the physically well-motivated electromagnetic boundary conditions to fields of arbitrary spin, thus arriving at physically reasonable boundary conditions and Casimir forces for a selection of interesting fields. For example, the so-called `bag model' boundary conditions from nuclear physics emerge from our generalised boundary condition as a special case, as do the linearised gravity boundary conditions suggested in a remarkable recent proposal concerning possible measurement of gravitonic Casimir forces. Supported by the UK Engineering and Physical Sciences Research Council (EPSRC).
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
Irrelevance and conditioning in first-order probabilistic logic
Koller, D.; Halpern, J.Y.
1996-12-31
First-order probabilistic logic is a powerful knowledge representation language. Unfortunately, deductive reasoning based on the standard semantics for this logic does not support certain desirable patterns of reasoning, such as indifference to irrelevant information or substitution of constants into universal rules. We show that both these patterns rely on a first-order version of probabilistic independence, and provide semantic conditions to capture them. The resulting insight enables us to understand the effect of conditioning on independence, and allows us to describe a procedure for determining when independencies are preserved under conditioning. We apply this procedure in the context of a sound and powerful inference algorithm for reasoning from statistical knowledge bases.
A critical study of higher-order numerical methods for solving the boundary-layer equations
NASA Technical Reports Server (NTRS)
Wornom, S. F.
1977-01-01
A fourth-order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations. The efficiency of the present method is compared with other two-point and three-point higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, and the three-point spline methods. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.
Critical study of higher order numerical methods for solving the boundary-layer equations
NASA Technical Reports Server (NTRS)
Wornom, S. F.
1978-01-01
A fourth order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method, which is the natural extension of the second order box scheme to fourth order, was demonstrated with application to the incompressible, laminar and turbulent, boundary layer equations. The efficiency of the present method is compared with two point and three point higher order methods, namely, the Keller box scheme with Richardson extrapolation, the method of deferred corrections, a three point spline method, and a modified finite element method. For equivalent accuracy, numerical results show the present method to be more efficient than higher order methods for both laminar and turbulent flows.
Application of higher-order numerical methods to the boundary-layer equations
NASA Technical Reports Server (NTRS)
Wornom, S. F.
1978-01-01
A fourth-order method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations for both attached and separated flows. The efficiency of the present method is compared with other higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, the three-point spline methods, and a modified finite-element method. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.
Noisy contact interactions of multi-layer mechanical structures coupled by boundary conditions
NASA Astrophysics Data System (ADS)
Awrejcewicz, J.; Krysko, V. A., Jr.; Yakovleva, T. V.; Krysko, V. A.
2016-05-01
In this work mathematical models of temporal part of chaos at chosen spatial locations of a plate locally reinforced by ribs taking into account an interplay of their interactions are derived and studied numerically for the most relevant dynamical parameters. In addition, an influence of the additive external noise on chaotic vibrations of multi-layer beam-plate structures coupled only by boundary conditions is investigated. We illustrate and discuss novel nonlinear phenomena of the temporal regular and chaotic contact/no-contact dynamics with the help of Morlet wavelets and Fourier analysis. We show how the additive white noise cancels deterministic chaos close to the boundary of chaotic region in the space of parameters, and we present windows of on/off switching of the frequencies during the contact dynamics between structural members. In order to solve the mentioned design type nonlinear problem we apply methods of qualitative theory of differential equations, the Bubnov-Galerkin method in higher approximations, the Runge-Kutta methods of 4th, 6th and 8th order, as well as the computation and analysis of the largest Lyapunov exponent (Benettin's and Wolf's algorithms are used). The agreement of outcomes of all applied qualitatively different numerical approaches validate our simulation results. In particular, we have illustrated that the Fourier analysis of the studied mechanical structures may yield erroneous results, and hence the wavelet-based analysis is used to investigate chaotic dynamics in the system parameter space.
da Silva, Wilton Pereira; E Silva, Cleide M D P S; Gomes, Josivanda Palmeira
2014-11-01
Turmeric is harvested with high moisture content and should be dried before the storage. It is observed that drying is quickest when the rhizomes are peeled and cut in small cylindrical pieces. In order to describe the process, normally a diffusive model is used, considering boundary condition of the first kind for the diffusion equation. This article uses analytical solutions considering boundaries conditions of the first (model 1) and third (model 2) kinds coupled to an optimizer to describe the drying process. It is shown that, for model 1, the fit of the analytical solution to the experimental data is biased, despite the good statistical indicators (chi-square χ(2) equal to 1.7095 × 10(-3) and coefficient of correlation R(2) of 0.9988). For model 2, the errors of the experimental points about the simulated curve can be considered randomly distributed, and the statistical indicators are much better than those obtained for model 1: χ(2) = 3.5596 × 10(-4) and R(2) = 0.9996. PMID:26396310
Charged hadrons in local finite-volume QED+QCD with C⋆ boundary conditions
NASA Astrophysics Data System (ADS)
Lucini, B.; Patella, A.; Ramos, A.; Tantalo, N.
2016-02-01
In order to calculate QED corrections to hadronic physical quantities by means of lattice simulations, a coherent description of electrically-charged states in finite volume is needed. In the usual periodic setup, Gauss's law and large gauge transformations forbid the propagation of electrically-charged states. A possible solution to this problem, which does not violate the axioms of local quantum field theory, has been proposed by Wiese and Polley, and is based on the use of C⋆ boundary conditions. We present a thorough analysis of the properties and symmetries of QED in isolation and QED coupled to QCD, with C⋆ boundary conditions. In particular we learn that a certain class of electrically-charged states can be constructed in a fully consistent fashion without relying on gauge fixing and without peculiar complications. This class includes single particle states of most stable hadrons. We also calculate finite-volume corrections to the mass of stable charged particles and show that these are much smaller than in non-local formulations of QED.
NASA Astrophysics Data System (ADS)
Zhong, Siyang; Zhang, Xin; Huang, Xun
2016-05-01
A new method, which can be effectively and efficiently applied in the simulations of broadband noise problems, is proposed for time domain impedance boundary condition implementations by using the so-called controllable canonical form that is well known in linear system. Usually, the impedance boundary condition can be defined in frequency domain as a rational polynomial function with poles in the negative half of the complex plane to guarantee stability; otherwise, causality might be violated in the corresponding time domain implementation. To address this issue, various methodologies have been proposed previously that usually lead to complicated polynomials, whose numerical implementations are often indirect and intricate. The proposed method with a controllable canonical form, on the other hand, directly transforms the frequency domain transfer function (a quotient of rational polynomials) to an equivalent state space model, which consists of a series of first-order ordinary differential equations that can be numerically implemented in a straightforward way. The proposed method is demonstrated by using two benchmark problems: a two-dimensional Gaussian pulse propagating in a uniform flow with a lined wall and the test cases from the NASA Langley grazing incidence tube experiments. Good agreements demonstrate the potential of the proposed computational method.
Chiruta, Daniel; Linares, Jorge E-mail: miya@spin.phys.s.u-tokyo.ac.jp; Boukheddaden, Kamel; Miyashita, Seiji E-mail: miya@spin.phys.s.u-tokyo.ac.jp
2014-05-21
In order to explain clearly the role of the open boundary conditions (OBCs) on phase transition in one dimensional system, we consider an Ising model with both short-range (J) and long-range (G) interactions, which has allowed us to study the cooperative nature of spin-crossover (SCO) materials at the nanometer scale. At this end, we developed a transfer-matrix method for one-dimensional (1D) SCO system with free boundary conditions, and we give numerical evidences for how the thermal spin transition curves vary as a function of the physical parameters (J, G) or an applied pressure. Moreover for OBCs case, we have derived the bulk, surface and finite-size contributions to the free energy and we have investigated the variation of these energies as function of J and system size. We have found that the surface free energy behaves like J〈σ〉{sup 2}, where 〈σ〉 is the average magnetization per site. Since the properties of the nanometric scale are dramatically influenced by the system's size (N), our analytical outcomes for the size dependence represent a step to achieve new characteristic of the future devices and also a way to find various novel properties which are absent in the bulk materials.
Doha, E.H.; Abd-Elhameed, W.M.; Youssri, Y.H.
2014-01-01
Two families of certain nonsymmetric generalized Jacobi polynomials with negative integer indexes are employed for solving third- and fifth-order two point boundary value problems governed by homogeneous and nonhomogeneous boundary conditions using a dual Petrov–Galerkin method. The idea behind our method is to use trial functions satisfying the underlying boundary conditions of the differential equations and the test functions satisfying the dual boundary conditions. The resulting linear systems from the application of our method are specially structured and they can be efficiently inverted. The use of generalized Jacobi polynomials simplify the theoretical and numerical analysis of the method and also leads to accurate and efficient numerical algorithms. The presented numerical results indicate that the proposed numerical algorithms are reliable and very efficient. PMID:26425358
NASA Astrophysics Data System (ADS)
Lam, Yun Fat; Cheung, Hung Ming; Fu, Joshua; Huang, Kan
2015-04-01
Applying Global Chemistry Model (GCM) for regional Boundary Conditions (BC) has become a common practice to account for long-range transport of air pollutants in the regional air quality modeling. The limited domain model such as CMAQ and CAMx requires a global BC to prescribe the real-time chemical flux at the boundary grids, in order to give a realistic estimate of boundary impacts. Several GCMs have become available recently for use in regional air quality studies. In this study, three GCM models (i.e., GEOS-chem, CHASER and IFS-CB05 MACC provided by Seoul National University, Nagoya University and ECWMF, respectively) for the year of 2010 were applied in CMAQ for the East Asia domain under the framework of Model Inter-comparison Study Asia Phase III (MISC-Asia III) and task force on Hemispheric Transport of Air Pollution (HTAP) jointed experiments. Model performance evaluations on vertical profile and spatial distribution of O3 and PM2.5 have been made on those three models to better understand the model uncertainties from the boundary conditions. Individual analyses on various mega-cities (i.e., Hong Kong, Guangzhou, Taipei, Chongqing, Shanghai, Beijing, Tianjin, Seoul and Tokyo) were also performed. Our analysis found that the monthly estimates of O3 for CHASER were a bit higher than GEOS-Chem and IFS-CB05 MACC, particularly in the northern part of China in the winter and spring, while the monthly averages of PM2.5 in GEOS-Chem were the lowest among the three models. The hourly maximum values of PM2.5 from those three models (GEOS-Chem, CHASER and IFS-CB05 MACC are 450, 321, 331 μg/m3, while the maximum O3 are 158, 212, 380 ppbv, respectively. Cross-comparison of CMAQ results from the 45 km resolution were also made to investigate the boundary impacts from the global GCMs. The results presented here provide insight on how global GCM selection influences the regional air quality simulation in East Asia.
The PPP model of alternant cyclic polyenes with modified boundary conditions
Bendazzoli, G.L.; Evangelisti, S.
1995-08-15
The extension of the PPP Hamiltonian for alternant cyclic polyenes to noninteger values of the pseudomomentum by imposing modified boundary conditions is discussed in detail. It is shown that a computer program for periodic boundary conditions can be easily adapted to the new boundary conditions. Full CI computations are carried out for some low-lying states of the PPP model of alternant cyclic polyenes (CH){sub N} (N even) at half-filling. The energy values obtained by using periodic (Bloch) and antiperiodic (Moebius) orbitals are used to perform energy extrapolations for N {yields} {infinity}. 38 refs., 2 figs., 5 tabs.
Multiple Boundary Condition Tests (MBCT) for verification of large space structures
NASA Technical Reports Server (NTRS)
Wada, B. K.; Kuo, C. P.; Glaser, R. J.
1986-01-01
The Multiple Boundary Condition Tests (MBCT) approach is evaluated and recent modifications are described. For the application of MBCT, 12 different boundary conditions are selected and the results of applying MBCT in conjunction with a nonlinear formulation are indicated schematically. It is concluded that the nonlinear formulation enhances the ability to implement the MBCT test approach on large space structures which cannot be ground tested without the artificial boundary conditions incorporated in MBCT. In addition, it leads to significant improvements in the convergence to the correct solution.
Ion boundary conditions in semi-infinite fluid models of electron beam-plasma interaction
Levko, Dmitry
2014-10-15
The modified Bohm criterion is derived for the plasma consisting of the monoenergetic electron beam and thermal electrons. This criterion allows us to define the accurate ion boundary conditions for semi-infinite collisionless fluid models of electron beam–plasma interaction. In the absence of electron beam, these boundary conditions give the classical sheath parameters. When the monoenergetic electron beam propagates through the plasma, the fluid model with proposed boundary conditions gives the results, which are in qualitative agreement with the results obtained earlier in M. Sharifian and B. Shokri, Phys. Plasmas 14, 093503 (2007). However, dynamics and parameters of the plasma sheath are different.
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.
Higher order correlation beams in atmosphere under strong turbulence conditions.
Avetisyan, H; Monken, C H
2016-02-01
Higher order correlation beams, that is, two-photon beams obtained from the process of spontaneous parametric down-conversion pumped by Hermite-Gauss or Laguerre-Gauss beams of any order, can be used to encode information in many modes, opening the possibility of quantum communication with large alphabets. In this paper we calculate, analytically, the fourth-order correlation function for the Hermite-Gauss and Laguerre-Gauss coherent and partially coherent correlation beams propagating through a strong turbulent medium. We show that fourth-order correlation functions for correlation beams have, under certain conditions, expressions similar to those of intensities of classical beams and are degraded by turbulence in a similar way as the classical beams. Our results can be useful in establishing limits for the use of two-photon beams in quantum communications with larger alphabets under atmospheric turbulence. PMID:26906808
Quintic nonpolynomial spline solutions for fourth order two-point boundary value problem
NASA Astrophysics Data System (ADS)
Ramadan, M. A.; Lashien, I. F.; Zahra, W. K.
2009-04-01
In this paper, we develop quintic nonpolynomial spline methods for the numerical solution of fourth order two-point boundary value problems. Using this spline function a few consistency relations are derived for computing approximations to the solution of the problem. The present approach gives better approximations and generalizes all the existing polynomial spline methods up to order four. This approach has less computational cost. Convergence analysis of these methods is discussed. Two numerical examples are included to illustrate the practical usefulness of our methods.
Solution of second order quasi-linear boundary value problems by a wavelet method
Zhang, Lei; Zhou, Youhe; Wang, Jizeng
2015-03-10
A wavelet Galerkin method based on expansions of Coiflet-like scaling function bases is applied to solve second order quasi-linear boundary value problems which represent a class of typical nonlinear differential equations. Two types of typical engineering problems are selected as test examples: one is about nonlinear heat conduction and the other is on bending of elastic beams. Numerical results are obtained by the proposed wavelet method. Through comparing to relevant analytical solutions as well as solutions obtained by other methods, we find that the method shows better efficiency and accuracy than several others, and the rate of convergence can even reach orders of 5.8.
Geomagnetic Secular Variation Prediction with Thermal Heterogeneous Boundary Conditions
NASA Technical Reports Server (NTRS)
Kuang, Weijia; Tangborn, Andrew; Jiang, Weiyuan
2011-01-01
It has long been conjectured that thermal heterogeneity at the core-mantle boundary (CMB) affects the geodynamo substantially. The observed two pairs of steady and strong magnetic flux lobes near the Polar Regions and the low secular variation in the Pacific over the past 400 years (and perhaps longer) are likely the consequences of this CMB thermal heterogeneity. There are several studies on the impact of the thermal heterogeneity with numerical geodynamo simulations. However, direct correlation between the numerical results and the observations is found very difficult, except qualitative comparisons of certain features in the radial component of the magnetic field at the CMB. This makes it difficult to assess accurately the impact of thermal heterogeneity on the geodynamo and the geomagnetic secular variation. We revisit this problem with our MoSST_DAS system in which geomagnetic data are assimilated with our geodynamo model to predict geomagnetic secular variations. In this study, we implement a heterogeneous heat flux across the CMB that is chosen based on the seismic tomography of the lowermost mantle. The amplitude of the heat flux (relative to the mean heat flux across the CMB) varies in the simulation. With these assimilation studies, we will examine the influences of the heterogeneity on the forecast accuracies, e.g. the accuracies as functions of the heterogeneity amplitude. With these, we could be able to assess the model errors to the true core state, and thus the thermal heterogeneity in geodynamo modeling.
NASA Astrophysics Data System (ADS)
Stück, Arthur
2015-11-01
Inconsistent discrete expressions in the boundary treatment of Navier-Stokes solvers and in the definition of force objective functionals can lead to discrete-adjoint boundary treatments that are not a valid representation of the boundary conditions to the corresponding adjoint partial differential equations. The underlying problem is studied for an elementary 1D advection-diffusion problem first using a node-centred finite-volume discretisation. The defect of the boundary operators in the inconsistently defined discrete-adjoint problem leads to oscillations and becomes evident with the additional insight of the continuous-adjoint approach. A homogenisation of the discretisations for the primal boundary treatment and the force objective functional yields second-order functional accuracy and eliminates the defect in the discrete-adjoint boundary treatment. Subsequently, the issue is studied for aerodynamic Reynolds-averaged Navier-Stokes problems in conjunction with a standard finite-volume discretisation on median-dual grids and a strong implementation of noslip walls, found in many unstructured general-purpose flow solvers. Going out from a base-line discretisation of force objective functionals which is independent of the boundary treatment in the flow solver, two improved flux-consistent schemes are presented; based on either body wall-defined or farfield-defined control-volumes they resolve the dual inconsistency. The behaviour of the schemes is investigated on a sequence of grids in 2D and 3D.
Boundary conditions for General Relativity on AdS3 and the KdV hierarchy
NASA Astrophysics Data System (ADS)
Pérez, Alfredo; Tempo, David; Troncoso, Ricardo
2016-06-01
It is shown that General Relativity with negative cosmological constant in three spacetime dimensions admits a new family of boundary conditions being labeled by a nonnegative integer k. Gravitational excitations are then described by "boundary gravitons" that fulfill the equations of the k-th element of the KdV hierarchy. In particular, k = 0 corresponds to the Brown-Henneaux boundary conditions so that excitations are described by chiral movers. In the case of k = 1, the boundary gravitons fulfill the KdV equation and the asymptotic symmetry algebra turns out to be infinite-dimensional, abelian and devoid of central extensions. The latter feature also holds for the remaining cases that describe the hierarchy ( k > 1). Our boundary conditions then provide a gravitational dual of two noninteracting left and right KdV movers, and hence, boundary gravitons possess anisotropic Lifshitz scaling with dynamical exponent z = 2 k + 1. Remarkably, despite spacetimes solving the field equations are locally AdS, they possess anisotropic scaling being induced by the choice of boundary conditions. As an application, the entropy of a rotating BTZ black hole is precisely recovered from a suitable generalization of the Cardy formula that is compatible with the anisotropic scaling of the chiral KdV movers at the boundary, in which the energy of AdS spacetime with our boundary conditions depends on z and plays the role of the central charge. The extension of our boundary conditions to the case of higher spin gravity and its link with different classes of integrable systems is also briefly addressed.
Solution of Poisson's Equation with Global, Local and Nonlocal Boundary Conditions
ERIC Educational Resources Information Center
Aliev, Nihan; Jahanshahi, Mohammad
2002-01-01
Boundary value problems (BVPs) for partial differential equations are common in mathematical physics. The differential equation is often considered in simple and symmetric regions, such as a circle, cube, cylinder, etc., with global and separable boundary conditions. In this paper and other works of the authors, a general method is used for the…
High-order boundary layer analysis using B-splines on hybrid unstructured meshes
NASA Astrophysics Data System (ADS)
Zhang, Alvin; Sahni, Onkar
2015-11-01
Boundary layer flows are present in many engineering applications. In such flows, boundary layers span only a fraction of the characteristic length of the problem near the walls and possess large velocity gradients in the wall normal direction. This mandates use of a layered and graded mesh with a dense anisotropic h-resolution near the walls in order to accurately resolve the boundary layer. To account for complex geometries, a hybrid unstructured mesh approach is adopted. In this approach, the mesh is decomposed into wall normal and wall parallel directions. An alternative to an anisotropic h-resolution is to use a similar setting for both h- and p-resolution possibly with greater smoothness. For this purpose a mixed B-spline basis becomes attractive, where B-splines are used in the wall-normal direction and a C0 basis in the wall-parallel directions as well as the fully unstructured region of the mesh. A mixed B-spline basis offers several advantages over the traditional C0 basis utilized in finite element methods, which include greater accuracy per degree-of-freedom, ease of p-refinement as well as potential for k-refinement. In this study we demonstrate that the mixed B-spline basis, defined for the hybrid unstructured mesh, accurately models the boundary layer behavior.
A Boundary Mixture Approach to Violations of Conditional Independence
ERIC Educational Resources Information Center
Braeken, Johan
2011-01-01
Conditional independence is a fundamental principle in latent variable modeling and item response theory. Violations of this principle, commonly known as local item dependencies, are put in a test information perspective, and sharp bounds on these violations are defined. A modeling approach is proposed that makes use of a mixture representation of…
Schrauwen, Jelle T C; Coenen, Adriaan; Kurata, Akira; Wentzel, Jolanda J; van der Steen, Antonius F W; Nieman, Koen; Gijsen, Frank J H
2016-07-26
The aim of this research was finding the influence of anatomy-based and functional-based outflow boundary conditions for computational fluid dynamics (CFD) on fractional flow reserve (FFR) and wall shear stress (WSS) in mildly diseased coronary bifurcations. For 10 patient-specific bifurcations three simulations were set up with different outflow conditions, while the inflow was kept constant. First, the outflow conditions were based on the diameter of the outlets. Second, they were based on the volume estimates of the myocardium that depended on the outlets. Third, they were based on a myocardial flow measure derived from computed tomography perfusion imaging (CTP). The difference in outflow ratio between the perfusion-based and the diameter-based approach was -7 p.p. [-14 p.p.:7 p.p.] (median percentage point and interquartiles), and between the perfusion-based and volume-based this was -2 p.p. [-2 p.p.:1 p.p.]. Despite of these differences the computed FFRs matched very well. A quantitative analysis of the WSS results showed very high correlations between the methods with an r(2) ranging from 0.90 to 1.00. But despite the high correlations the diameter-based and volume-based approach generally underestimated the WSS compared to the perfusion-based approach. These differences disappeared after normalization. We demonstrated the potential of CTP for setting patient-specific boundary conditions for atherosclerotic coronary bifurcations. FFR and normalized WSS were unaffected by the variations in outflow ratios. In order to compute absolute WSS a functional measure to set the outflow ratio might be of added value in this type of vessels. PMID:26654676
Generalized adjoint consistent treatment of wall boundary conditions for compressible flows
NASA Astrophysics Data System (ADS)
Hartmann, Ralf; Leicht, Tobias
2015-11-01
In this article, we revisit the adjoint consistency analysis of Discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations with application to the Reynolds-averaged Navier-Stokes and k- ω turbulence equations. Here, particular emphasis is laid on the discretization of wall boundary conditions. While previously only one specific combination of discretizations of wall boundary conditions and of aerodynamic force coefficients has been shown to give an adjoint consistent discretization, in this article we generalize this analysis and provide a discretization of the force coefficients for any consistent discretization of wall boundary conditions. Furthermore, we demonstrate that a related evaluation of the cp- and cf-distributions is required. The freedom gained in choosing the discretization of boundary conditions without loosing adjoint consistency is used to devise a new adjoint consistent discretization including numerical fluxes on the wall boundary which is more robust than the adjoint consistent discretization known up to now. While this work is presented in the framework of Discontinuous Galerkin discretizations, the insight gained is also applicable to (and thus valuable for) other discretization schemes. In particular, the discretization of integral quantities, like the drag, lift and moment coefficients, as well as the discretization of local quantities at the wall like surface pressure and skin friction should follow as closely as possible the discretization of the flow equations and boundary conditions at the wall boundary.
A new package for simulating periodic boundary conditions in MODFLOW and SEAWAT
NASA Astrophysics Data System (ADS)
Post, V. E. A.
2011-11-01
Modeling of coastal groundwater systems is a challenging problem due to their highly dynamic boundary conditions and the coupling between the equations for groundwater flow and solute transport. A growing number of publications on aquifers subject to tides have demonstrated various modeling approaches, ranging from analytical solutions to comprehensive numerical models. The United States Geological Survey code SEAWAT has been a popular choice in studies of this type. Although SEAWAT allows the incorporation of time-variant boundary conditions, the implementation of tidal boundaries is not straightforward, especially when a seepage face develops during falling tide. Here, a new package is presented, called the periodic boundary condition (PBC) package, that can be incorporated into MODFLOW and SEAWAT to overcome the difficulties encountered with tidal boundaries. It dynamically updates the boundary conditions for head and concentration during the simulation depending on a user-defined tidal signal and allows for the development of a seepage face. The package has been verified by comparing it to four different published models of tidally influenced groundwater systems of varying complexity. Excellent agreement was obtained in all cases. The new package is an important extension to the existing capabilities of MODFLOW and SEAWAT with respect to simulating periodic boundary conditions.
Boundary Conditions and the Aeolian Sediment State of the Olympia Undae Dune Field, Mars
NASA Astrophysics Data System (ADS)
Middlebrook, W.; Ewing, R. C.; Ayoub, F.; Bridges, N. T.; Smith, I.; Spiga, A.
2015-05-01
We evaluate the boundary conditions in Olympia Undae. We map two and three dimensional dune parameters from two locations proximal and distal to Planum Boreum and constrain sediment fluxes. We compare our results with a mesoscale atmospheric model.
On a regular problem for an elliptic-parabolic equation with a potential boundary condition
NASA Astrophysics Data System (ADS)
Arepova, Gauhar
2016-08-01
In this paper, we construct a lateral boundary condition for an elliptic-parabolic equation in a finite domain. Theorem on existence and uniqueness of a solution of the considered problem is proved by method of theory potential.
Influence of Boundary Conditions on Simulated U.S. Air Quality
One of the key inputs to regional-scale photochemical models frequently used in air quality planning and forecasting applications are chemical boundary conditions representing background pollutant concentrations originating outside the regional modeling domain. A number of studie...
Shifted periodic boundary conditions for simulations of wall-bounded turbulent flows
NASA Astrophysics Data System (ADS)
Munters, Wim; Meneveau, Charles; Meyers, Johan
2016-02-01
In wall-bounded turbulent flow simulations, periodic boundary conditions combined with insufficiently long domains lead to persistent spanwise locking of large-scale turbulent structures. This leads to statistical inhomogeneities of 10%-15% that persist in time averages of 60 eddy turnover times and more. We propose a shifted periodic boundary condition that eliminates this effect without the need for excessive streamwise domain lengths. The method is tested based on a set of direct numerical simulations of a turbulent channel flow, and large-eddy simulations of a high Reynolds number rough-wall half-channel flow. The method is very useful for precursor simulations that generate inlet conditions for simulations that are spatially inhomogeneous, but require statistically homogeneous inlet boundary conditions in the spanwise direction. The method's advantages are illustrated for the simulation of a developing wind-farm boundary layer.
NASA Technical Reports Server (NTRS)
Beam, R. M.; Warming, R. F.; Yee, H. C.
1981-01-01
Implicit, noniterative, finite difference schemes were recently developed by several authors for multidimensional systems of nonlinear hyperbolic partial differential equations. When applied to linear model equations with periodic boundary conditions those schemes are unconditionally stable (A-stable). As applied in practice the algorithms often face a severe time step restriction. A major source of the difficulty is the treatment of the numerical boundary conditions. One conjecture was that unconditional stability requires implicit numerical boundary conditions. An apparent counter example was the space time extrapolation considered by Gustafsson, Kreiss, and Sunstrom. Spatial (implicit) and space time (explicit) extrapolation using normal mode analysis for a finite and infinite number of spatial mesh intervals are examined. The results indicate that for unconditional stability with a finite number of spatial mesh intervals, the numerical boundary conditions must be implicit.
Invariance of decay rate with respect to boundary conditions in thermoelastic Timoshenko systems
NASA Astrophysics Data System (ADS)
Alves, M. S.; Jorge Silva, M. A.; Ma, T. F.; Muñoz Rivera, J. E.
2016-06-01
This paper is mainly concerned with the polynomial stability of a thermoelastic Timoshenko system recently introduced by Almeida Júnior et al. (Z Angew Math Phys 65(6):1233-1249, 2014) that proved, in the general case when equal wave speeds are not assumed, different polynomial decay rates depending on the boundary conditions, namely, optimal rate {t^{-1/2}} for mixed Dirichlet-Neumann boundary condition and rate {t^{-1/4}} for full Dirichlet boundary condition. Here, our main achievement is to prove the same polynomial decay rate {t^{-1/2}} (corresponding to the optimal one) independently of the boundary conditions, which improves the existing literature on the subject. As a complementary result, we also prove that the system is exponentially stable under equal wave speeds assumption. The technique employed here can probably be applied to other kind of thermoelastic systems.
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.
X. Z. Tang
2000-12-18
Subtleties of implementing the standard perfectly conducting wall boundary condition in a general toroidal geometry are clarified for a mixed scalar magnetic field representation. An iterative scheme based on Ohm's law is given.
Evaluation of wall boundary condition parameters for gas-solids fluidized bed simulations
Li, Tingwen; Benyahia, Sofiane
2013-10-01
Wall boundary conditions for the solids phase have significant effects on numerical predictions of various gas-solids fluidized beds. Several models for the granular flow wall boundary condition are available in the open literature for numerical modeling of gas-solids flow. In this study, a model for specularity coefficient used in Johnson and Jackson boundary conditions by Li and Benyahia (AIChE Journal, 2012, 58, 2058-2068) is implemented in the open-source CFD code-MFIX. The variable specularity coefficient model provides a physical way to calculate the specularity coefficient needed by the partial-slip boundary conditions for the solids phase. Through a series of 2-D numerical simulations of bubbling fluidized bed and circulating fluidized bed riser, the model predicts qualitatively consistent trends to the previous studies. Furthermore, a quantitative comparison is conducted between numerical results of variable and constant specularity coefficients to investigate the effect of spatial and temporal variations in specularity coefficient.
PRESBC: pressure boundary conditions for the K-FIX code. Supplement III
Travis, J.R.; Rivard, W.C.
1980-07-01
Recommended pressure boundary condition modifications are described for the computer code K-FIX, which has been published in the report LA-NUREG-6623 and released to the National Energy Software Center in April 1977.
Integrabilities of the long-range t-J models with twisted boundary conditions
Liu, J.T.; Wang, D.F.
1997-02-01
The integrability of the one-dimensional long-range supersymmetric t-J model has previously been established for both open systems and those closed by periodic boundary conditions through explicit construction of its integrals of motion. Recently the system has been extended to include the effect of magnetic flux, which gives rise to a closed chain with twisted boundary conditions. While the t-J model with twisted boundary conditions has been solved for the ground state and full energy spectrum, proof of its integrability has so far been lacking. In this paper we extend the proof of integrability of the long-range supersymmetric t-J model and its SU(m{vert_bar}n) generalization to include the case of twisted boundary conditions. {copyright} {ital 1997} {ital The American Physical Society}
NASA Astrophysics Data System (ADS)
Wang, Qingshan; Shi, Dongyan; Pang, Fuzhen; Liang, Qian
2016-04-01
A Fourier-Ritz method for predicting the free vibration of composite laminated circular panels and shells of revolution subjected to various combinations of classical and non-classical boundary conditions is presented in this paper. A modified Fourier series approach in conjunction with a Ritz technique is employed to derive the formulation based on the first-order shear deformation theory. The general boundary condition can be achieved by the boundary spring technique in which three types of liner and two types of rotation springs along the edges of the composite laminated circular panels and shells of revolution are set to imitate the boundary force. Besides, the complete shells of revolution can be achieved by using the coupling spring technique to imitate the kinematic compatibility and physical compatibility conditions of composite laminated circular panels at the common meridian with θ = 0 and 2π. The comparisons established in a sufficiently conclusive manner show that the present formulation is capable of yielding highly accurate solutions with little computational effort. The influence of boundary and coupling restraint parameters, circumference angles, stiffness ratios, numbers of layer and fiber orientations on the vibration behavior of the composite laminated circular panels and shells of revolution are also discussed.
NASA Astrophysics Data System (ADS)
Kumar, Rajneesh; Kumar, Anoop; Goel, Varun
2016-06-01
The force convective heat transfer in an equilateral triangular duct of different wall heat flux configurations was analysed for the laminar hydro-dynamically developed and thermally developing flow by the use of finite volume method. Unstructured meshing was generated by multi-block technique and set of governing equations were discretized using second-order accurate up-wind scheme and numerically solved by SIMPLE Algorithm. For ensuring accuracy, grid independence study was also done. Numerical methodology was verified by comparing results with previous work and predicted results showed good agreement with them (within error of ±5 %). The different combinations of constant heat flux boundary condition were analysed and their effect on heat transfer and fluid flow for different Reynolds number was also studied. The results of different combinations were compared with the case of force convective heat transfer in the equilateral triangular duct with constant heat flux on all three walls.
NASA Technical Reports Server (NTRS)
Gnoffo, Peter A.; Johnston, Christopher O.
2011-01-01
Implementations of a model for equilibrium, steady-state ablation boundary conditions are tested for the purpose of providing strong coupling with a hypersonic flow solver. The objective is to remove correction factors or film cooling approximations that are usually applied in coupled implementations of the flow solver and the ablation response. Three test cases are considered - the IRV-2, the Galileo probe, and a notional slender, blunted cone launched at 10 km/s from the Earth's surface. A successive substitution is employed and the order of succession is varied as a function of surface temperature to obtain converged solutions. The implementation is tested on a specified trajectory for the IRV-2 to compute shape change under the approximation of steady-state ablation. Issues associated with stability of the shape change algorithm caused by explicit time step limits are also discussed.
High-Order Simulation of Induced Disturbance in a Mach 6 Boundary Layer
NASA Technical Reports Server (NTRS)
Atkins, Harold L.
2013-01-01
Simulations of the early evolution of induced unstable disturbances in a Mach 6 hypersonic boundary layer are presented for the purposes of validating a high-order discontinuous Galerkin Navier-Stokes simulation code. The simulations are modeled after experiments performed in the Boeing/AFOSR Mach-6 Quiet Tunnel at Purdue University. In these experiments, a forcing mechanism was employed to induce reproducible disturbances in a hypersonic boundary layer providing for the controlled study of the growth and breakdown of these disturbances into turbulent spots. Simulations revealed that the form and strength of the excitation can greatly influence the growth of the disturbance. In particular, at large forcing amplitude, the simulated forcing produces large advecting transients that appear to enhance the growth of the wave packet, relative to that of low amplitude forcing. Simulation results with large amplitude forcing agree well with experimental results while results from low amplitude forcing agree with linear stability theory.
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.
A critique of some recent second-order turbulence closure models for compressible boundary layers
NASA Technical Reports Server (NTRS)
Rubesin, M. W.; Crisalli, A. J.; Horstman, C. C.; Acharya, M.; Lanfranco, M. J.
1977-01-01
Computations based on two recently developed second-order turbulence closure models are compared with a series of boundary-layer experiments and with predictions of these experiments using an algebraic mixing length model. One of the models employs an eddy viscosity, whereas the other evaluates components of the Reynolds stress tensor. For flat plates, the computations are compared with the van Driest skin-friction transformation to assess the handling of compressibility. For boundary layers in pressure gradients, four experiments at Mach 4 and one at Mach 6.7 are used as the bases for comparison. In general, both models represent mean velocities and skin friction reasonably well, but represent the turbulence shear stress less accurately.
A bridging technique to analyze the influence of boundary conditions on instability patterns
Hu Heng; Damil, Noureddine; Potier-Ferry, Michel
2011-05-10
In this paper, we present a new numerical technique that permits to analyse the effect of boundary conditions on the appearance of instability patterns. Envelope equations of Landau-Ginzburg type are classically used to predict pattern formation, but it is not easy to associate boundary conditions for these macroscopic models. Indeed, envelope equations ignore boundary layers that can be important, for instance in cases where the instability starts first near the boundary. In this work, the full model is considered close to the boundary, an envelope equation in the core and they are bridged by the Arlequin method . Simulation results are presented for the problem of buckling of long beams lying on a non-linear elastic foundation.
Kinematics and shear heat pattern of ductile simple shear zones with `slip boundary condition'
NASA Astrophysics Data System (ADS)
Mulchrone, Kieran F.; Mukherjee, Soumyajit
2016-04-01
Extrusion by Poiseuille flow and simple shear of hot lower crust has been deciphered from large hot orogens, and partial-slip boundary condition has been encountered in analogue models. Shear heat and velocity profiles are deduced from a simplified form of Navier-Stokes equation for simple shear together with extrusive Poiseuille flow and slip boundary condition for Newtonian viscous rheology. A higher velocity at the upper boundary of the shear zone promotes higher slip velocity at the lower boundary. The other parameters that affect the slip are viscosity and thickness of the shear zone and the resultant pressure gradient that drives extrusion. In the partial-slip case, depending on flow parameters (resultant pressure gradient, density and viscosity) and thickness of the shear zone, the velocity profiles can curve and indicate opposite shear senses. The corresponding shear heat profiles can indicate temperature maximum inside shear zones near either boundaries of the shear zone, or equidistant from them.
Unsteady Validation of a Mean Flow Boundary Condition for Computational Aeroacoustics
NASA Technical Reports Server (NTRS)
Hixon, R.; Zhen, F.; Nallasamy, M.; Sawyer, S>
2004-01-01
In this work, a previously developed mean flow boundary condition will be validated for unsteady flows. The test cases will be several reference benchmark flows consisting of vortical gusts convecting in a uniform mean flow, as well as the more realistic case of a vortical gust impinging on a loaded 2D cascade. The results will verify that the mean flow boundary condition both imposes the desired mean flow as well as having little or no effect on the instantaneous unsteady solution.
NASA Technical Reports Server (NTRS)
Wada, B. K.; Kuo, C.-P.; Glaser, R. J.
1986-01-01
A major challenge to the structural dynamicist is to validate mathematical models of large space structures which cannot be ground tested because of its size and/or flexibility. The paper presents a Multiple Boundary Condition Test (MBCT) approach which allows a systematic validation of the mathematical model by performing a number of ground tests on a large structure with variable boundary conditions. A numerical simulation is presented which illustrates the validity of the MBCT including some of the potential limitations.
NASA Astrophysics Data System (ADS)
Gasymov, E. A.; Guseinova, A. O.; Gasanova, U. N.
2016-07-01
One of the methods for solving mixed problems is the classical separation of variables (the Fourier method). If the boundary conditions of the mixed problem are irregular, this method, generally speaking, is not applicable. In the present paper, a generalized separation of variables and a way of application of this method to solving some mixed problems with irregular boundary conditions are proposed. Analytical representation of the solution to this irregular mixed problem is obtained.
NASA Technical Reports Server (NTRS)
Beggs, John H.; Luebbers, Raymond J.; Kunz, Karl S.; Yee, Kane 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 a 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. A 1-D implementation for a surface impedance boundary condition for good conductors in the Finite Difference Time Domain (FDTD) technique.
Fourth order solutions of singularly perturbed boundary value problems by quarter-sweep iteration
NASA Astrophysics Data System (ADS)
Sulaiman, J.; Hasan, M. K.; Othman, M.; Abdul Karim, S. A.
2013-04-01
In previous studies, the effectiveness of the second-order quarter-sweep finite difference approximation equations has been shown in solving singularly perturbed boundary value problems. In this paper, however, we investigate the application of the fourth-order quarter-sweep finite difference approximation equation based on the fourth-order standard central difference scheme. To solve the problems numerically, discretization of the singularly perturbed problems via second-order and fourth-order finite difference schemes is proposed to form the corresponding system of linear algebraic equations. For comparison purpose, we also discuss on how to derive the basic formulation and implementation for the family of Successive Over-Relaxation (SOR) iterative methods such as FSSOR, HSSOR and QSSOR in solving the corresponding linear systems generated from the fourth-order discretization schemes based on full, half- and quarter-sweep cases. Some numerical tests were conducted to show that the accuracy of fourth-order finite difference schemes via the corresponding GS methods is more accurate than second-order schemes.
ALmost EXact boundary conditions for transient Schrödinger-Poisson system
NASA Astrophysics Data System (ADS)
Bian, Lei; Pang, Gang; Tang, Shaoqiang; Arnold, Anton
2016-05-01
For the Schrödinger-Poisson system, we propose an ALmost EXact (ALEX) boundary condition to treat accurately the numerical boundaries. Being local in both space and time, the ALEX boundary conditions are demonstrated to be effective in suppressing spurious numerical reflections. Together with the Crank-Nicolson scheme, we simulate a resonant tunneling diode. The algorithm produces numerical results in excellent agreement with those in Mennemann et al. [1], yet at a much reduced complexity. Primary peaks in wave function profile appear as a consequence of quantum resonance, and should be considered in selecting the cut-off wave number for numerical simulations.
Research of a boundary condition quantifiable correction method in the assembly homogenization
Peng, L. H.; Liu, Z. H.; Zhao, J.; Li, W. H.
2012-07-01
The methods and codes currently used in assembly homogenization calculation mostly adopt the reflection boundary conditions. The influences of real boundary conditions on the assembly homogenized parameters were analyzed. They were summarized into four quantifiable effects, and then the mathematical expressions could be got by linearization hypothesis. Through the calculation of a test model, it had been found that the result was close to transport calculation result when considering four boundary quantifiable effects. This method would greatly improve the precision of a core design code which using the assembly homogenization methods, but without much increase of the computing time. (authors)
A stable penalty method for the compressible Navier-Stokes equations. 1: Open boundary conditions
NASA Technical Reports Server (NTRS)
Hesthaven, J. S.; Gottlieb, D.
1994-01-01
The purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible Navier-Stokes equations in three spatial dimensions. The treatment uses the conservation form of the Navier-Stokes equations and utilizes linearization and localization at the boundaries based on these variables. The proposed boundary conditions are applied through a penalty procedure, thus ensuring correct behavior of the scheme as the Reynolds number tends to infinity. The versatility of this method is demonstrated for the problem of a compressible flow past a circular cylinder.
A method for implementing Dirichlet and third-type boundary conditions in PTRW simulations
NASA Astrophysics Data System (ADS)
Koch, J.; Nowak, W.
2014-02-01
We present an efficient and accurate numerical method for implementing Dirichlet boundary conditions in particle tracking random walk (PTRW) simulations of advective-dispersive transport. This is a challenge, because defining concentrations for Dirichlet boundary conditions requires invoking control volumes of some kind, which are not natural to the Lagrangian-based PTRW concept. Our method performs a Galerkin projection of PTRW-based particle densities onto control volumes that discretize the boundary. Thus, we obtain concentration values at the boundary condition and can control the particle release rates such that the prescribed boundary values are met. This allows for complex-shaped internal and external boundaries, where concentration values are fixed to prescribed values. Third-type boundary conditions can be addressed as well. We test and illustrate the properties and behavior of our method in a series of test cases. The results are benchmarked against the conceptually related semianalytical method MASST (multiple analytical source superposition technique) and to those of a finite element method (FEM). While MASST is restricted to uniform velocity fields due to the underlying analytical solutions, FEM is limited in heterogeneous velocity fields at large Péclet numbers by numerical dispersion in the feasible discretization range. The results demonstrate that our proposed method performs better than the other methods in both regimes.
NASA Astrophysics Data System (ADS)
Renardy, M.
1986-02-01
Steady flows of viscoelastic fluids can not be uniquely determined by imposing boundary conditions only for the velocities as in the Newtonian case. The reason for this is that the fluids have memory, and therefore the flow inside the domain is affected by what happened before the fluid entered the domain. This leads to the need for extra boundary conditions at an inflow boundary. The nature of these inflow boundary conditions has not been analyzed previously, and it is certainly dependent on the constitutive law. In this paper, we look at the special case of differential constitutive relations with a single relaxation mode. We consider steady transverse flows across a strip which are small perturbations of a flow with constant velocity. It turns out that in this case two extra inflow boundary conditions are required in two dimensions, and four in three dimensions. This is what would be expected from an analysis of characteristics, but it contradicts the belief of many rheologists that it is possible to prescribe the extra stress at an inflow boundary. The problem studied here is of potential relevance for numerical simulations of steady flows. Many of the flows currently simulated are on infinite domains. Numerically, these domains are truncated, and on the inflow boundary of the truncated domain people usually prescribe the extra stress. According to the analysis in this paper, this is an overdetermined problem, and therefore errors must be expected from this procedure.
Analytical solutions with Generalized Impedance Boundary Conditions (GIBC)
NASA Technical Reports Server (NTRS)
Ricoy, Mark A.; Volakis, John L.
1990-01-01
The diffraction by a material discontinuity in a thick dielectric/ferrite layer is considered by modeling the layer as a distributed current sheet obeying generalized sheet transition conditions (GSTC's). The sheet currents are then formulated and solved via the standard dual integral equation approach. This yields the diffracted field in terms of unknown constants which underscore the non-uniqueness of the GSTC current sheet representation. The constants are dependent on the geometry and properties of the discontinuity and are determined by enforcing field continuity across the material junction. This requires the field internal to the slab which are determined from the external ones via analytic continuity. Results are given which validate the solution and demonstrate the importance of the constants.
Towed body measurements of flow noise from a turbulent boundary layer under sea conditions.
Abshagen, J; Nejedl, V
2014-02-01
Results from an underwater experiment under sea conditions on flow noise beneath a flat-plate turbulent boundary layer are presented. The measurements were performed with a towed body at towing speeds U=2.3,…,6.1 m/s and depths h=-150,…,-100 m. Flow noise is measured with a linear array of equally spaced hydrophones (Δx=70 mm) that is orientated in streamwise direction and embedded within a laterally attached flat plate. In order to separate flow noise from ocean ambient noise and other acoustical noise sources wavenumber-frequency filtering is applied. The (nondimensionalized) spectral power density of flow noise Φ(ω) ⟨U∞⟩/ (⟨δ(∗)⟩ (1/2ρ ⟨U∞⟩)(2)) is found to scale like (ω⟨δ(∗)⟩/⟨U∞⟩)(-4.3) in a wide frequency range at higher towing speeds. Here, ω, ⟨δ(∗)⟩, and ⟨U∞⟩ denote frequency, boundary layer displacement thickness, and potential flow velocity in the array region, respectively. Potential flow velocity is estimated from numerical simulations around a symmetrical, two-dimensional body with a semi-elliptical nose. Evidence is given that a χ(2)-(Tsallis) superstatistics provides a reasonable representation of the probability distribution function of flow noise at higher towing speeds. PMID:25234873
NASA Astrophysics Data System (ADS)
Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre
2013-11-01
A Continuous Boundary Force (CBF) method was developed for implementing Robin (Navier) boundary condition (BC) that can describe no-slip or slip conditions (slip length from zero to infinity) at the fluid-solid interface. In the CBF method the Robin BC is replaced by a homogeneous Neumann BC and an additional volumetric source term in the governing momentum equation. The formulation is derived based on an approximation of the sharp boundary with a diffuse interface of finite thickness, across which the BC is reformulated by means of a smoothed characteristic function. The CBF method is easy to be implemented in Lagrangian particle-based methods. We first implemented it in smoothed particle hydrodynamics (SPH) to solve numerically the Navier-Stokes equations subject to spatial-independent or dependent Robin BC in two and three dimensions. The numerical accuracy and convergence is examined through comparisons with the corresponding finite difference or finite element solutions. The CBF method is further implemented in smoothed dissipative particle dynamics (SDPD), a mesoscale scheme, for modeling slip flows commonly existent in micro/nano channels and microfluidic devices. The authors acknowledge the funding support by the ASCR Program of the Office of Science, U.S. Department of Energy.
NASA Astrophysics Data System (ADS)
Jacob, Chinthaka; Anderson, William
2016-06-01
Aeolian erosion of flat, arid landscapes is induced (and sustained) by the aerodynamic surface stress imposed by flow in the atmospheric surface layer. Conceptual models typically indicate that sediment mass flux, Q (via saltation or drift), scales with imposed aerodynamic stress raised to some exponent, n, where n > 1 . This scaling demonstrates the importance of turbulent fluctuations in driving aeolian processes. In order to illustrate the importance of surface-stress intermittency in aeolian processes, and to elucidate the role of turbulence, conditional averaging predicated on aerodynamic surface stress has been used within large-eddy simulation of atmospheric boundary-layer flow over an arid, flat landscape. The conditional-sampling thresholds are defined based on probability distribution functions of surface stress. The simulations have been performed for a computational domain with ≈ 25 H streamwise extent, where H is the prescribed depth of the neutrally-stratified boundary layer. Thus, the full hierarchy of spatial scales are captured, from surface-layer turbulence to large- and very-large-scale outer-layer coherent motions. Spectrograms are used to support this argument, and also to illustrate how turbulent energy is distributed across wavelengths with elevation. Conditional averaging provides an ensemble-mean visualization of flow structures responsible for erosion `events'. Results indicate that surface-stress peaks are associated with the passage of inclined, high-momentum regions flanked by adjacent low-momentum regions. Fluid in the interfacial shear layers between these adjacent quasi-uniform momentum regions exhibits high streamwise and vertical vorticity.
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
a Simple Algorithm to Enforce Dirichlet Boundary Conditions in Complex Geometries
NASA Astrophysics Data System (ADS)
Huber, Christian; Dufek, Josef; Chopard, Bastien
We present a new algorithm to implement Dirichlet boundary conditions for diffusive processes in arbitrarily complex geometries. In this approach, the boundary conditions around the diffusing object is replaced by the fictitious phase transition of a pure substance where the energy cost of the phase transition largely overwhelms the amount of energy stored in the system. The computing cost of this treatment of the boundary condition is independent of the topology of the boundary. Moreover, the implementation of this new approach is straightforward and follows naturally from enthalpy-based numerical methods. This algorithm is compatible with a wide variety of discretization methods, finite differences, finite volume, lattice Boltzmann methods and finite elements, to cite a few. We show, here, using both lattice Boltzmann and finite-volume methods that our model is in excellent agreement with analytical solutions for high symmetry geometries. We also illustrate the advantages of the algorithm to handle more complex geometries.
A far-field non-reflecting boundary condition for two-dimensional wake flows
NASA Technical Reports Server (NTRS)
Danowitz, Jeffrey S.; Abarbanel, Saul A.; Turkel, Eli
1995-01-01
Far-field boundary conditions for external flow problems have been developed based upon long-wave perturbations of linearized flow equations about a steady state far field solution. The boundary improves convergence to steady state in single-grid temporal integration schemes using both regular-time-stepping and local-time-stepping. The far-field boundary may be near the trailing edge of the body which significantly reduces the number of grid points, and therefore the computational time, in the numerical calculation. In addition the solution produced is smoother in the far-field than when using extrapolation conditions. The boundary condition maintains the convergence rate to steady state in schemes utilizing multigrid acceleration.
Nonreflecting far-field boundary conditions for unsteady transonic flow computation
NASA Technical Reports Server (NTRS)
Kwak, D.
1980-01-01
The approximate nonreflecting far-field boundary condition, as proposed by Engquist and Majda, is implemented in the computer code LTRAN2. This code solves the implicit finite-difference representation of the small disturbance equations for unsteady transonic flows about airfoils. The nonreflecting boundary condition and the description of the algorithm for implementing these conditions in LTRAN2 are discussed. Various cases are computed and compared with results from the older, more conventional procedures. One concludes that the nonreflecting far-field boundary approximation allows the far-field boundary to be located closer to the airfoil; this permits a decrease in the computer time required to obtain the solution through the use of fewer mesh points.
Nonreflecting Far-Field Boundary Conditions for Unsteady Transonic Flow Computation
NASA Technical Reports Server (NTRS)
Kwak, D.
1981-01-01
The approximate nonreflecting far-field boundary condition, as proposed by Engquisi and Majda, is implemented In the computer code LTRAN2. This code solves the Implicit finite-difference representation of the small-disturbance equations for unsteady transonic flows about airfoils. The nonreflecting boundary condition and the description of the algorithm for Implementing these conditions In LTRAN2 tire discussed. Various cases re computed and compared with results from the older, more conventional procedures. One concludes that the nonreflecting far-field boundary approximation allows the far-field boundary to be located closer to the airfoil; this permits a decrease in the computer lime required to obtain the solution through the use of fewer mesh points.
Fluid flow in nanopores: An examination of hydrodynamic boundary conditions
NASA Astrophysics Data System (ADS)
Sokhan, V. P.; Nicholson, D.; Quirke, N.
2001-08-01
Steady-state Poiseuille flow of a simple fluid in carbon slit pores under a gravity-like force is simulated using a realistic empirical many-body potential model for carbon. In this work we focus on the small Knudsen number regime, where the macroscopic equations are applicable, and simulate different wetting conditions by varying the strength of fluid-wall interactions. We show that fluid flow in a carbon pore is characterized by a large slip length even in the strongly wetting case, contrary to the predictions of Tolstoi's theory. When the surface density of wall atoms is reduced to values typical of a van der Waals solid, the streaming velocity profile vanishes at the wall, in accordance with earlier findings. From the velocity profiles we have calculated the slip length and by analyzing temporal profiles of the velocity components of particles colliding with the wall we obtained values of the Maxwell coefficient defining the fraction of molecules thermalized by the wall.
Boundary conditions in the research of stress-strain state by optical tomography method
Patrikeyev, I.; Shakhurdin, V.
1994-12-31
Mechanical stresses appear in the elastic body under the influence of external loading. In these conditions optical isotropic medium becomes optical anisotropic and behaves itself as a crystal. In photoelasticity on the analogy with a classification of natural crystal anisotropy three problems of the stress strain state can be distinguished. The tasks in which the stress strain state is caused by a uniform compression or expansion belong to the first problem. It is the most common case. The plane problems belong to the second group of problems. In this case stress strain state is described by the tensor of the second order with three or four components not equal to zero. All the rest problems belong to the third group. The stress strain state of the medium is described by the second order tensor with six components different from zero. The investigation of such problems required new transillumination schemes and algorithms for the treatment of experimental results which radically differ from the classical tomography schemes and methods. The role of boundary conditions for the correct formulation photoelasticity problems based on the restoration of tensor fields by means of optical tomography is presented in this article.
A direct approach to finding unknown boundary conditions in steady heat conduction
NASA Technical Reports Server (NTRS)
Martin, Thomas J.; Dulikravich, George S.
1993-01-01
The capability of the boundary element method (BEM) in determining thermal boundary conditions on surfaces of a conducting solid where such quantities are unknown was demonstrated. The method uses a non-iterative direct approach in solving what is usually called the inverse heat conduction problem (IHCP). Given any over-specified thermal boundary conditions such as a combination of temperature and heat flux on a surface where such data is readily available, the algorithm computes the temperature field within the object and any unknown thermal boundary conditions on surfaces where thermal boundary values are unavailable. A two-dimensional, steady-state BEM program was developed and was tested on several simple geometries where the analytic solution was known. Results obtained with the BEM were in excellent agreement with the analytic values. The algorithm is highly flexible in treating complex geometries, mixed thermal boundary conditions, and temperature-dependent material properties and is presently being extended to three-dimensional and unsteady heat conduction problems. The accuracy and reliability of this technique was very good but tended to deteriorate when the known surface conditions were only slightly over-specified and far from the inaccessible surface.
NASA Astrophysics Data System (ADS)
Grobbelaar-Van Dalsen, Marié
2015-02-01
In this article, we are concerned with the polynomial stabilization of a two-dimensional thermoelastic Mindlin-Timoshenko plate model with no mechanical damping. The model is subject to Dirichlet boundary conditions on the elastic as well as the thermal variables. The work complements our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 64:1305-1325, 2013) on the polynomial stabilization of a Mindlin-Timoshenko model in a radially symmetric domain under Dirichlet boundary conditions on the displacement and thermal variables and free boundary conditions on the shear angle variables. In particular, our aim is to investigate the effect of the Dirichlet boundary conditions on all the variables on the polynomial decay rate of the model. By once more applying a frequency domain method in which we make critical use of an inequality for the trace of Sobolev functions on the boundary of a bounded, open connected set we show that the decay is slower than in the model considered in the cited work. A comparison of our result with our polynomial decay result for a magnetoelastic Mindlin-Timoshenko model subject to Dirichlet boundary conditions on the elastic variables in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047-1065, 2012) also indicates a correlation between the robustness of the coupling between parabolic and hyperbolic dynamics and the polynomial decay rate in the two models.
A solution of the geodetic boundary value problem to order e3
NASA Technical Reports Server (NTRS)
Mather, R. S.
1973-01-01
A solution is obtained for the geodetic boundary value problem which defines height anomalies to + or - 5 cm, if the earth were rigid. The solution takes into account the existence of the earth's topography, together with its ellipsoidal shape and atmosphere. A relation is also established between the commonly used solution of Stokes and a development correct to order e cubed. The data requirements call for a complete definition of gravity anomalies at the surface of the earth and a knowledge of elevation characteristics at all points exterior to the geoid. In addition, spherical harmonic representations must be based on geocentric rather than geodetic latitudes.
NASA Astrophysics Data System (ADS)
Yakushev, Evgeniy
2013-04-01
Climate Change affects oxygen depletion and leads to spreading of the bottom areas with hypoxic and anoxic conditions in the coastal areas of the seas and inland waters. This work aimed in estimation of a role of changes of redox conditions in the biogeochemical structure there. We use a 1-dimensional C-N-P-Si-O-S-Mn-Fe vertical transport-reaction model describing the water column, bottom boundary layer and benthic boundary layer with biogeochemical block simulating redox conditions changeability. A biogeochemical block is based on ROLM (RedOx Layer Model), that was constructed to simulate basic features of the water column biogeochemical structure changes in oxic, anoxic and changeable conditions (Yakushev et al., 2007). Organic matter formation and decay, reduction and oxidation of species of nitrogen, sulfur, manganese, iron, and the transformation of phosphorus species are parameterized in the model. ROLM includes a simplified ecological model with phytoplankton, zooplankton, aerobic autotrophic and heterotrophic bacteria, anaerobic autotrophic and heterotrophic bacteria. We simulate changes in the parameters distributions and fluxes connected with the vertical displacement of redox interface from the sediments to the water.
NASA Technical Reports Server (NTRS)
Kwak, D.
1981-01-01
Various nonreflecting far-field boundary condition procedures are compared by implementing them in the computer code LTRAN2. This code solves the implicit finite-difference representation of the small-disturbance equations for transonic flows about airfoils. The first- and second-approximate nonreflecting conditions, as proposed by Engquist and Majda, are compared with the condition derived from the full-characteristic equation. The far-field boundary conditions and the description of the algorithm for implementing these conditions in LTRAN2 are discussed. Various cases are computed and compared with results from the older, more conventional procedures. One concludes that the full-characteristic equation produces the most effective results, thus allowing the far-field boundary to be located closer to the airfoil; this decreases the computer time required to obtain the solution because fewer mesh points are required.