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Appropriate Boundary Conditions (appropriate + boundary_condition)
Selected AbstractsA new integral equation approach to the Neumann problem in acoustic scatteringMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16 2001P. A. Krutitskii We suggest a new approach of reduction of the Neumann problem in acoustic scattering to a uniquely solvable Fredholm integral equation of the second kind with weakly singular kernel. To derive this equation we placed an additional boundary with an appropriate boundary condition inside the scatterer. The solution of the problem is obtained in the form of a single layer potential on the whole boundary. The density in the potential satisfies a uniquely solvable Fredholm integral equation of the second kind and can be computed by standard codes. Copyright © 2001 John Wiley & Sons, Ltd. [source] Numerical study of boundary conditions for solute transport through a porous mediumINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2001Glen P. Peters Abstract A transition region may be defined as a region of rapid change in medium properties about the interface between two porous media or at the interface between a porous medium and a reservoir. Modelling the transition region between different porous media can assist in the selection of the most appropriate boundary conditions for the standard advection,dispersion equation (ADE). An advantage of modelling the transition region is that it removes the need for explicitly defining boundary conditions, though boundary conditions may be recovered as limiting cases. As the width of a transition region is reduced, the solution of the transition region model (TR model) becomes equivalent to the solution of the standard ADE model with correct boundary conditions. In this paper numerical simulations using the TR model are employed to select the most appropriate boundary conditions for the standard ADE under a variety of configurations and conditions. It is shown that at the inlet boundary between a reservoir and porous medium, continuity of solute mass flux should be used as the boundary condition. At the boundary interface between two porous media both continuity of solute concentration and solute mass flux should be used. Finally, in a finite porous medium where the solute is allowed to advect freely from the exit point, both continuity of solute concentration and solute mass flux should be used as the outlet boundary condition. The findings made here are discussed with reference to a detailed review of previous relevant theoretical and experimental observations. Copyright © 2001 John Wiley & Sons, Ltd. [source] Non-reflecting artificial boundaries for transient scalar wave propagation in a two-dimensional infinite homogeneous layerINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2003Chongbin Zhao Abstract This paper presents an exact non-reflecting boundary condition for dealing with transient scalar wave propagation problems in a two-dimensional infinite homogeneous layer. In order to model the complicated geometry and material properties in the near field, two vertical artificial boundaries are considered in the infinite layer so as to truncate the infinite domain into a finite domain. This treatment requires the appropriate boundary conditions, which are often referred to as the artificial boundary conditions, to be applied on the truncated boundaries. Since the infinite extension direction is different for these two truncated vertical boundaries, namely one extends toward x ,, and another extends toward x,- ,, the non-reflecting boundary condition needs to be derived on these two boundaries. Applying the variable separation method to the wave equation results in a reduction in spatial variables by one. The reduced wave equation, which is a time-dependent partial differential equation with only one spatial variable, can be further changed into a linear first-order ordinary differential equation by using both the operator splitting method and the modal radiation function concept simultaneously. As a result, the non-reflecting artificial boundary condition can be obtained by solving the ordinary differential equation whose stability is ensured. Some numerical examples have demonstrated that the non-reflecting boundary condition is of high accuracy in dealing with scalar wave propagation problems in infinite and semi-infinite media. Copyright © 2003 John Wiley & Sons, Ltd. [source] An iterative defect-correction type meshless method for acousticsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2003V. Lacroix Abstract Accurate numerical simulation of acoustic wave propagation is still an open problem, particularly for medium frequencies. We have thus formulated a new numerical method better suited to the acoustical problem: the element-free Galerkin method (EFGM) improved by appropriate basis functions computed by a defect correction approach. One of the EFGM advantages is that the shape functions are customizable. Indeed, we can construct the basis of the approximation with terms that are suited to the problem which has to be solved. Acoustical problems, in cavities , with boundary T, are governed by the Helmholtz equation completed with appropriate boundary conditions. As the pressure p(x,y) is a complex variable, it can always be expressed as a function of cos,(x,y) and sin,(x,y) where ,(x,y) is the phase of the wave in each point (x,y). If the exact distribution ,(x,y) of the phase is known and if a meshless basis {1, cos,(x,y), sin, (x,y) } is used, then the exact solution of the acoustic problem can be obtained. Obviously, in real-life cases, the distribution of the phase is unknown. The aim of our work is to resolve, as a first step, the acoustic problem by using a polynomial basis to obtain a first approximation of the pressure field p(x,y). As a second step, from p(x,y) we compute the distribution of the phase ,(x,y) and we introduce it in the meshless basis in order to compute a second approximated pressure field p(x,y). From p(x,y), a new distribution of the phase is computed in order to obtain a third approximated pressure field and so on until a convergence criterion, concerning the pressure or the phase, is obtained. So, an iterative defect-correction type meshless method has been developed to compute the pressure field in ,. This work will show the efficiency of this meshless method in terms of accuracy and in terms of computational time. We will also compare the performance of this method with the classical finite element method. Copyright © 2003 John Wiley & Sons, Ltd. [source] Asymptotics for steady-state voltage potentials in a bidimensional highly contrasted medium with thin layerMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2008Clair Poignard Abstract We study the behaviour of steady-state voltage potentials in two kinds of bidimensional media composed of material of complex permittivity equal to 1 (respectively, ,) surrounded by a thin membrane of thickness h and of complex permittivity , (respectively, 1). We provide in both cases a rigorous derivation of the asymptotic expansion of steady-state voltage potentials at any order as h tends to zero, when Neumann boundary condition is imposed on the exterior boundary of the thin layer. Our complex parameter , is bounded but may be very small compared to 1, hence our results describe the asymptotics of steady-state voltage potentials in all heterogeneous and highly heterogeneous media with thin layer. The asymptotic terms of the potential in the membrane are given explicitly in local coordinates in terms of the boundary data and of the curvature of the domain, while these of the inner potential are the solutions to the so-called dielectric formulation with appropriate boundary conditions. The error estimates are given explicitly in terms of h and , with appropriate Sobolev norm of the boundary data. We show that the two situations described above lead to completely different asymptotic behaviours of the potentials. Copyright © 2007 John Wiley & Sons, Ltd. [source] An interpolated spatial images method for the analysis of multilayered shielded microwave circuitsMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 9 2008J. S. Gómez-Díaz Abstract In this article, an efficient interpolation method is presented to compute the Green's function associated with electrical sources, when they are placed inside cylindrical cavities. The interpolation scheme is formulated in the frame of the spatial images technique recently developed. The original idea was to calculate, for every location of a point electric source, the complex values of the electric dipole and charge images, placed outside the cavity, to impose the appropriate boundary conditions for the potentials. To considerably reduce the computational cost of the original technique, a simple interpolation method is proposed to obtain the complex values of the images for any source location. To do that, a rectangular spatial subdivision inside the cavity is proposed. Each new subregion is controlled by means of the exact image values obtained when the source is placed at the four corners of the region. The key idea is to use a bilinear interpolation to obtain the image complex values when the source is located anywhere inside this subregion. The interpolated images provide the Green's functions of the new source positions fast, and with high accuracy. This new approach can be directly applied to analyze printed planar filters. Two examples with CPU time comparisons are provided, showing the high accuracy and computational gain achieved with the technique just derived. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 2294,2300, 2008; Published online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/mop.23683 [source] UNSTEADY STATE DISPERSION OF AIR POLLUTANTS UNDER THE EFFECTS OF DELAYED AND NONDELAYED REMOVAL MECHANISMSNATURAL RESOURCE MODELING, Issue 4 2009MANJU AGARWAL Abstract In this paper, we present a two-dimensional time-dependent mathematical model for studying the unsteady state dispersion of air pollutants emitted from an elevated line source in the atmosphere under the simultaneous effects of delayed (slow) and nondelayed (instantaneous) removal mechanisms. The wind speed and coefficient of diffusion are taken as functions of the vertical height above the ground. The deposition of pollutants on the absorptive ground and leakage into the atmosphere at the inversion layer are also included in the model by applying appropriate boundary conditions. The model is solved numerically by the fractional step method. The Lagrangian approach is used to solve the advection part, whereas the Eulerian finite difference scheme is applied to solve the part with the diffusion and removal processes. The solutions are analyzed to observe the effects of coexisting delayed and nondelayed removal mechanisms on overall dispersion. Comparison of delayed and nondelayed removal processes of equal capacity shows that the latter (nondelayed) process is more effective than the former (delayed removal) in the removal of pollutants from the atmosphere. [source] | ||||||||||