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Artificial Boundaries (artificial + boundary)

Distribution by Scientific Domains
Engineering66%
Mathematics and Statistics33%

Terms modified by Artificial Boundaries

  • artificial boundary condition
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    Selected Abstracts

    Boundary and border considerations in hydrology

    HYDROLOGICAL PROCESSES, Issue 7 2004
    Ming-ko Woo
    Abstract This paper examines several issues related to hydrological boundaries and their border zones. In a two-dimensional space, a boundary is a line that separates two domains possessing different hydrological properties or dominated by different hydrological processes, and a border is an area that experiences an edge effect owing to transitions or mixing of processes. Hydrological boundaries may be static, such as drainage divides, or dynamic, such as the edges of a seasonal snow cover. They may be open or closed to the transfer of matter and energy, although most boundaries tend to be perforated, permitting different rates of movement across different segments. Borders may be narrow or the edge effect can affect large areas, as happens to the sensible heat flux over a highly fragmented melting snowfield. The introduction of artificial boundaries, notably the grid patterns of remote sensing pixels, digital elevation models and land surface schemes, gives rise to problems of mismatch with the natural hydrological boundaries. Incorrect demarcation, omission and generalization of boundaries can produce errors that are hard to rectify. Serious biases are involved when point observations are used to calibrate parameters or to validate model outputs integrated over a bounded area. Examples are drawn mainly from cold climate hydrology to illustrate the boundary issues but the questions transcend disciplinary areas. The intent of this presentation is to stimulate discussions that could be a prelude to finding solutions to many boundary problems which have thus far eluded hydrological investigations. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    Non-reflecting artificial boundaries for transient scalar wave propagation in a two-dimensional infinite homogeneous layer

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2003
    Chongbin 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]

    Nonreflecting boundary conditions based on nonlinear multidimensional characteristics

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2010
    Qianlong Liu
    Abstract Nonlinear characteristic boundary conditions based on nonlinear multidimensional characteristics are proposed for 2- and 3-D compressible Navier,Stokes equations with/without scalar transport equations. This approach is consistent with the flow physics and transport properties. Based on the theory of characteristics, which is a rigorous mathematical technique, multidimensional flows can be decomposed into acoustic, entropy, and vorticity waves. Nonreflecting boundary conditions are derived by setting corresponding characteristic variables of incoming waves to zero and by partially damping the source terms of the incoming acoustic waves. In order to obtain the resulting optimal damping coefficient, analysis is performed for problems of pure acoustic plane wave propagation and arbitrary flows. The proposed boundary conditions are tested on two benchmark problems: cylindrical acoustic wave propagation and the wake flow behind a cylinder with strong periodic vortex convected out of the computational domain. This new approach substantially minimizes the spurious wave reflections of pressure, density, temperature, and velocity as well as vorticity from the artificial boundaries, where strong multidimensional flow effects exist. The numerical simulations yield accurate results, confirm the optimal damping coefficient obtained from analysis, and verify that the method substantially improves the 1-D characteristics-based nonreflecting boundary conditions for complex multidimensional flows. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Elliptic and parabolic problems in unbounded domains

    MATHEMATISCHE NACHRICHTEN, Issue 1 2004
    Patrick Guidotti
    Abstract We consider elliptic and parabolic problems in unbounded domains. We give general existence and regularity results in Besov spaces and semi-explicit representation formulas via operator-valued fundamental solutions which turn out to be a powerful tool to derive a series of qualitative results about the solutions. We give a sample of possible applications including asymptotic behavior in the large, singular perturbations, exact boundary conditions on artificial boundaries and validity of maximum principles. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

    Finite element analysis of time-dependent semi-infinite wave-guides with high-order boundary treatment

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2003
    Dan Givoli
    Abstract A new finite element (FE) scheme is proposed for the solution of time-dependent semi-infinite wave-guide problems, in dispersive or non-dispersive media. The semi-infinite domain is truncated via an artificial boundary ,, and a high-order non-reflecting boundary condition (NRBC), based on the Higdon non-reflecting operators, is developed and applied on ,. The new NRBC does not involve any high derivatives beyond second order, but its order of accuracy is as high as one desires. It involves some parameters which are chosen automatically as a pre-process. A C0 semi-discrete FE formulation incorporating this NRBC is constructed for the problem in the finite domain bounded by ,. Augmented and split versions of this FE formulation are proposed. The semi-discrete system of equations is solved by the Newmark time-integration scheme. Numerical examples concerning dispersive waves in a semi-infinite wave guide are used to demonstrate the performance of the new method. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    High-order boundary conditions for linearized shallow water equations with stratification, dispersion and advection,

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2004
    Vince J. van Joolen
    Abstract The two-dimensional linearized shallow water equations are considered in unbounded domains with density stratification. Wave dispersion and advection effects are also taken into account. The infinite domain is truncated via a rectangular artificial boundary ,, and a high-order open boundary condition (OBC) is imposed on ,. Then the problem is solved numerically in the finite domain bounded by ,. A recently developed boundary scheme is employed, which is based on a reformulation of the sequence of OBCs originally proposed by Higdon. The OBCs can easily be used up to any desired order. They are incorporated here in a finite difference scheme. Numerical examples are used to demonstrate the performance and advantages of the computational method, with an emphasis is on the effect of stratification. Published in 2004 by John Wiley & Sons, Ltd. [source]

    Artificial boundary conditions for viscoelastic flows

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 8 2008
    Sergueï A. Nazarov
    Abstract The steady three-dimensional exterior flow of a viscoelastic non-Newtonian fluid is approximated by reducing the corresponding nonlinear elliptic,hyperbolic system to a bounded domain. On the truncation surface with a large radius R, nonlinear, local second-order artificial boundary conditions are constructed and a new concept of an artificial transport equation is introduced. Although the asymptotic structure of solutions at infinity is known, certain attributes cannot be found explicitly so that the artificial boundary conditions must be constructed with incomplete information on asymptotics. To show the existence of a solution to the approximation problem and to estimate the asymptotic precision, a general abstract scheme, adapted to the analysis of coupled systems of elliptic,hyperbolic type, is proposed. The error estimates, obtained in weighted Sobolev norms with arbitrarily large smoothness indices, prove an approximation of order O(R,2+,), with any ,>0. Our approach, in contrast to other papers on artificial boundary conditions, does not use the standard assumptions on compactly supported right-hand side f, leads, in particular, to pointwise estimates and provides error bounds with constants independent of both R and f. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Oseen coupling method for the exterior flow.

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2004
    Part II: Well-posedness analysis
    Abstract In this paper, we recall the Oseen coupling method for solving the exterior unsteady Navier,Stokes equations with the non-homogeneous boundary conditions. Moreover, we derive the coupling variational formulation of the Oseen coupling problem by using of the integral representations of the solution of the Oseen equations at an infinity domain. Finally, we provide some properties of the integral operators over the artificial boundary and the well-posedness of the coupling variational formulation. Copyright © 2004 John Wiley & Sons, Ltd. [source]