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  • 1
    Electronic Resource
    Electronic Resource
    ADVANCES IN THE BOUNDARY INTEGRAL EQUATION METHOD IN SUBSURFACE FLOW (1987)
    Oxford, UK : Blackwell Publishing Ltd
    Journal of the American Water Resources Association 23 (1987), S. 0 
    Details
    ISSN: 1752-1688
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Architecture, Civil Engineering, Surveying , Geography
    Notes: : This paper explores some of the advances of the boundary element method, as applied to ground-water problems, during the last five years. Although the method is still somewhat limited compared to solution by finite elements, the range of solutions has increased considerably. Diffusion and advection-diffusion solutions are done efficiently. These include the incorporation of inhomogeneity, anisotropy, and nonlinear diffusion. The difficult problem of stream-aquifer interaction is an important application as it is much easier to follow a free surface with its multiple configurations. The application must be able to cycle between ground-water connection and disconnection with the stream and include seepage surfaces. Flow in fractured media is a natural application where the flow in fractures can usually be treated without a computational exception in spite of extremely high aspect ratios. The case of seawater intrusion forms a type of free surface problem and thus is a case for which the method has special advantages. For these and other applications the boundary element method provides an inexpensive technique for calculation where the data preparation and setup time is minimal. In most of these cases, programs can and have been written on microcomputers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1752-1688.1987.tb00838.x
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  • 2
    Electronic Resource
    Electronic Resource
    A consistent boundary element method for free surface hydrodynamic calculations (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 835-857 
    Details
    ISSN: 0271-2091
    Keywords: Boundary element ; Free surface ; Hydrodynamic ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Free surface phenomena are described by equations that exhibit two types of non-linearities. The first is inherent to the equations themselves and the second is caused by the application of boundary conditions at a free surface at an unknown location. Numerical calculations usually do not specifically recognize the second non-linearity, nor treat it in a fashion consistent with the more obvious non-linearities in the boundary conditions. A consistent formulation is introduced in the present paper. The field equation is integrated and the free surface boundary conditions are applied on the unknown geometry by means of appropriate series expansions. The consistent formulation introduces improvements in accuracy and computing speed. The method is demonstrated on several hydrodynamic free surface problems and an error analysis is included.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650120904
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  • 3
    Electronic Resource
    Electronic Resource
    Taylor-least-squares finite element for two-dimensional advection-dominated unsteady advection-diffusion problems (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 21-38 
    Details
    ISSN: 0271-2091
    Keywords: Advection ; Diffusion ; Finite element ; Two-dimensional ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new finite element method, the Taylor-least-squares, is proposed to approximate the advection-dominated unsteady advection-diffusion equation. The new scheme is a direct generalization of the Taylor-Galerkin and least-squares finite element methods. Higher-order spatial derivatives in the new formulation necessitate higher-degree polynomials. Hermite cubic shape functions are used. Extensive comparisons with other methods in one dimension proved that the new scheme is a step forward in modelling this difficult problem. The method offers straightforward generalizations to higher dimensions without losing the accuracy demonstrated in one dimension, i.e. the method preserves the important property of the Taylor-Galerkin scheme of being free of numerical crosswind diffusion. Several numerical experiments were made in two dimensions and excellent results were obtained from the representative experiments.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650110103
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  • 4
    Electronic Resource
    Electronic Resource
    Dispersion analysis in homogeneous lakes (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 1627-1642 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is devoted to a comparison of the relative accuracy of two-dimensional vs. three-dimensional finite element representations of contaminant dispersion in shallow lakes. Formulations of both types are developed, followed by numerical calculations of a hypothetical lake. The results indicate that for typical lakes a two-dimensional dispersion analysis can be employed in the absence of a significant advective contribution. With significant advection the two-dimensional approach is not sufficiently accurate. A two-dimensional dispersion analysis requires approximately the same computational resources as a three-dimensional circulation analysis.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620151106
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  • 5
    Electronic Resource
    Electronic Resource
    Two-dimensional stress intensity factor computations using the boundary element method (1981)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 387-404 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A multidomain boundary element formulation for the analysis of general two-dimensional plane strain/stress crack problems is presented. The numerical results were accurate and efficient. The analyses were performed using traction singular quater-point boundary elements on each side of the crack tip(s) with and without transition elements. Traction singular quarter-point boundary elements contain the correct √r displacement and 1/√r traction variations at the crack tip. Transition elements are appended to the traction singular elements to model the √r displacement variation. The 1/√r traction singularity is not represented with these elements. Current research studies for the crack propagation analysis of quasi-static and fatigue fracture problems are discussed.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620170308
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  • 6
    Electronic Resource
    Electronic Resource
    An integral formulation applied to the diffusion and Boussinesq equations (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1057-1079 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new integral method is proposed here to solve the diffusion equation (confined flow) and the Boussinesq equation (unconfined flow) in a two-dimensional porous medium. The method, based on Green's theorem, derives its integral representation from the portion of the original differential equation with the highest space derivatives so that the resulting kernel of the integral representation is not time dependent. Compared to an earlier integral formulation, namely the direct Green function, based on the same theorem, the kernel is simpler so that the present theory provides a more efficient numerical model without compromising accuracy. An iterative scheme is employed along with the theory to achieve solutions to the non-linear Boussinesq equation. Concepts used in the finite difference and finite element methods enable simplification of the temporal derivative. The method is tested with success on a number of numerical examples from groundwater flow.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230606
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  • 7
    Electronic Resource
    Electronic Resource
    Boundary integral equation method for linear porous-elasticity with applications to soil consolidation (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 255-278 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For physical phenomena governed by the Biot model of porous-elasticity, a reciprocal relation, similar to the Betti's recoprocal theorem in elasticity, is constructed in Laplace transformed space. Integrating the reciprocal relation enables one to formulate boundary integral equations. The fundamental kernels for the integral equations are solved in closed forms for the case of isotropic material. Numerical implementation of two-dimensional problems includes finite element ideas of discretization and polynomial interpolation, and numerical inversion of a Laplace transform. Practical applications of the method are found in consolidation problems in soils which contain compressible as well as incompressible pore fluids. Also, as a numerical experiment, consolidation of partially saturated soil is simulated and interesting phenomena are observed. The currently developed boundary integral equation method (BIEM) for porous-elasticity may be viewed as an efficient and accurate alternative of existing finite element and finite difference methods. For linear consolidation problems, application of BIEM is always preferred to the other numerical methods whenever possible.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620200206
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  • 8
    Electronic Resource
    Electronic Resource
    Boundary integral equation method for linear porous-elasticity with applications to fracture propagation (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 279-296 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For the semi-infinite crack propagating quasi-statically in a porous-elastic medium, the boundary integral equation method (BIEM), based on a reciprocal principle, is formulated for the governing equations of the Biot model of linear porous-elasticity. The resulting numerical scheme is efficient since the discretization of the solution unknowns is required only along the axis of symmetry of a fracture. Fracture propagation criteria based on both elastic and plastic constitutive relations are investigated. Practical applications of the model are expected in the failure of overconsolidated clay, earthquake prediction and underground hydraulic fracturing for energy exploration.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620200207
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  • 9
    Electronic Resource
    Electronic Resource
    Three-dimensional boundary-element computation of potential flow in fractured rock (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 2319-2330 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The use of the boundary-element method (BEM) for three-dimensional potential flow problems is described herein. The specific application for which the program is designed is the flow in fractured porous media. There are several enhancements to the usual boundary-element calculations. The method uses linear elements to approximate better the boundary conditions and the solution on the surfaces as compared to constant elements; accurate integration over high-aspect-ratio triangles is achieved by computing all the integrals in closed form, as opposed to numerical cubature or mixed exact-numerical integration schemes; and the zoning for inhomogeneous regions uses an efficient method which reduces the size of the problem and avoids difficulties with singularities.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620261013
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  • 10
    Electronic Resource
    Electronic Resource
    Boundary elements in zoned media: Direct and indirect methods (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1727-1735 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Several formulations of the Boundary Element Method (BEM) are examined herein in the context of heterogeneous media. A strong singularity develops at re-entrant interzonal corners and its effect is made more acute by large differences in the material properties. The effects of this singularity on the performance of the various BEM formulations are illustrated with examples. It is concluded that the direct BEM, either in the collocation or Galerkin formulations, is unable to give good results in zones of low conductivity. On the other hand the indirect BEM does not adequately reproduce the behaviour of the flow field near boundaries. A multi-step version of the direct BEM is formulated to eliminate the difficulties introduced by the interzonal singularities.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290808
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