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  • 1
    Electronic Resource
    Electronic Resource
    Modeling full-tensor anisotropy in groundwater flow via an iterative scheme for mixed finite elements (1996)
    Springer
    Transport in porous media 25 (1996), S. 147-165 
    Details
    ISSN: 1573-1634
    Keywords: mixed finite elements ; anisotropy ; groundwater flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract This paper presents an iterative scheme for the efficient simulation of groundwater flow in a two-dimensional, heterogeneous aquifer in which the hydraulic conductivity is anisotropic. The scheme is applicable to matrix equations arising from both mixed finite-element and cell-centered finite-difference approximations to the flow equations, and it extends readily to three space dimensions. The scheme, which generalizes an earlier technique for isotropic aquifer, admits a fast multigrid solver for hydraulic heads. Numerical experiments illustrate both the effectiveness of the scheme and the importance of accurately treating anisotropy: Small changes in the off-diagonal terms in the conductivity tensor cause relatively large changes in both the predicted heads and the Darcy velocities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00135853
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  • 2
    Electronic Resource
    Electronic Resource
    Network Model of Flow, Transport and Biofilm Effects in Porous Media (1998)
    Springer
    Transport in porous media 30 (1998), S. 1-23 
    Details
    ISSN: 1573-1634
    Keywords: biofilm ; network model ; permeability ; transport ; numerical diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract In this paper, we develop a network model to determine porosity and permeability changes in a porous medium as a result of changes in the amount of biomass. The biomass is in the form of biofilms. Biofilms form when certain types of bacteria reproduce, bond to surfaces, and produce extracellular polymer (EPS) filaments that link together the bacteria. The pore spaces are modeled as a system of interconnected pipes in two and three dimensions. The radii of the pipes are given by a lognormal probability distribution. Volumetric flow rates through each of the pipes, and through the medium, are determined by solving a linear system of equations, with a symmetric and positive definite matrix. Transport through the medium is modeled by upwind, explicit finite difference approximations in the individual pipes. Methods for handling the boundary conditions between pipes and for visualizing the results of numerical simulations are developed. Increases in biomass, as a result of transport and reaction, decrease the pipe radii, which decreases the permeability of the medium. Relationships between biomass accumulation and permeability and porosity reduction are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006560705680
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  • 3
    Electronic Resource
    Electronic Resource
    Macroscale Properties of Porous Media from a Network Model of Biofilm Processes (1998)
    Springer
    Transport in porous media 31 (1998), S. 39-66 
    Details
    ISSN: 1573-1634
    Keywords: network model ; biofilm ; biobarrier ; permeability ; Monod kinetics ; adsorption
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract We demonstrate how a network model can predict porosity and permeability changes in a porous medium as a result of biofilm buildup in the pore spaces. A biofilm consists of bacteria and extracellular polymeric substances (EPS) bonded together and attached to a surface. In this case, the surface consists of the walls of the porous medium, which we model as a random network of pipes. Our model contains five species. Four of these are bacteria and EPS in both fluid and adsorbed phases. The fifth species is nutrient, which we assume to reside in the fluid phase only. Bacteria and EPS transfer between the adsorbed and fluid phases through adsorption and erosion or sloughing. The adsorbed species influence the effective radii of the pipes in the network, which affect the porosity and permeability. We develop a technique for integrating the coupled system of ordinary and partial differential equations that govern transport of these species in the network. We examine ensemble averages of simulations using different arrays of pipe radii having identical statistics. These averages show how different rate parameters in the biofilm transport processes affect the concentration and permeability profiles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006506104835
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  • 4
    Electronic Resource
    Electronic Resource
    Application of conjugate-gradient-like methods to a hyperbolic problem in porous-media flow (1987)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 551-566 
    Details
    ISSN: 0271-2091
    Keywords: Generalized Conjugate Residual Method ; Nested Factorization ; Buckley-Leverett Equation ; Preconditioned Conjugate Gradients ; 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: This paper presents the application of a preconditioned conjugate-gradient-like method to a non-self-adjoint problem of interest in underground flow simulation. The method furnishes a reliable iterative solution scheme for the non-symmetric matrices arising at each iteration of the non-linear time-stepping scheme. The method employs a generalized conjugate residual scheme with nested factorization as a preconditioner. Model runs demonstrate significant computational savings over direct sparse matrix solvers.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650070603
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  • 5
    Electronic Resource
    Electronic Resource
    How upstream collocation works (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1753-1763 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The smoothing effects of upstream collocation in convective problems are attributable to a dissipative error term analogous to that in upstream-weighted finite differences.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620191203
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  • 6
    Electronic Resource
    Electronic Resource
    Domain-decomposition approach to local grid refinement in finite element collocation (1992)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 8 (1992), S. 341-355 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Advection-dominated flows occur widely in the transport of groundwater contaminants, the movements of fluids in enhanced oil recovery projects, and many other contexts. In numerical models of such flows, adaptive local grid refinement is a conceptually attractive approach for resolving the sharp fronts or layers that tend to characterize the solutions. However, this approach can be difficult to implement in practice. A domain decomposition method developed by Bramble, Ewing, Pasciak, and Schatz, known as the BEPS method, overcomes many of the difficulties. We demonstrate the applicability of BEPS ideas to finite element collocation on trial spaces of piecewise Hermite cubics. The resulting scheme allows one to refine selected parts of a spatial grid without destroying algebraic efficiencies associated with the original coarse grid. We apply the method to steady-state problems with boundary and interior layers and a time-dependent advection-diffusion problem.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690080404
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  • 7
    Electronic Resource
    Electronic Resource
    A finite element collocation method for variably saturated flows in porous media (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 229-239 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: One common formulation of Richard's equation for variably saturated flows in porous media treats pressure head as the principal unknown and moisture content as a constitutive variable. Numerical approximations to this “head-based” formulation often exhibit mass-balance errors arising from inaccuracies in the temporal discretization. This article presents a finite-element collocation scheme using a mass-conserving formulation. The article also proposes a computable index of global mass balance.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690010306
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  • 8
    Electronic Resource
    Electronic Resource
    Error analysis of the finite-strip method for parabolic equations (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 667-690 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The finite-strip method (FSM) is a hybrid technique which combines spectral and finite-element methods. Finite-element approximations are made for each mode of a finite Fourier series expansion. The Galerkin formulated method is set apart from other weighted-residual techniques by the selection of two types of basis functions, a piecewise linear interpolating function and a trigonometric function. The efficiency of the FSM is due in part to the orthogonality of the complex exponential basis: The linear system which results from the weak formulation is decoupled into several smaller systems, each of which may be solved independently. An error analysis for the FSM applied to time-dependent, parabolic partial differential equations indicates the numerical solution error is O(h2 + M-r). M represents the Fourier truncation mode number and h represents the finite-element grid mesh. The exponent r ≥ 2 increases with the exact solution smoothness in the respective dimension. This error estimate is verified computationally. Extending the result to the finite-layer method, where a two-dimensional trigonometric basis is used, the numerical solution error is O(h2 + M-r + N-q). The N and q represent the trucation mode number and degree of exact solution smoothness in the additional dimension. © 1993 John Wiley & Sons, Inc.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690090605
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  • 9
    Electronic Resource
    Electronic Resource
    Downstream implicit schemes for advection (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 315-318 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Downstream-weighted implicit difference schemes for pure advection are stable for Courant numbers λ ≥ 1. They are numerically diffusive when λ 〉 1.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690040404
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  • 10
    Electronic Resource
    Electronic Resource
    Difference approximations for wave equations via finite elements. I. Construction and performance (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 127-146 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Many practical applications of wave equations involve media in which there are interfaces, or discontinuities in material properties. The accurate numerical representation of these interfaces is important in mathematical models. One can develop generalizations of standard finite-difference methods that accommodate sharp interfaces by modifying a straightforward finite-element approach. In two space dimensions, these methods yield explicit, 5-point or 9-point difference schemes that accurately capture reflection, transmission, and refraction at interfaces. The approach also extends readily to the simulation of waves in elastic media. A companion article presents an error analysis for the approach. © 1995 John Wiley & Sons, Inc.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690110203
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