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  • 1
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Ground water 36 (1998), S. 0 
    ISSN: 1745-6584
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Energy, Environment Protection, Nuclear Power Engineering , Geosciences
    Notes: One benefit of a coupled geochemistry/transport approach is that interactions between chemical constituents that can change the mobility of species (such as pH) can be treated explicitly, rather than lumping all of the geochemistry into a single term (i.e., the retardation factor). A two-tiered approach to modeling coupled geochemistry/transport is presented here, which allows a comparison of the results of different methods as well as better efficiency in modeling time. The codes ParSSim, a coupled transport code for supercomputers, and PHREEQC, an advective geochemistry code, were used to model Sr mobility under varying pH. The problem was based on liquid low level radioactive waste that was disposed at Oak Ridge National Laboratory (Oak Ridge, Tennessee) in a highly alkaline solution to try to enhance precipitation and sorption. Interactions with carbonate rock and ground water lowered the pH and led to mobilization of radionuclides such as 90Sr. Simulation of contaminant migration in this mixing environment requires a coupled geochemistry and transport model. The interplay between propagation of a pH front (which was retarded) and propagation of the Sr front leads to a fast-moving pulse of Sr as well as a strongly retarded front of Sr. This behavior could not have been predicted by a geochemistry or a transport code alone.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Computational geosciences 4 (2000), S. 337-349 
    ISSN: 1573-1499
    Keywords: discontinuous approximations ; discontinuous coefficients ; porous media ; single phase flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Computer Science
    Notes: Abstract Discontinuous Galerkin numerical simulations of single phase flow problem are described in this paper. The simulations show the advantages of using discontinuous approximation spaces. hp convergence results are obtained for smooth solutions. Unstructured meshes and unsmooth solutions are also considered.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1573-1499
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Computer Science
    Notes: Abstract A new parallel solution technique is developed for the fully implicit three‐dimensional two‐phase flow model. An expandedcell‐centered finite difference scheme which allows for a full permeability tensor is employed for the spatial discretization, and backwardEuler is used for the time discretization. The discrete systems are solved using a novel inexact Newton method that reuses the Krylov information generated by the GMRES linear iterative solver. Fast nonlinear convergence can be achieved by composing inexact Newton steps with quasi‐Newton steps restricted to the underlying Krylov subspace. Furthermore, robustness and efficiency are achieved with a line‐search backtracking globalization strategy for the nonlinear systems and a preconditioner for each coupled linear system to be solved. This inexact Newton method also makes use of forcing terms suggested by Eisenstat and Walker which prevent oversolving of the Jacobian systems. The preconditioner is a new two‐stage method which involves a decoupling strategy plus the separate solutions of both nonwetting‐phase pressure and saturation equations. Numerical results show that these nonlinear and linear solvers are very effective.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1573-1499
    Keywords: discontinuous spaces ; elliptic equations ; error estimates ; constrained spaces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Computer Science
    Notes: Abstract Three Galerkin methods using discontinuous approximation spaces are introduced to solve elliptic problems. The underlying bilinear form for all three methods is the same and is nonsymmetric. In one case, a penalty is added to the form and in another, a constraint on jumps on each face of the triangulation. All three methods are locally conservative and the third one is not restricted. Optimal a priori hp error estimates are derived for all three procedures.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Transport in porous media 6 (1991), S. 667-702 
    ISSN: 1573-1634
    Keywords: Modified method of characteristics ; time-splitting ; in situ biorestoration ; adsorption ; contaminant transport
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract A convergent numerical method for modeling in situ biorestoration of contaminated groundwater is outlined. This method treats systems of transport-biodegradation equations by operator splitting in time. Transport is approximated by a finite element modified method of characteristics. The biodegradation terms are split from the transport terms and treated as a system of ordinary differential equations. Numerical results for vertical cross-sectional flow are presented. The effects of variable hydraulic conductivity and variable linear adsorption are studied.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 119-138 
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Finite differences are combined with the modified method of characteristics to develop an explicit scheme for solving convection-dominated convection-diffusion problems in one spatial dimension. Error analysis shows that the new algorithm is stable under a mild stability criterion. Problems with known analytical solutions are used to test the algorithm and demonstrate its convergence. Numerical solutions are free of numerical dispersion, undershoot and overshoot. The algorithm is easy to implement and requires small computational times for the test problems considered.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 10 (1994), S. 271-294 
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Superconvergent error estimates in l2(H1) and l∞(H1) norms are derived for recovered gradients of finite difference in time/piecewise linear Galerkin approximations in space for linear and quasinonlinear parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the parabolic context, and covers problems in regions with nonsmooth boundaries under certain assumptions on the regularity of the solutions. © 1994 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
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