Analysis of an Euler implicit-mixed finite element scheme for reactive solute transport in porous media

Radu, Florin A.; Pop, Sorin; Attinger, Sabine

doi:10.1002/num.20436

Cited by 31 publications

(34 citation statements)

References 36 publications

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“…Non-Lipschitz, but Hölder continuous rates are considered using conformal finite element method (FEM) schemes in [4,5]. Similarly, for Hölder continuous rates (including equilibrium and nonequilibrium cases), MFEMs are analyzed rigorously in [36,38], whereas [37] provides error estimates for the coupled system describing unsaturated flow and reactive transport. In all these cases, the continuity of the reaction rates allows error estimates to be obtained.…”

mentioning

confidence: 99%

Convergence Analysis of Mixed Numerical Schemes for Reactive Flow in a Porous Medium

Kumar¹,

Pop²,

Radu³

2013

SIAM J. Numer. Anal.

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mentioning

confidence: 99%

Convergence Analysis of Mixed Numerical Schemes for Reactive Flow in a Porous Medium

Kumar¹,

Pop²,

Radu³

2013

SIAM J. Numer. Anal.

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“…The convergence of the scheme was discussed in [6] in a very general framework including also the case of transport with equilibrium (nonlinear) sorption. The existence and uniqueness of a solution of Problem 2.3 is also treated there.…”

Section: Mfem Schemes For the Flow And Transport Problemsmentioning

confidence: 99%

“…Initial c(t = 0) = c I and boundary conditions complete the model. We refer to [5,6] for a more extensive mathematical model including equilibrium/non-equilibrium sorption and saturated/unsaturated flow. For the spatial discretization of the flow problem as well as of the transport we use the MFEM.…”

Section: Introductionmentioning

confidence: 99%

Stochastic simulations based on mixed finite elements for solute transport in groundwater

Radu

Suciu

2009

Proc Appl Math and Mech

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An accurate mixed finite element method to solve both flow and transport is developed for stochastic simulations of transport in saturated aquifers characterized by random log-hydraulic conductivity fields. The main advantage of the mixed finite element is that it is local mass conservative. Unlike in stochastic finite element methods, this approach yields concentration fields and concentration moments for samples of the random field. In this way, it will be possible to analyze the behavior of different ensemble average observables of the transport process as well as the behavior of their fluctuations. Results of the stochastic simulations described here can be used to assess the reliability for real cases of the ensemble average quantities provided by stochastic modeling of transport in groundwater.

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“…Since larger number of modes yield closer approximations for the random velocity fields with exponential correlations, considered in this numerical setup, the occurrence of non-zero mean memory terms can be associated with the lack of smoothness of the samples of such random fields [Yaglom, 1987]. Simulations based on the mixed finite element method for both water flow [Radu et al, 2004] and solute transport [Radu et al, 2008] will be compared in a forthcoming paper with the present simulations, which are based on first-order approximations of the velocity field. A conclusion is yet premature and further work is needed to clarify whether the mean memory terms reflect irregularities of the velocity model or whether they are finite size effects inherent in numerical simulations which always reproduce the nominal values of the velocity statistics with some finite precision.…”

Section: Memory Effects and Ergodicitymentioning

confidence: 99%

Memory effects induced by dependence on initial conditions and ergodicity of transport in heterogeneous media

Suciu

Vamoş

Vereecken

et al. 2008

Water Resources Research

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[1] For transport in statistically homogeneous random velocity fields with properties that are routinely assumed in stochastic groundwater models, the one-particle dispersion (i.e., second central moment of the ensemble average concentration for a point source) is a ''memory-free'' quantity independent of initial conditions. Nonergodic behavior of large initial plumes, as manifest in deviations of actual solute dispersion from one-particle dispersion, is associated with a ''memory term'' consisting of correlations between initial positions and displacements of solute molecules. Reliable numerical experiments show that increasing the source dimensions has two opposite effects: it reduces the uncertainty related to the randomness of center of mass, but, at the same time, it yields large memory terms. The memory effects increase with the source dimension and depend on its shape and orientation. Large narrow sources oriented transverse to the mean flow direction yield ergodic behavior with respect to the one-particle dispersion of the longitudinal dispersion and nonergodic behavior of the transverse dispersion, whereas for large longitudinal sources, the longitudinal dispersion behaves nonergodically, and the transverse dispersion behaves ergodically. Such memory effects are significantly large over hundreds of heterogeneity scales and should therefore be considered in practical applications, for instance, calibration of model parameters, forecasting, and identification of the contaminant source.

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Analysis of an Euler implicit-mixed finite element scheme for reactive solute transport in porous media

Cited by 31 publications

References 36 publications

Convergence Analysis of Mixed Numerical Schemes for Reactive Flow in a Porous Medium

Convergence Analysis of Mixed Numerical Schemes for Reactive Flow in a Porous Medium

Stochastic simulations based on mixed finite elements for solute transport in groundwater

Memory effects induced by dependence on initial conditions and ergodicity of transport in heterogeneous media

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