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Schwarze, Holger; Jaekel, Uwe; Vereecken, Harry

doi:10.1023/a:1010771123844

Cited by 53 publications

(13 citation statements)

References 21 publications

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“…Ensemble averages are estimated over 256 realizations of the ln K field. These parameters provide fairly good approximations of the random Darcy velocity field and of the stochastic advection-dispersion process [32,9]. Since the porosity does not play a major role in saturated flows it is set to θ = 1.…”

Section: Influence Of the Heterogeneity On The Biodegradation Processmentioning

confidence: 99%

Global random walk solvers for reactive transport and biodegradation processes in heterogeneous porous media

Suciu,

Radu

2021

Preprint

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Flow and multicomponent reactive transport in saturated/unsaturated porous media are modeled by ensembles of computational particles moving on regular lattices according to specific random walk rules. The occupation number of the lattice sites is updated with a global random walk (GRW) procedure which simulates the evolution of the ensemble with computational costs comparable to those for a single random walk simulation in sequential procedures. To cope with the nonlinearity and the degeneracy of the Richards equation the GRW flow solver uses linearization techniques similar to the L-scheme developed in finite element/volume approaches. Numerical schemes for reactive transport, coupled with the flow solver via numerical solutions for saturation and water flux, are implemented in splitting procedures. Diffusion-advection steps are solved by GRW algorithms using either biased or unbiased random walk probabilities. Since the number of particles in GRW simulations can be as large as the number of molecules involved in chemical reactions, one avoids the cumbersome problem of rescaling particle densities to approximate concentrations. Reaction steps are therefore formulated in terms of concentrations, as in deterministic approaches. The numerical convergence of the new schemes is demonstrated by comparisons with manufactured analytical solutions. Coupled flow and reactive transport problems of contaminant biodegradation described by the Monod model are further solved and the influence of flow nonlinearity/degeneracy and of the spatial heterogeneity of the medium is investigated numerically.

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Section: Influence Of the Heterogeneity On The Biodegradation Processmentioning

confidence: 99%

Global random walk solvers for reactive transport and biodegradation processes in heterogeneous porous media

Suciu,

Radu

2021

Preprint

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“…The flow velocity is approximated by the Kraichnan procedure described in [39, Appendix C.3.2.2] as sum of 100 cosine random modes, with amplitudes, wavenumbers and phases determined by the parameters of the random log-hydraulic conductivity field ln K. The latter is a statistically homogeneous random function with isotropic Gaussian correlation with correlation length λ = 0.01 and variance σ 2 = 0.1. The Kraichnan procedure is equivalent to a linearization of the flow equation for saturated aquifers and provides accurate approximations of the solution for small variances σ 2 of the statistically homogeneous ln K field [32]. The chosen number of cosine random modes also ensures accurate simulations of passive transport with random velocity over traveled distances of the same order, i.e.…”

Section: Monod Reactions In Heterogeneous Aquifersmentioning

confidence: 99%

Space-time upscaling of reactive transport in porous media

Suciu¹,

Radu²

2021

Preprint

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Reactive transport in saturated/unsaturated porous media is numerically upscaled to the spacetime scale of a hypothetical measurement through coarse grained space-time (CGST) averages. The one-dimensional reactive transport is modeled at the fine-grained Darcy scale by the actual number of molecules involved in reactions which undergo advective and diffusive movements described by global random walk (GRW) simulations. The CGST averages verify identities similar to a local scale balance equation which allow us to derive expressions for the flow velocity and the intrinsic diffusion coefficient in terms of averaged microscopic quantities. The latter are further used to verify the CGST-GRW numerical approach. The upscaling approach is applied to biodegradation processes in saturated aquifers and variably saturated soils and the CGST averages are compared to classical volume averages. One finds that if the process is characterized by slow variations in time, as in homogeneous systems or in case of observations of reactive transport in heterogeneous aquifers made at large times or far away from the contaminant source, the differences between the two averages are negligible. Instead, the differences are significant if the averages are computed close to the source at early times, in case of aquifer simulations, and can be extremely large in simulations of biodegradation in soils. In the latter case, the volume average is totally inappropriate as model for experimental measurements, leading for instance to overestimations by 100% of the CGST average.

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“…3.3.2.1]. Further, the jumps' amplitude d is chosen such that the jump probabilities verify the constraint r x + r z ≤ 1, imposed by the first relation (29).…”

Section: Unbiased Grw Algorithm For Transport Problemsmentioning

confidence: 99%

Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media (extended version)

Suciu,

Illiano,

Prechtel

et al. 2020

Preprint

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In this article, we present new random walk methods to solve flow and transport problems in unsaturated/saturated porous media, including coupled flow and transport processes in soils, heterogeneous systems modeled through random hydraulic conductivity and recharge fields, processes at the field and regional scales. The numerical schemes are based on global random walk algorithms (GRW) which approximate the solution by moving large numbers of computational particles on regular lattices according to specific random walk rules. To cope with the nonlinearity and the degeneracy of the Richards equation and of the coupled system, we implemented the GRW algorithms by employing linearization techniques similar to the L-scheme developed in finite element/volume approaches. The resulting GRW L-schemes converge with the number of iterations and provide numerical solutions that are first-order accurate in time and second-order in space. A remarkable property of the flow and transport GRW solutions is that they are practically free of numerical diffusion. The GRW solutions are validated by comparisons with mixed finite element and finite volume solutions in one-and two-dimensional benchmark problems. They include Richards' equation fully coupled with the advection-diffusion-reaction equation and capture the transition from unsaturated to saturated flow regimes. For completeness, we also consider decoupled flow and transport model problems for saturated aquifers.

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Cited by 53 publications

References 21 publications

Global random walk solvers for reactive transport and biodegradation processes in heterogeneous porous media

Global random walk solvers for reactive transport and biodegradation processes in heterogeneous porous media

Space-time upscaling of reactive transport in porous media

Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media (extended version)

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