Accuracy of numerical simulations of contaminant transport in heterogeneous aquifers: A comparative study

Radu, Florin A.; Suciu, Nicolae; Hoffmȧnn, J.; Vogel, Andreas; Kolditz, Olaf; Park, C.-H.; Attinger, Sabine

doi:10.1016/j.advwatres.2010.09.012

Cited by 54 publications

(64 citation statements)

References 34 publications

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“…Therefore, instead of using finite difference/element schemes, solution methods for PDF equations are based on equivalent representations as systems of computational particles. Particle methods also avoid the increase of computational errors by numerical diffusion [16], unavoidable in classical schemes for PDF equations, which usually result in strongly advectiondominated problems. For either Pope's particles approach or particle tracking solutions to the system of Itô equations (3)-(4), the computational cost increases linearly with the number of particles.…”

Section: Grw Solutions To Pdf Equationsmentioning

confidence: 99%

A Fokker–Planck approach for probability distributions of species concentrations transported in heterogeneous media

Suciu

Radu

Attinger

et al. 2015

Journal of Computational and Applied Mathematics

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a b s t r a c tWe identify sufficient conditions under which evolution equations for probability density functions (PDF) of random concentrations are equivalent to Fokker-Planck equations. The novelty of our approach is that it allows consistent PDF approximations by densities of computational particles governed by Itô processes in concentration-position spaces. Accurate numerical solutions are obtained with a global random walk (GRW) algorithm, stable, free of numerical diffusion, and insensitive to the increase of the total number of computational particles. The system of Itô equations is specified by drift and diffusion coefficients describing the PDF transport in the physical space, provided by up-scaling procedures, as well as by drift and mixing coefficients describing the PDF transport in concentration spaces. Mixing models can be obtained similarly to classical PDF approaches or, alternatively, from measured or simulated concentration time series. We compare their performance for a GRW-PDF numerical solution to a problem of contaminant transport in heterogeneous groundwater systems.

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Section: Grw Solutions To Pdf Equationsmentioning

confidence: 99%

A Fokker–Planck approach for probability distributions of species concentrations transported in heterogeneous media

Suciu

Radu

Attinger

et al. 2015

Journal of Computational and Applied Mathematics

Self Cite

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“…[7], [17]) or hybridization (see e.g. [4] for the diffusion equation and [18] for convectiondiffusion problems). Incidentally the method proposed in [18] can be applied also to BDM elements to obtain optimal estimates [5] improving in this way the classical BDM method for convection-diffusion equations [9] or for stabilization purposes [18,6] like in several previous work on the subject.…”

Section: Discussionmentioning

confidence: 99%

Hermite analogs of the lowest order Raviart–Thomas mixed method for convection–diffusion equations

Ruas

Radu

2017

Comp. Appl. Math.

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The Raviart-Thomas mixed finite element method of the lowest order [19] commonly known as the RT 0 method, is a well-established and popular numerical tool to solve diffusion-like problems providing flux continuity across inter-element boundaries. Douglas & Roberts extended the method to the case of more general second order boundary value problems including the convection-diffusion equations (cf. this journal [10]). The main drawback of these methods however is the poor representation of the primal variable by piecewise constant functions. The Hermite analog of the RT 0 method for treating pure diffusion phenomena proposed in [21] proved to be a valid alternative to attain higher order approximation of the primal variable, while keeping intact the matrix structure and the quality of the discrete flux variable of the original RT 0 method. Non trivial extensions of this method are studied here, that can be viewed as Hermite analogs of the two Douglas & Roberts' versions of the RT 0 method, to solve convection-diffusion equations. A detailed convergence study is carried out for one of the Hermite methods, and numerical results illustrate the performance of both of them, as compared to each other and to the corresponding mixed methods.

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“…; Radu et al . ). Typical hydrogeological characterization methods have significant limitations in this regard, as there exists a wide gap in terms of spatial coverage and resolution between local borehole‐based studies and larger‐scale aquifer tests (e.g.…”

Section: Introductionmentioning

confidence: 97%

Estimation of the 3D correlation structure of an alluvial aquifer from surface‐based multi‐frequency ground‐penetrating radar reflection data

Irving

Lindsay

et al. 2019

Geophysical Prospecting

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Knowledge about the stochastic nature of heterogeneity in subsurface hydraulic properties is critical for aquifer characterization and the corresponding prediction of groundwater flow and contaminant transport. Whereas the vertical correlation structure of the heterogeneity is often well constrained by borehole information, the lateral correlation structure is generally unknown because the spacing between boreholes is too large to allow for its meaningful inference. There is, however, evidence to suggest that information on the lateral correlation structure may be extracted from the correlation statistics of the subsurface reflectivity structure imaged by surface‐based ground‐penetrating radar measurements. To date, case studies involving this approach have been limited to 2D profiles acquired at a single antenna centre frequency in areas with limited complementary information. As a result, the practical reliability of this methodology has been difficult to assess. Here, we extend previous work to 3D and consider reflection ground‐penetrating radar data acquired using two antenna centre frequencies at the extensively explored and well‐constrained Boise Hydrogeophysical Research Site. We find that the results obtained using the two ground‐penetrating radar frequencies are consistent with each other, as well as with information from a number of other studies at the Boise Hydrogeophysical Research Site. In addition, contrary to previous 2D work, our results indicate that the surface‐based reflection ground‐penetrating radar data are not only sensitive to the aspect ratio of the underlying heterogeneity, but also, albeit to a lesser extent, to the so‐called Hurst number, which is a key parameter characterizing the local variability of the fine‐scale structure.

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Accuracy of numerical simulations of contaminant transport in heterogeneous aquifers: A comparative study

Cited by 54 publications

References 34 publications

A Fokker–Planck approach for probability distributions of species concentrations transported in heterogeneous media

A Fokker–Planck approach for probability distributions of species concentrations transported in heterogeneous media

Hermite analogs of the lowest order Raviart–Thomas mixed method for convection–diffusion equations

Estimation of the 3D correlation structure of an alluvial aquifer from surface‐based multi‐frequency ground‐penetrating radar reflection data

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