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New Challenges in Grid Generation and Adaptivity for Scientific Computing pp 231–260Cite as

Anisotropic Mesh and Time Step Adaptivity for Solute Transport Modeling in Porous Media

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Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 5))

Abstract

We assess the impact of space-time mesh adaptivity on the modeling of solute transport in porous media. This approach allows an automatic selection of both the spatial mesh and the time step on the basis of a suitable recovery-based error estimator. In particular, we deal with an anisotropic control of the spatial mesh. The solver coupled with the adaptive module deals with an advection-dispersion equation to model the transport of dissolved species, which are assumed to be convected by a Darcy flow field. The whole solution-adaptation procedure is assessed through two-dimensional numerical tests. A numerical convergence analysis of the spatial mesh adaptivity is first performed by considering a test-case with analytical solution. Then, we validate the space-time adaptive procedure by reproducing a set of experimental observations associated with solute transport in a homogeneous sand pack. The accuracy and the efficiency of the methodology are discussed and numerical results are compared with those associated with fixed uniform space-time discretizations. This assessment shows that the proposed approach is robust and reliable. In particular, it allows us to obtain a significant improvement of the simulation quality of the early solute arrivals times at the outlet of the medium.

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Acknowledgements

We kindly acknowledge Prof. Brian Berkowitz for sharing with us the experimental data. The financial support of MIUR (Project “Innovative methods for water resources under hydro-climatic uncertainty scenarios”, PRIN 2010/2011) is also gratefully acknowledged.

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Authors and Affiliations

  1. Dipartimento di Ingegneria Civile ed Ambientale, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133, Milano, Italy

    Bahman Esfandiar, Giovanni Porta & Alberto Guadagnini

  2. MOX—Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133, Milano, Italy

    Simona Perotto

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  1. Bahman Esfandiar
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  2. Giovanni Porta
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  4. Alberto Guadagnini
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Correspondence to Giovanni Porta .

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  1. MOX Dipartimento di Matematica, Politecnico di Milano, Milano, Milano, Italy

    Simona Perotto

  2. MOX Dipartimento di Matematica, Politecnico di Milano, Milano, Milano, Italy

    Luca Formaggia

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Esfandiar, B., Porta, G., Perotto, S., Guadagnini, A. (2015). Anisotropic Mesh and Time Step Adaptivity for Solute Transport Modeling in Porous Media. In: Perotto, S., Formaggia, L. (eds) New Challenges in Grid Generation and Adaptivity for Scientific Computing. SEMA SIMAI Springer Series, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-06053-8_12

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