Simulation of density-driven flow in fractured porous media

Grillo, Alfio; Logashenko, D.; Stichel, S.; Wittum, Gabriel

doi:10.1016/j.advwatres.2010.08.004

Cited by 36 publications

(26 citation statements)

References 33 publications

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“…Similar approaches which rely upon nodal renumbering, as proposed in this study, have been used in other application such as e.g. [32] and [33]. While the proposed method bears similarities with other approaches, the way it is applied in this study is novel and unique due to the specific requirements imposed by the bidomain models where two spaces interpenetrate and isolation has to be enforced only in one of them.…”

Section: Discussionmentioning

confidence: 99%

An Efficient Finite Element Approach for Modeling Fibrotic Clefts in the Heart

Costa

Campos

Prassl

et al. 2014

IEEE Trans. Biomed. Eng.

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Advanced medical imaging technologies provide a wealth of information on cardiac anatomy and structure at a paracellular resolution, allowing to identify micro-structural discontinuities which disrupt the intracellular matrix. Current state-of-the-art computer models built upon such datasets account for increasingly finer anatomical details, however, structural discontinuities at the paracellular level are typically discarded in the model generation process, owing to the significant costs which incur when using high resolutions for explicit representation. In this study, a novel discontinuous finite element (dFE) approach for discretizing the bidomain equations is presented, which accounts for fine-scale structures in a computer model without the need to increase spatial resolution. In the dFE method this is achieved by imposing infinitely thin lines of electrical insulation along edges of finite elements which approximate the geometry of discontinuities in the intracellular matrix. Simulation results demonstrate that the dFE approach accounts for effects induced by microscopic size scale discontinuities, such as the formation of microscopic virtual electrodes, with vast computational savings as compared to high resolution continuous finite element models. Moreover, the method can be implemented in any standard continuous finite element code with minor effort.

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Section: Discussionmentioning

confidence: 99%

An Efficient Finite Element Approach for Modeling Fibrotic Clefts in the Heart

Costa

Campos

Prassl

et al. 2014

IEEE Trans. Biomed. Eng.

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“…We thus obtain the first part of the theorem. 15 In order to show the second part, let us use in (4.1) with η = id the test function Another approximation argument (using again the result from [23]) and the chain rule show that the modulus of the right hand side is dominated by c 6 |t − s| + c 7 t s TV g(τ ) u(τ ) dτ ψ L ∞ (M) .…”

Section: Total Variation Estimatesmentioning

confidence: 99%

Scalar conservation laws on constant and time-dependent Riemannian manifolds

Lengeler

Müller

2013

Journal of Differential Equations

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In this paper we establish well-posedness for scalar conservation laws on closed manifolds M endowed with a constant or a timedependent Riemannian metric for initial values in L ∞ (M). In particular we show the existence and uniqueness of entropy solutions as well as the L 1 contraction property and a comparison principle for these solutions. Throughout the paper the flux function is allowed to depend on time and to have non-vanishing divergence. Furthermore, we derive estimates of the total variation of the solution for initial values in BV(M), and we give, in the case of a time-independent metric, a simple geometric characterisation of flux functions that give rise to total variation diminishing estimates.

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“…Iterative processes can require long CPU times, making simulations of variable-density flow possibly unsuccessful. This is especially true for variable-density flow and transport problems in fractured-porous rock, where complicated fracture network geometries further reduce the numerical efficiency of simulations [16].…”

Section: Introductionmentioning

confidence: 99%

“…Contrasting hydraulic properties of fractured and porous media determine the rate and direction of groundwater movement [1]. Flow velocity within fracture networks is several orders of magnitude higher than that in unfractured rock, such that fractures increase the mass flux of groundwater and of dissolved contaminants [16]. Depending on the geometry of the fracture network and the individual orientation of the fractures, highly erratic heterogeneity can be introduced by the fractures into the medium [25].…”

Section: Introductionmentioning

confidence: 99%