A comparison of Eulerian and Lagrangian transport and non-linear reaction algorithms

Benson, David A.; Aquino, Tomás; Bolster, Diogo; Engdahl, Nicholas B.; Henri, Christopher V.; Fernàndez-García, Daniel

doi:10.1016/j.advwatres.2016.11.003

Cited by 80 publications

(71 citation statements)

References 97 publications

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“…Viewed in this way, the particle reaction codes have the potential to reside in simulations of field-scale phenomena-particularly slow reactions and heterogeneous chemistry-that arise from pore-scale processes. This work is underway [45].…”

Section: Summary and Future Workmentioning

confidence: 98%

Chemical Reactions in Diffusion-Limited Environments at the Pore-Scale

Benson¹

2015

Pore Scale Phenomena

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In many natural systems, the lack of mixing is a primary limiting factor in the rate of chemical reactions. The poor mixing can be imparted by substrate structure, such as heterogeneous pore networks, or selfimposed by reactant segregation. The classical differential equations (DEs) of chemical reaction assume perfect mixing among reactants, and this assumption is transmitted to the most common solution methods. These methods are based on an Eulerian framework, in which space is partitioned into blocks of some size, within which the well-mixed solution is applied. Our recent work aims to rectify the problems associated with the well-mixed assumption in both theoretical and applied settings. First, we examine the effect of sub-grid concentration fluctuations on Eulerian simulations of reaction. Second, we show how a Lagrangian transport and reaction algorithm accounts for the diffusionlimited mixing of reactants. Third, we review the coarse-grained deterministic DEs that include the effects of concentration perturbation growth. This method includes the transport Green function, which can incorporate the specifics of the transport process. Finally, we review the connection between continuum perturbation methods and the numerical (Lagrangian) techniques, providing a map between the new and classical methods to predict chemical reaction rates. Because our methods are derived as scale-independent, virtually any reactive system that suffers from imperfect mixing-whether imposed by underlying structure (i.e., pore networks) or self-imposed by organization of reactants-will benefit from the added realism. 11.

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Section: Summary and Future Workmentioning

confidence: 98%

Chemical Reactions in Diffusion-Limited Environments at the Pore-Scale

Benson¹

2015

Pore Scale Phenomena

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“…Also, because W ij = W ji , we now strictly define W ij to be the normalized weight for the mass transfer from particle j to particle i (the converse is no longer true). Equation (17) may be rewritten in an analogous form to (8), with…”

Section: Analytical Solution For Mass-transfer Weight Functionmentioning

confidence: 99%

A mass-transfer particle-tracking method for simulating transport with discontinuous diffusion coefficients

Schmidt

Engdahl

Pankavich

et al. 2020

Advances in Water Resources

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The problem of a spatially discontinuous diffusion coefficient (D(x)) is one that may be encountered in hydrogeologic systems due to natural geological features or as a consequence of numerical discretization of flow properties. To date, mass-transfer particle-tracking (MTPT) methods, a family of Lagrangian methods in which diffusion is jointly simulated by random walk and diffusive mass transfers, have been unable to solve this problem. This manuscript presents a new mass-transfer (MT) algorithm that enables MTPT methods to accurately solve the problem of discontinuous D(x). To achieve this, we derive a semi-analytical solution to the discontinuous D(x) problem by employing a predictor-corrector approach, and we use this semi-analytical solution as the weighting function in a reformulated MT algorithm. This semi-analytical solution is generalized for cases with multiple 1D interfaces as well as for 2D cases, including a 2 × 2 tiling of 4 subdomains that corresponds to a numericallygenerated diffusion field. The solutions generated by this new mass-transfer algorithm closely agree with an analytical 1D solution or, in more complicated cases, trusted numerical results, demonstrating the success of our proposed approach.

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“…For infinite Péclet numbers (purely hyperbolic equation), the transport can be fully characterised by the streamlines. This is particularly convenient as, within an Eulerian formulation, specific advection schemes and highly refined meshes would be needed to avoid significant numerical artificial diffusion or instabilities [6]. Streamlines are integrated with the streamLine post-processing tool available in OpenFOAM 4, and they are generated seeding a cloud of points that can be located wherever within the domain.…”

Section: Residence Time Distribution and Breakthrough Curvesmentioning

confidence: 99%

Computational analysis of transport in three-dimensional heterogeneous materials

Boccardo

Crevacore

Passalacqua

et al. 2020

Comput. Visual Sci.

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Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated approach to generate, study and upscale transport equations in random and periodic porous structures. The geometry generation is based on random algorithms or ballistic deposition. In particular, a new algorithm is proposed to generate random packings of ellipsoids with random orientation and tunable porosity and connectivity. The porous structure is then meshed using locally refined Cartesian-based or unstructured strategies. Transport equations are thus solved in a finite-volume formulation with quasi-periodic boundary conditions to simplify the upscaling problem by solving simple closure problems consistent with the classical theory of homogenisation for linear advectiondiffusion-reaction operators. Existing simulation codes are extended with novel developments and integrated to produce a fully open-source simulation pipeline. A showcase of a few interesting three-dimensional applications of these computational approaches is then presented. Firstly, convergence properties and the transport and dispersion properties of a periodic arrangement of spheres are studied. Then, heat transfer problems are considered in a pipe with layers of deposited particles of different heights, and in heterogeneous anisotropic materials.

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A comparison of Eulerian and Lagrangian transport and non-linear reaction algorithms

Cited by 80 publications

References 97 publications

Chemical Reactions in Diffusion-Limited Environments at the Pore-Scale

Chemical Reactions in Diffusion-Limited Environments at the Pore-Scale

A mass-transfer particle-tracking method for simulating transport with discontinuous diffusion coefficients

Computational analysis of transport in three-dimensional heterogeneous materials

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