2017
DOI: 10.1016/j.advwatres.2017.02.018
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Upscaling of dilution and mixing using a trajectory based Spatial Markov random walk model in a periodic flow domain

Abstract: The Spatial Markov Model (SMM) is an upscaled model that has been used successfully to predict effective mean transport across a broad range of hydrologic settings. Here we propose a novel variant of the SMM, applicable to spatially periodic systems. This SMM is built using particle trajectories, rather than travel times. By applying the proposed SMM to a simple benchmark problem we demonstrate that it can predict mean effective transport, when compared to data from fully resolved direct numerical simulations.… Show more

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Cited by 28 publications
(26 citation statements)
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“…Spatial Markov models (SMMs; Bolster & Dentz, 2012;Kang et al, 2014;Sund et al, 2016) are a family of models that represent memory of speed and direction through the use of a transition matrix. While these models have been applied to a broad range of systems (e.g., Bolster et al, 2014;Kang et al, 2014Kang et al, , 2015aKang et al, , 2016Le Borgne et al, 2008b, 2008aSund et al, 2015bSund et al, , 2015aSund et al, , 2017bSund et al, , 2017a, they typically rely on parameterizing a transition matrix, which can be difficult to do, although approaches applicable to real data have emerged recently (Kang et al, 2015a;Sherman et al, 2017). Another approach has involved sampling of particle trajectories (Sund et al, 2017b), which in turn can be used for mixed upscaling and downscaling models.…”
Section: /2018wr023552mentioning
confidence: 99%
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“…Spatial Markov models (SMMs; Bolster & Dentz, 2012;Kang et al, 2014;Sund et al, 2016) are a family of models that represent memory of speed and direction through the use of a transition matrix. While these models have been applied to a broad range of systems (e.g., Bolster et al, 2014;Kang et al, 2014Kang et al, , 2015aKang et al, , 2016Le Borgne et al, 2008b, 2008aSund et al, 2015bSund et al, , 2015aSund et al, , 2017bSund et al, , 2017a, they typically rely on parameterizing a transition matrix, which can be difficult to do, although approaches applicable to real data have emerged recently (Kang et al, 2015a;Sherman et al, 2017). Another approach has involved sampling of particle trajectories (Sund et al, 2017b), which in turn can be used for mixed upscaling and downscaling models.…”
Section: /2018wr023552mentioning
confidence: 99%
“…For this to be representative of heterogeneous systems, each spatial displacement must be larger than the length scales over which velocities or transit times are statistically dependent (e.g., correlated). However, for the independence assumption to hold, the spatial resolution Water Resources Research 10.1029/2018WR023552 of CTRW-based transport simulations is limited (from below) by a spatial scale defined by a correlation length ind (Berkowitz et al, 2006;Bolster & Dentz, 2012;Bolster et al, 2014;Le Borgne et al, 2011;Schumer et al, 2001;Sund et al, 2017b). It is important to note that the representation of transport as a CTRW does not mean at all that correlation is neglected.…”
Section: /2018wr023552mentioning
confidence: 99%
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“…It has been successful in modeling transport across a diverse range of synthetic systems of interest, including flows through highly heterogeneous permeability fields (Le Borgne et al, , ), complex pore‐scale systems (Kang et al, ), inertially dominated systems (Bolster et al, ; Sund et al, ), and fractured media (Kang et al, , , ). Recently, it was also extended to predict reactive transport (Sund et al, ; Sund, Porta, Bolster, & Parashar, ) as well as mixing and dilution effects (Sund, Porta, & Bolster, ).…”
Section: Introductionmentioning
confidence: 99%