A New Simulation Framework for Soil–Root Interaction, Evaporation, Root Growth, and Solute Transport

Koch, Timo; Heck, Katharina; Schröder, Natalie; Class, Holger; Helmig, Rainer

doi:10.2136/vzj2017.12.0210

Cited by 49 publications

(38 citation statements)

References 98 publications

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“…Model coupling is one of the key features in DuMu x [47,9] and has been a driving force in the development of DuMu x 3, which features a new, consistent framework for implementing coupled models, that is, models composed of multiple coupled sub-models. Figure 2 shows different types of model coupling that can be realized in this framework.…”

Section: Multi-domain Simulationsmentioning

confidence: 99%

“…The soil flow is modeled with the Richards equation, and the flow inside the root xylem is modeled using a bundle-of-tubes approach, resulting in a Darcy-type flow model, cf. [9]. The nonlinear PDE system…”

Section: Root-soil Interactionmentioning

confidence: 99%

“…with the average soil pressurep s = 1 2π 2π 0 p s | R dθ, and an analogous definition forx κ w,s [9,78], is solved for water pressure p w and tracer mole fraction x κ w for a period of 3 d with a maximum time step size of 1 h. The symbols and parameter values are given in Table 2. The subscripts r and s denote root and soil quantities wherever they need to be distinguished.…”

Section: Root-soil Interactionmentioning

confidence: 99%

See 2 more Smart Citations

DuMux 3 – an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling

Koch

Gläser

Weishaupt

et al. 2021

Computers & Mathematics with Applications

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113

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We present version 3 of the open-source simulator for flow and transport processes in porous media DuMu x . DuMu x is based on the modular C++ framework Dune (Distributed and Unified Numerics Environment) and is developed as a research code with a focus on modularity and reusability. We describe recent efforts in improving the transparency and efficiency of the development process and community-building, as well as efforts towards quality assurance and reproducible research. In addition to a major redesign of many simulation components in order to facilitate setting up complex simulations in DuMu x , version 3 introduces a more consistent abstraction of finite volume schemes. Finally, the new framework for multi-domain simulations is described, and three numerical examples demonstrate its flexibility.

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Section: Multi-domain Simulationsmentioning

confidence: 99%

Section: Root-soil Interactionmentioning

confidence: 99%

Section: Root-soil Interactionmentioning

confidence: 99%

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DuMux 3 – an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling

Koch

Gläser

Weishaupt

et al. 2021

Computers & Mathematics with Applications

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113

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“…in terms of accuracy or computational cost. The most commonly used type of functional-structural root architecture models represent the structure of the root system as a 1-dimensional branched network of discrete segments which is geometrically embedded in a 3-dimensional soil domain (Koch et al, 2018b). The root architecture may either be known from measurements, such as 2D or 3D images, or from root architectural models.…”

Section: Introductionmentioning

confidence: 99%

Call for participation: Collaborative benchmarking of functional-structural root architecture models. The case of root water uptake

Schnepf

Black

Couvreur

et al. 2019

Preprint

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1 functional-structural root architecture models. 2 The case of root water uptake. Abstract 35Three-dimensional models of root growth, architecture and function are becoming im-36 portant tools that aid the design of agricultural management schemes and the selection of 37 beneficial root traits. However, while benchmarking is common in many disciplines that use 38 numerical models such as natural and engineering sciences, functional-structural root archi-39 tecture models have never been systematically compared. The following reasons might induce 40 disagreement between the simulation results of different models: different representation of 41 root growth, sink term of root water and solute uptake and representation of the rhizosphere. 42Presently, the extent of discrepancies is unknown, and a framework for quantitatively com-43 paring functional-structural root architecture models is required. We propose, in a first step, 44 to define benchmarking scenarios that test individual components of complex models: root 45 architecture, water flow in soil and water flow in roots. While the latter two will focus mainly 46 on comparing numerical aspects, the root architectural models have to be compared at a con-47 ceptual level as they generally differ in process representation. Therefore defining common 48 inputs that allow recreating reference root systems in all models will be a key challenge. In 49 a second step, benchmarking scenarios for the coupled problems are defined. We expect that 50 the results of step 1 will enable us to better interpret differences found in step 2. This bench-51 marking will result in a better understanding of the different models and contribute towards 52 improving them. Improved models will allow us to simulate various scenarios with greater 53 confidence and avoid bugs, numerical errors or conceptual misunderstandings. This work will 54 set a standard for future model development. 55 1 Introduction 56 A growing number of different modelling techniques and software libraries are now available to 57 build functional-structural root architecture models. Different available models of root architec-58 ture and functions have been discussed and qualitatively compared in Dunbabin et al. (2013). 59The available models differ in the way they represent different processes such as root growth, wa-60 ter flow, solute transport are captured and translated into mathematical equations (process-level 61 differences); in how they solve mathematical problems by their choice of analytical or numerical 62 approach, numerical scheme, programming technique (solution-level differences); and in how they 63 couple the different processes to the full model (coupling-level differences). However, the extent of 64 discrepancies is currently unknown. Thus, a framework for quantitatively comparing functional-65 structural root architecture models is required. In addition to the explanatory or predictive power 66 of a model, it is also important to understand the performance of these models, e.g. in terms of 67 ac...

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“…implementation of the mixed-dimension embedded tissue perfusion model is based on a 368 recent extension of DuMu x for multi-domain porous media problems, first described 369 in [58] for the simulation of root-soil interaction in the vadose zone. We refer to this 370 publication for a more detailed description of the discretization, assembly procedure, 371 and software implementation of mixed-dimension embedded models.…”

mentioning

confidence: 99%

A multi-scale sub-voxel perfusion model to estimate diffusive capillary wall conductivity in multiple sclerosis lesions from perfusion MRI data

Koch

Flemisch

Helmig

et al. 2018

Preprint

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We propose a new mathematical model to infer capillary leakage coefficients from dynamic susceptibility contrast MRI data. To this end, we derive an embedded mixed-dimension flow and transport model for brain tissue perfusion on a sub-voxel scale. This model is used to obtain the contrast agent concentration distribution in a single MRI voxel during a perfusion MRI sequence. We further present a magnetic resonance signal model for the considered sequence including a model for local susceptibility effects. This allows modeling MR signal-time curves that can be compared to clinical MRI data. The proposed model can be used as a forward model in the inverse modeling problem of inferring model parameters such as the diffusive capillary wall conductivity. Acute multiple sclerosis lesions are associated with a breach in the integrity of the blood brain barrier. Applying the model to perfusion MR data of a patient with acute multiple sclerosis lesions, we conclude that diffusive capillary wall Common indicators derived from such models are the cerebral blood volume (CBV ), 52 the cerebral blood flow (CBF ), the mean transit time (MTT ), and leakage 53 coefficients [10,12,19]. 54A routinely used state-of-the-art post-processing procedure and model is described 55 in [12]. Such models have to reflect two processes: (1) the perfusion process governed 56 mainly by bio-fluid-mechanical principles, and (2) the physical process of nuclear 57 December 20, 2018 4/45 magnetic resonance (NMR) exploited to acquire the MR image. There have been many 58suggestions for improving the modeling of the latter process [20][21][22][23]. The authors 59 of [24,25] show that the local, sub-voxel tissue structure has a significant effect on the 60 NMR signal. However, all previous studies, including the recent study by [23], rely on 61 state-of-the-art two-compartment models for the perfusion process providing only 62 average concentrations in two tissue compartments within a voxel. 63To overcome the limitations of two-compartment models, we present a perfusion 64 model on a sub-voxel scale, including the capillary network structure. Fully, 65 three-dimensionally resolved fluid-mechanical models of brain tissue perfusion imply 66 prohibitively complex and computationally expensive simulations due to the large 67 number of vessels, their non-trivial geometrical embedding, and the complex geometry 68 of the extra-vascular, extra-cellular space [26]. To reduce complexity, we use a 69 mixed-dimension embedded model description, where blood vessels are represented by a 70 network of cylindrical segments which are embedded into the extra-vascular space, 71represented by a homogenized three-dimensional continuum. The model reduction, 72 which is described in more detail in the following, leads to a coupled system of 73 one-dimensional partial differential equations for flow and transport in the vessels, and 74 three-dimensional partial differential equations for flow and transport in the 75 extra-vascular space. Related models have been used to stud...

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A New Simulation Framework for Soil–Root Interaction, Evaporation, Root Growth, and Solute Transport

Cited by 49 publications

References 98 publications

DuMux 3 – an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling

DuMux 3 – an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling

Call for participation: Collaborative benchmarking of functional-structural root architecture models. The case of root water uptake

A multi-scale sub-voxel perfusion model to estimate diffusive capillary wall conductivity in multiple sclerosis lesions from perfusion MRI data

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