2005
DOI: 10.1029/2004wr003624
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A new numerical reduction scheme for fully coupled multicomponent transport‐reaction problems in porous media

Abstract: [1] A new systematic approach for the efficient computation of the transport and reaction of a multispecies multireaction system is developed. The objective of this approach is to reduce the number of coupled nonlinear differential equations drastically, while splitting errors are avoided. The reduction mechanism is able to handle both kinetic reactions and heterogeneous equilibrium reactions and mobile and immobile species. It leads to a formulation of the nonlinear system with a Jacobian that has very few no… Show more

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Cited by 61 publications
(57 citation statements)
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“…For instance, first-order degradation reactions of a single species can be included into PTMs by assigning to every particle a variable mass, which develops in time according to first-order kinetics [Kinzelbach, 1987;Wen and Gomez-Hernandez, 1996]. When all species share the same transport operator, certain reactions in chemical equilibrium can be easily simulated with particle tracking by using conservative components [Molins et al, 2004;Kr€ autle and Knabner, 2005;De Simoni et al, 2005;FernandezGarcia et al, 2008;Fernandez-Garcia and Sanchez-Vila, 2011], i.e., a linear combination of the species concentrations that can be used to decouple the system of equations into simpler problems. Fast kinetic reactions have been properly simulated by applying simple proximity relationships between nearby particles [Edery et al, 2009[Edery et al, , 2010.…”
Section: Introductionmentioning
confidence: 99%
“…For instance, first-order degradation reactions of a single species can be included into PTMs by assigning to every particle a variable mass, which develops in time according to first-order kinetics [Kinzelbach, 1987;Wen and Gomez-Hernandez, 1996]. When all species share the same transport operator, certain reactions in chemical equilibrium can be easily simulated with particle tracking by using conservative components [Molins et al, 2004;Kr€ autle and Knabner, 2005;De Simoni et al, 2005;FernandezGarcia et al, 2008;Fernandez-Garcia and Sanchez-Vila, 2011], i.e., a linear combination of the species concentrations that can be used to decouple the system of equations into simpler problems. Fast kinetic reactions have been properly simulated by applying simple proximity relationships between nearby particles [Edery et al, 2009[Edery et al, , 2010.…”
Section: Introductionmentioning
confidence: 99%
“…Since these techniques are already known from [27,28] (but strictly needed for our subsequent analysis), we will keep this section as short as possible. First, we apply the decoupling technique proposed in [27,28] to the PDE-ODE system (3.14)-(3.15). This will lead to a decoupling of some linear PDEs.…”
Section: Transformation Of the Dynamic Systemmentioning
confidence: 99%
“…In Chapter 3 background information is given, the problem is formulated and its mathematical model is given. Afterwards an equivalence transformation is applied to the PDE-ODE-AE-CC system (going back to [27,28,25]). The motivation for this reformulation is a decoupling of some (linear) PDEs, leading to a smaller nonlinear system.…”
Section: Introductionmentioning
confidence: 99%
“…Hoffmann et al [19] mainly study the impact from theory view, while Kräutle and Knabner' work [18] is based on a transient model to study computational efficiency in different time steps of two approaches. In this paper, we focused on the number of meshes and different solvers.…”
Section: Introductionmentioning
confidence: 99%
“…And Huo et al [17] extend its applications to heterogeneous media. Some efficiency tests are done by Kräutle and Knabner [18] and Hoffmann et al [19] to study the resulting improvement. In recent years, the decoupling approach is widely used in both engineering applications and laboratory experiments.…”
Section: Introductionmentioning
confidence: 99%