Jacobian Free Methods for Coupling Transport with Chemistry in Heterogenous Porous Media

Amir, Laila; Kern, Michel

doi:10.3390/w13030370

Cited by 4 publications

(4 citation statements)

References 56 publications

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“…In particular, coding the Jacobian is difficult and error-prone. Therefore, some researchers have opted for generic, including Jacobian-free, solvers [65,254,255]. In particular, the Method of Lines [256], a general method for solving coupled PDEs, has been used with notable success to solve RT problems [257,258].…”

Section: Solution Methods and Toolsmentioning

confidence: 99%

Reactive Transport: A Review of Basic Concepts with Emphasis on Biochemical Processes

et al. 2022

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Reactive transport (RT) couples bio-geo-chemical reactions and transport. RT is important to understand numerous scientific questions and solve some engineering problems. RT is highly multidisciplinary, which hinders the development of a body of knowledge shared by RT modelers and developers. The goal of this paper is to review the basic conceptual issues shared by all RT problems, so as to facilitate advancement along the current frontier: biochemical reactions. To this end, we review the basic equations to indicate that chemical systems are controlled by the set of equilibrium reactions, which are easy to model, but whose rate is controlled by mixing. Since mixing is not properly represented by the standard advection-dispersion equation (ADE), we conclude that this equation is poor for RT. This leads us to review alternative transport formulations, and the methods to solve RT problems using both the ADE and alternative equations. Since equilibrium is easy, difficulties arise for kinetic reactions, which is especially true for biochemistry, where numerous challenges are open (how to represent microbial communities, impact of genomics, effect of biofilms on flow and transport, etc.). We conclude with the basic eleven conceptual issues that we consider fundamental for any conceptually sound RT effort.

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Section: Solution Methods and Toolsmentioning

confidence: 99%

Reactive Transport: A Review of Basic Concepts with Emphasis on Biochemical Processes

et al. 2022

View full text Add to dashboard Cite

show abstract

“…In particular, coding the Jacobian is difficult and error-prone. Therefore, some researchers have opted for generic, including Jacobian-free, solvers [64,253,254]. In particular, the Method Of Lines [255], a general method for solving coupled PDEs, has been used with notable success to solve RT problems [256,257].…”

Section: Solution Methods and Toolsmentioning

confidence: 99%

Reactive Transport: A Review of Basic Concepts with Emphasis on Biochemical Processes

Carrera¹,

Saaltink²,

Soler-Sagarra³

et al. 2021

Preprint

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Reactive transport (RT) couples bio-geo-chemical reactions and transport. RT is important to understand numerous scientific questions and solve some engineering problems. RT is highly multidisciplinary, which hinders the development of a body of knowledge shared by RT modelers and developers. The goal of this paper is to review the basic conceptual issues shared by all RT problems, so as to facilitate advance along the current frontier: biochemical reactions. To this end, we review the basic equations to point that chemical systems are controlled by the set of equilibrium reactions, which are easy to model, but whose rate is controlled by mixing. Since mixing is not properly represented by the standard advection-dispersion equation (ADE), we conclude that this equation is poor for RT. This leads us to review alternative transport formulations, and the methods to solve RT problems using both the ADE and alternative equations. Since equilibrium is easy, difficulties arise for kinetic reactions, which is especially true for biochemistry, where numerous frontiers are open (how to represent microbial communities, impact of genomics, effect of biofilms on flow and transport, etc.). We conclude with the basic 10 issues that we consider fundamental for any conceptually sound RT effort.

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“…Amir and Kern [27] proposed a new method for an efficient solution of the large nonlinear system governing reactive transport in heterogeneous porous media. The system combines partial differential equations describing the transport of chemical species with nonlinear algebraic or differential equations describing the chemical reactions.…”

Section: Improved Numerical Methods For Flow and Mass Transport Simulationmentioning

confidence: 99%

Modeling of Flow and Transport in Saturated and Unsaturated Porous Media

Younès

Fahs

Ackerer

2021

Water

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Modeling fluid flow and transport processes in porous media is a relevant topic for a wide range of applications. In water resources problems, this topic presents specific challenges related to the multiphysical processes, large time and space scales, heterogeneity and anisotropy of natural porous media, and complex mathematical models characterized by coupled nonlinear equations. This Special Issue aims at collecting papers presenting new developments in the field of flow and transport in porous media. The 25 published papers deal with different aspects of physical processes and applications such as unsaturated and saturated flow, flow in fractured porous media, landslide, reactive transport, seawater intrusion, and transport within hyporheic zones. Based on their objectives, we classified these papers into four categories: (i) improved numerical methods for flow and mass transport simulation, (ii) looking for reliable models and parameters, (iii) laboratory scale experiments and simulations, and (iv) modeling and simulations for improved process understanding. Current trends on modeling fluid flow and transport processes in porous media are discussed in the conclusion.

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Jacobian Free Methods for Coupling Transport with Chemistry in Heterogenous Porous Media

Cited by 4 publications

References 56 publications

Reactive Transport: A Review of Basic Concepts with Emphasis on Biochemical Processes

Reactive Transport: A Review of Basic Concepts with Emphasis on Biochemical Processes

Reactive Transport: A Review of Basic Concepts with Emphasis on Biochemical Processes

Modeling of Flow and Transport in Saturated and Unsaturated Porous Media

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