The Experts below are selected from a list of 306 Experts worldwide ranked by ideXlab platform
Thomas Gimmi - One of the best experts on this subject based on the ideXlab platform.
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solving the nernst Planck Equation in heterogeneous porous media with finite volume methods averaging approaches at interfaces
Water Resources Research, 2020Co-Authors: Christophe Tournassat, Thomas Gimmi, Carl I SteefelAbstract:Molecular diffusion of dissolved species is a fundamental mass transport process affecting many environmental and technical processes. Whereas diffusive transport of single tracers can be described by Fick's law, a multicomponent approach based on the Nernst‐Planck Equation is required for charge‐coupled transport of ions. The numerical solution of the Nernst‐Planck Equation requires special attention with regard to properties that are required at interfaces of numerical cells when using a finite difference or finite volume method. Weighted arithmetic and harmonic averages are used in most codes that can solve the Nernst‐Planck Equation. This way of averaging is correct for diffusion coefficients but inappropriate for solute concentrations at interfaces. This averaging approach leads to charge balance problems and thus to numerical instabilities near interfaces separating grid volumes with contrasting properties. We argue that a logarithmic‐differential average should be used. Here this result is generalized, and it is demonstrated that it generally leads to improved numerical stability and accuracy of concentrations computed near material interfaces. It is particularly relevant when modeling semipermeable clay membranes or membranes used in water treatment processes.
Christophe Tournassat - One of the best experts on this subject based on the ideXlab platform.
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solving the nernst Planck Equation in heterogeneous porous media with finite volume methods averaging approaches at interfaces
Water Resources Research, 2020Co-Authors: Christophe Tournassat, Thomas Gimmi, Carl I SteefelAbstract:Molecular diffusion of dissolved species is a fundamental mass transport process affecting many environmental and technical processes. Whereas diffusive transport of single tracers can be described by Fick's law, a multicomponent approach based on the Nernst‐Planck Equation is required for charge‐coupled transport of ions. The numerical solution of the Nernst‐Planck Equation requires special attention with regard to properties that are required at interfaces of numerical cells when using a finite difference or finite volume method. Weighted arithmetic and harmonic averages are used in most codes that can solve the Nernst‐Planck Equation. This way of averaging is correct for diffusion coefficients but inappropriate for solute concentrations at interfaces. This averaging approach leads to charge balance problems and thus to numerical instabilities near interfaces separating grid volumes with contrasting properties. We argue that a logarithmic‐differential average should be used. Here this result is generalized, and it is demonstrated that it generally leads to improved numerical stability and accuracy of concentrations computed near material interfaces. It is particularly relevant when modeling semipermeable clay membranes or membranes used in water treatment processes.
Carl I Steefel - One of the best experts on this subject based on the ideXlab platform.
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solving the nernst Planck Equation in heterogeneous porous media with finite volume methods averaging approaches at interfaces
Water Resources Research, 2020Co-Authors: Christophe Tournassat, Thomas Gimmi, Carl I SteefelAbstract:Molecular diffusion of dissolved species is a fundamental mass transport process affecting many environmental and technical processes. Whereas diffusive transport of single tracers can be described by Fick's law, a multicomponent approach based on the Nernst‐Planck Equation is required for charge‐coupled transport of ions. The numerical solution of the Nernst‐Planck Equation requires special attention with regard to properties that are required at interfaces of numerical cells when using a finite difference or finite volume method. Weighted arithmetic and harmonic averages are used in most codes that can solve the Nernst‐Planck Equation. This way of averaging is correct for diffusion coefficients but inappropriate for solute concentrations at interfaces. This averaging approach leads to charge balance problems and thus to numerical instabilities near interfaces separating grid volumes with contrasting properties. We argue that a logarithmic‐differential average should be used. Here this result is generalized, and it is demonstrated that it generally leads to improved numerical stability and accuracy of concentrations computed near material interfaces. It is particularly relevant when modeling semipermeable clay membranes or membranes used in water treatment processes.
Gimmi Thomas - One of the best experts on this subject based on the ideXlab platform.
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Solving the Nernst‐Planck Equation in Heterogeneous Porous Media with Finite Volume Methods: Averaging Approaches at Interfaces
'American Geophysical Union (AGU)', 2020Co-Authors: Tournassa Christophe, Steefel Carl, Gimmi ThomasAbstract:International audienceMolecular diffusion of dissolved species is a fundamental mass transport process affecting many environmental and technical processes. Whereas diffusive transport of single tracers can be described by Fick's law, a multicomponent approach based on the Nernst‐Planck Equation is required for charge‐coupled transport of ions. The numerical solution of the Nernst‐Planck Equation requires special attention with regard to properties that are required at interfaces of numerical cells when using a finite difference or finite volume method. Weighted arithmetic and harmonic averages are used in most codes that can solve the Nernst‐Planck Equation. This way of averaging is correct for diffusion coefficients, but inappropriate for solute concentrations at interfaces. This averaging approach leads to charge balance problems and thus to numerical instabilities near interfaces separating grid volumes with contrasting properties. We argue that a logarithmic‐differential average should be used. Here this result is generalized, and it is demonstrated that it generally leads to improved numerical stability and accuracy of concentrations computed near material interfaces. It is particularly relevant when modeling semi‐permeable clay membranes or membranes used in water treatment processes
Monmarché Pierre - One of the best experts on this subject based on the ideXlab platform.
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Uniform long-time and propagation of chaos estimates for mean field kinetic particles in non-convex landscapes
2020Co-Authors: Guilli Arnaud, Monmarché PierreAbstract:Combining the results of [14] and [10], the trend to equilibrium in large time is studied for a large particle system associated to a Vlasov-Fokker-Planck Equation. Under some conditions (that allow non-convex confining potentials) the convergence rate is proven to be independent from the number of particles. From this are derived uniform in time propagation of chaos estimates and an exponentially fast convergence for the nonlinear Equation itself
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Uniform long-time and propagation of chaos estimates for mean field kinetic particles in non-convex landscapes
HAL CCSD, 2020Co-Authors: Guilli Arnaud, Monmarché PierreAbstract:Combining the results of [14] and [10], the trend to equilibrium in large time is studied for a large particle system associated to a Vlasov-Fokker-Planck Equation. Under some conditions (that allow non-convex confining potentials) the convergence rate is proven to be independent from the number of particles. From this are derived uniform in time propagation of chaos estimates and an exponentially fast convergence for the semi-linear Equation itself
