Symposyium du Département de Chimie Analytique, Minérale et Appliquée Davide Alemani – University of Geneva Lattice Boltzmann (LB) and time splitting method for reaction-diffusion modelling 1.Reaction-diffusion in the environment. 2.The LB approach: why and how 3.The time splitting method: why and how 4.Some numerical results 5.Work in progress: grid refinement

The environmental problem

Schematic representation of various chemical species of a given element (M)

Schematic representation of the physicochemical problem under investigation Metal concentration: mol/m mol/m 3 Diffusion coefficient: m 2 /s m 2 /s Kinetic rate constants: s s -1

M L ML LB approach: Why and how Macroscopic Model Mesoscopic Model (LB)

The LBGK model (1D) LBGK Evolution Equations Flux Computation Schematic Representation (1D)

Time splitting method: Why and How Important when physical and chemical processes occur simultaneously and rate constants vary over many order of magnitudes Enables to split a complex problem into two or more sub-problems more simply handled NS RD

M L ML A detailed example of Time Splitting (RD) coupled with LBGK approach

Flux at the electrode for a semilabile complex Labile flux: Inert flux: Numerical flux:

Comparison between RD and NS with an exact solution Red circle values are taken from: De Jong et al., JEC 1987, 234, 1

Flux at the electrode for two complexes ML (1) and ML (2) with very different time scale reaction rates Labile flux: Inert flux: Numerical flux: M+L (1)  ML (1) labile – M+L (2)  ML (2) inert

Concentration profiles close to the electrode Strong variation close to the electrode surface M+L (1)  ML (1) labile – M+L (2)  ML (2) inert

Error vs grid size and the equilibrium constant

Work in progress M + L (n)  ML (n) Problem to solve A grid refinement approach for solving LBGK scheme

Conservation of mass and flux at the grid interface Work in progress A grid refinement approach for solving LBGK scheme

That’s all. Thanks to come Hoping to have been clear Have a nice day