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Subject: Finite Volume Method × WGL Institute: WIAS ×

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    A numerical method for mass conservative coupling between fluid flow and solute transport
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Fuhrmann, Jürgen; Langmach, Hartmut; Linke, Alexander
    We present a new coupled discretization approach for species transport in an incompressible fluid. The Navier-Stokes equations for the flow are discretized by the divergence-free Scott-Vogelius element on barycentrically refined meshes guaranteeing LBB stability. The convection-diffusion equation for species transport is discretized by the Voronoi finite volume method. In accordance to the continuous setting, due to the exact integration of the normal component of the flow through the Voronoi surfaces, the species concentration fulfills discrete global and local maximum principles. Besides of the the numerical scheme itself, we present important aspects of its implementation. Further, for the case of homogeneous Dirichlet boundary conditions, we give a convergence proof for the coupled scheme. We report results of the application of the scheme to the interpretation of limiting current measurements in an electrochemical flow cell with cylindrical shape.
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    Experimental and numerical model study of the limiting current in a channel flow cell with a cirvular electrode
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Fuhrmann, Jürgen; Zhao, H.; Holzbecher, E.; Langmach, H.; Chojak, M.; Halseid, R.; Jusys, Z.; Behm, R.J.
    We describe first measurement in a novel thin-layer channel flow cell designed for the investigation of heterogeneous electrocatalysis on porous catalysts. For the interpretation of the measurements, a macroscopic model for coupled species transport and reaction, which can be solved numerically, is feasible. In this paper, we focus on the limiting current. We compare numerical solutions of a macroscopic model to a generalization of a Leveque-type asymptotic estimate for circular electrodes, and to measurements obtained in the aforementioned flow cell. We establish, that on properly aligned meshes, the numerical method reproduces the asymptotic estimate. Furthermore, we demonstrate, that the measurements are partially performed in the sub-asymptotic regime, in which the boundary layer thickness exceeds the cell height. Using the inlet concentration and the diffusion coefficient from literature, we overestimate the limiting current. On the other hand, the use of fitted parameters leads to perfect agreement between model and experiment.