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Universität Augsburg
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Universität Augsburg
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Herr Dr. Markus Gahn
Universität Heidelberg
spricht am
Dienstag, 13. Mai 2025
um
16:00 Uhr
im
Raum 1309 (I2)
über das Thema:
| Abstract: |
| In this talk we rigorously derive a macroscopic model with effective interface conditions for a coupled model for fluid flow and solute transport in bulk regions separated by a thin porous layer. The layer is periodic in the tangential direction with periodicity of order $\varepsilon$ and also the thickness of the layer is of order $\varepsilon$. For $\varepsilon \to 0$ the layer reduces to a lower dimensional interface $\Sigma$, and the aim is the derivation of suitable interface conditions across $\Sigma$ in this limit. Hence, we have to deal with simultaneous homogenization and dimension reduction in the layer, additionally coupled to the processes in the bulk domains. To pass to the limit $\varepsilon \to 0$ in the thin layer we use in particular the concept of two-scale convergence in thin heterogeneous layers. The evolution of the solute concentrations is described by a reaction-diffusion-advection equation in the fluid domain, and a reaction-diffusion equation in the solid part of the membrane including different choices of scaling with respect to the parameter $\varepsilon$, allowing for example low and high diffusion. At the fluid-solid interface nonlinear reactions take place and therefore we need strong two-scale compactness for the concentration in the microscopic solutions. The fluid flow is modeled by an incompressible instationary Stokes system, where we consider a specific scaling within the layer, leading to effective mass transport in the limit through the interface. In the tangential direction we obtain a Navier-slip type boundary condition at the interface $\Sigma$ in the limit. Finally, we consider the case of an elastic membrane and analyze the influence of the fluid structure interaction on the effective interface conditions for the fluid flow. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Jan-Frederik Pietschmann |