Nemadjieu, Simplice Firmin: Finite Volume Methods for Advection Diffusion on Moving Interfaces and Application on Surfactant Driven Thin Film Flow. - Bonn, 2013. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-30919
@phdthesis{handle:20.500.11811/5604,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-30919,
title = {Finite Volume Methods for Advection Diffusion on Moving Interfaces and Application on Surfactant Driven Thin Film Flow},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2013,
month = jan,

note = {The thesis is divided into two parts. First, we present two finite volumes schemes for the discretization of convection-diffusion-reaction problems on moving surfaces. The first scheme extends the two point flux approximation finite volumes on moving surfaces. The second scheme presents a finite volume scheme of type O-method. Here, we construct around the mesh vertices a linear approximation of the solution to the given problem using the unknowns located at cells' centers. A suitable flux continuity on cells interfaces in incorporated. The method allows also the construction a second order upwind for convection operators; which makes the overall scheme second order in space. Next, we model the flow of a surfactant driven thin-film. Here, the use of tensor theory combined with lubrication approximation helps to reduce the Navier-Stokes equations describing the flow of the thin-film in three dimensions to a fourth order equation stated on the moving curved surface whose unknown is the film height. The surfactant, assumed to be insoluble, is modeled by a convection-diffusion equation on the fluid-air interface. We simulate the coupled system using an interface tracking method derived from the above defined finite volumes schemes. Several examples are computed to present the effectiveness and the accuracy of the methods.},
url = {https://hdl.handle.net/20.500.11811/5604}
}

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