518
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IGPM518.pdf October 2021 |
TITLE |
On derivations of evolving surface Navier-Stokes equations |
AUTHORS |
Philip Brandner, Arnold Reusken, Paul Schwering |
ABSTRACT |
In recent literature several derivations of incompressible Navier-Stokes type equations
that model the dynamics of an evolving fluidic surface have been presented. These derivations differ
in the physical principles used in the modeling approach and in the coordinate systems in which
the resulting equations are represented. This paper has overview character in the sense that we put
five different derivations of surface Navier-Stokes equations into one framework. This then allows
a systematic comparison of the resulting surface Navier-Stokes equations and shows that some, but
not all, of the resulting models are the same. Furthermore, based on a natural splitting approach in
tangential and normal components of the velocity we show that all five derivations that we consider
yield the same tangential surface Navier-Stokes equations. |
KEYWORDS |
surface PDEs, Navier-Stokes on surfaces |