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 is an overview paper 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.
Classification :
37-XX, 35-XX, 76-XX
Mots-clés :
Fluids on surfaces, Navier–Stokes equations on manifolds, differential geometry
Affiliations des auteurs :
Philip Brandner
1
;
Arnold Reusken
1
;
Paul Schwering
1
1
RWTH Aachen University, Germany
Philip Brandner; Arnold Reusken; Paul Schwering. On derivations of evolving surface Navier–Stokes equations. Interfaces and free boundaries, Tome 24 (2022) no. 4, pp. 533-563. doi: 10.4171/ifb/483
@article{10_4171_ifb_483,
author = {Philip Brandner and Arnold Reusken and Paul Schwering},
title = {On derivations of evolving surface {Navier{\textendash}Stokes} equations},
journal = {Interfaces and free boundaries},
pages = {533--563},
year = {2022},
volume = {24},
number = {4},
doi = {10.4171/ifb/483},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/483/}
}
TY - JOUR
AU - Philip Brandner
AU - Arnold Reusken
AU - Paul Schwering
TI - On derivations of evolving surface Navier–Stokes equations
JO - Interfaces and free boundaries
PY - 2022
SP - 533
EP - 563
VL - 24
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/483/
DO - 10.4171/ifb/483
ID - 10_4171_ifb_483
ER -
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%A Arnold Reusken
%A Paul Schwering
%T On derivations of evolving surface Navier–Stokes equations
%J Interfaces and free boundaries
%D 2022
%P 533-563
%V 24
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/483/
%R 10.4171/ifb/483
%F 10_4171_ifb_483
