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Vorticity‐stream function approaches are inappropriate to solve the surface Navier‐Stokes equation on a torus
Author(s) -
Nitschke Ingo,
Reuther Sebastian,
Voigt Axel
Publication year - 2021
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.202000006
Subject(s) - stream function , torus , vorticity , surface (topology) , scalar (mathematics) , vorticity equation , mathematics , partial differential equation , compressibility , function (biology) , navier–stokes equations , mathematical analysis , physics , vortex , mechanics , geometry , evolutionary biology , biology
The growing interest in interfacial flows in engineering and biological applications demands to numerically solve the incompressible surface (Navier)‐Stokes equation. A common approach, based on a vorticity‐stream function formulation reformulates the equation into a system of scalar‐valued surface partial differential equations, for which various numerical methods have been developed. However, on surfaces, which are not simply connected, this approach is not appropriate. We here explain the underlying situation and provide details and examples.