A surface finite element method for the Navier-Stokes equations on evolving surfaces

2023/06/15 by Krause, Veit, Kunze, Eric, Voigt, Axel
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2306.08917

Abstract

We introduce a surface finite element method for the numerical solution of Navier-Stokes equations on evolving surfaces with a prescribed deformation of the surface in normal direction. The method is based on approaches for the full surface Navier-Stokes equations in the context of fluid-deformable surfaces and adds a penalization of the normal component. Numerical results demonstrate the same optimal order as proposed for surface (Navier-)Stokes equations on stationary surfaces. The approach is applied to high-resolution 3D scans of clothed bodies in motion to provide interactive virtual fluid-like clothing.

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