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

Abstract

AbstractWe 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 the 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 of the velocity. Numerical results demonstrate the same optimal order of convergence as proposed for surface (Navier–)Stokes equations on stationary surfaces. The approach is applied to high‐resolution three‐dimensional scans of clothed bodies in motion to provide interactive virtual fluid‐like clothing.