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.

翻译：[translated abstract in Chinese] 本文针对法向变形给定的演化曲面上的Navier-Stokes方程，提出了一种曲面有限元数值求解方法。该方法基于流体可变形曲面框架下完整曲面Navier-Steson方程的求解途径，并引入了法向分量的惩罚项。数值结果表明，该方法与固定曲面上曲面(Navier-)Stokes方程所提的最优阶精度一致。本方法被应用于运动着装人体的高分辨率三维扫描数据，以实现交互式虚拟类流体服装模拟。