We consider surface finite elements and a semi-implicit time stepping scheme to simulate fluid deformable surfaces. Such surfaces are modeled by incompressible surface Navier-Stokes equations with bending forces. Here, we consider closed surfaces and enforce conservation of the enclosed volume. The numerical approach builds on higher order surface parameterizations, a Taylor-Hood element for the surface Navier-Stokes part, appropriate approximations of the geometric quantities of the surface mesh redistribution and a Lagrange multiplier for the constraint. The considered computational examples highlight the solid-fluid duality of fluid deformable surfaces and demonstrate convergence properties that are known to be optimal for different sub-problems.

翻译：本文采用曲面有限元方法和半隐式时间步进格式模拟流体可变形曲面。此类曲面由含弯曲力的不可压缩曲面纳维-斯托克斯方程建模。我们考虑封闭曲面，并强制约束所包围体积的守恒性。该数值方法基于高阶曲面参数化、用于曲面纳维-斯托克斯部分的泰勒-胡德单元、曲面网格重分布几何量的适当近似以及约束条件的拉格朗日乘子。所考虑的计算实例突出了流体可变形曲面的固-液二象性，并展示了已知针对不同子问题具有最优性的收敛性质。