一种具有封闭体积守恒的流体可变形曲面的数值方法
A numerical approach for fluid deformable surfaces with conserved enclosed volume
AI总结：
针对含弯曲力的闭合不可压缩流体可变形曲面的封闭体积守恒问题，提出基于高阶参数化、Taylor-Hood单元等的半隐式曲面有限元法，验证了固液二重性与最优收敛性。
摘要：
我们采用曲面有限元和半隐式时间步进格式来模拟流体可变形曲面。这类曲面由含弯曲力的不可压缩曲面Navier-Stokes方程建模，本文研究闭合曲面并强制实现其封闭体积的守恒。该数值方法基于高阶曲面参数化、用于曲面Navier-Stokes部分的Taylor-Hood单元、对曲面网格重分布几何量的恰当近似，以及用于约束的Lagrange乘子。所研究的计算示例凸显了流体可变形曲面的固液二重性，并验证了收敛性，这些收敛性对不同子问题而言是已知最优的。
英文摘要：
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.
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