论文标题
切向Navier-Stokes方程不断发展的表面：分析和仿真
Tangential Navier-Stokes equations on evolving surfaces: Analysis and simulations
论文作者
论文摘要
本文考虑了一个方程系统，该系统在嵌入$ \ mathbb {r}^3 $中的被动发展的表面上建模了Boussinesq-Scriven流体的横向流动。对于所得的Navier-Stokes类型系统，位于平滑的闭合时间依赖性表面上，我们在由表面演化定义的时空歧管上以功能空间的形式引入了弱公式。在任何有限的最后时间，弱的公式表现出良好的范围，并且在数据上没有较小的条件。我们进一步扩展了一种未限定的元素方法，即TraceFem，以计算流体系统的解决方案。该方法的收敛性在数值上被证明。在另一系列实验中，我们可视化材料表面平滑变形引起的侧向流。
The paper considers a system of equations that models a lateral flow of a Boussinesq--Scriven fluid on a passively evolving surface embedded in $\mathbb{R}^3$. For the resulting Navier-Stokes type system, posed on a smooth closed time-dependent surface, we introduce a weak formulation in terms of functional spaces on a space-time manifold defined by the surface evolution. The weak formulation is shown to be well-posed for any finite final time and without smallness conditions on data. We further extend an unfitted finite element method, known as TraceFEM, to compute solutions to the fluid system. Convergence of the method is demonstrated numerically. In another series of experiments we visualize lateral flows induced by smooth deformations of a material surface.
