The paper introduces a geometrically unfitted finite element method for the numerical solution of the tangential Navier--Stokes equations posed on a passively evolving smooth closed surface embedded in $\mathbb{R}^3$. The discrete formulation employs finite difference and finite elements methods to handle evolution in time and variation in space, respectively. A complete numerical analysis of the method is presented, including stability, optimal order convergence, and quantification of the geometric errors. Results of numerical experiments are also provided.
翻译:本文介绍了一种不适宜于几何的有限要素方法,用于在以$\mathbb{R ⁇ 3$嵌入的被动演变的平滑封闭表面上形成的相近导航-斯托克斯方程式的数字解决方案。离散配方采用有限差异和有限要素方法分别处理时间和空间变化的演变。对这种方法进行了完整的数字分析,包括稳定性、最佳顺序趋同和几何误差的量化。还提供了数字实验的结果。