An important ingredient of any moving-mesh method for fluid-structure interaction (FSI) problems is the mesh deformation technique (MDT) used to adapt the computational mesh in the moving fluid domain. An ideal technique is computationally inexpensive, can handle large mesh deformations without inverting mesh elements and can sustain an FSI simulation for extensive periods ot time without irreversibly distorting the mesh. Here we compare several commonly used techniques based on the solution of elliptic partial differential equations, including harmonic extension, bi-harmonic extension and techniques based on the equations of linear elasticity. Moreover, we propose a novel technique which utilizes ideas from continuation methods to efficiently solve the equations of nonlinear elasticity and proves to be robust even when the mesh is subject to extreme deformations. In addition to that, we study how each technique performs when combined with the Jacobian-based local stiffening. We evaluate each technique on a popular two-dimensional FSI benchmark reproduced by using an isogeometric partitioned solver with strong coupling.

中文翻译：

---

流固耦合中的网格变形技术：鲁棒性、累积变形和计算效率

任何用于流固耦合 (FSI) 问题的移动网格方法的一个重要组成部分是用于在移动流体域中调整计算网格的网格变形技术 (MDT)。理想的技术计算成本低，可以在不反转网格元素的情况下处理大的网格变形，并且可以在很长一段时间内维持 FSI 模拟而不会不可逆地扭曲网格。这里我们比较了几种常用的基于椭圆偏微分方程求解的技术，包括调和扩展、双调和扩展和基于线弹性方程的技术。而且，我们提出了一种新技术，它利用延续方法的思想来有效地求解非线性弹性方程，并且即使在网格受到极端变形的情况下也证明是稳健的。除此之外，我们研究了每种技术在与基于雅可比的局部硬化相结合时的表现。我们在流行的二维 FSI 基准测试中评估每种技术，该基准通过使用具有强耦合的等几何分区求解器再现。