Mesh deformation techniques in fluid-structure interaction: robustness, accumulated distortion and computational efficiency

Abstract: 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.