Three-field Fluid-Structure Interaction (FSI) formulations for fluid and solid are applied and compared to the standard two field-one field formulation for fluid and solid, respectively. Both formulations are applied in a non linear setting for a Newtonian fluid and a neo-Hookean solid in an updated Lagrangian form, both approximated using finite elements and stabilized by means of the Variational Multiscale (VMS) Method to permit the use of arbitrary interpolations. It is shown that this type of coupling leads to a more stable solution. Even though the new formulation poses the necessity of additional degrees of freedom, it is possible to achieve the same degree of accuracy as standard FSI by means of coarser meshes, thus making the method competitive. We enhance the stability of the formulation by assuming that the sub-grid scales of the model evolve through time. Benchmarking of the formulation is carried out. Numerical results are presented for semi-stationary and a fully transient cases for well known benchmarks for 2D and 3D scenarios.
翻译:两种配方都分别用于牛顿液体的非线性环境,新-Hookean固体以更新的拉格朗江形态,两种配方都大致使用有限的元素,并通过变式多尺度方法加以稳定,允许使用任意的内插,表明这种组合导致更稳定的解决方案。即使新配方需要更多自由度,但有可能通过粗金刚石来达到与标准FSI相同的准确度,从而使方法具有竞争性。我们假设模型的亚电网尺度随着时间演变,从而增强配方的稳定性。对配方进行基准调整。为半静态提出了数字结果,为2D和3D情景的已知基准提供了完全易变的例子。