Least-squares fluid-structure-interaction for incompressible flows

在拟议项目的实施过程中，将进一步开发第一个供资期内有前途的流体-结构相互作用方法，为复杂和现实的过程提供可靠和有效的模拟工具。一个重要的第一步，为现实问题的计算是扩展的研究应力-速度（SV）配方的三维。这包括在3D中构造H（div）-一致的高阶向量值插值函数。在下一步中，算法的自适应网格生成的时间依赖性问题的设计。因此，可以通过局部网格细化以及粗化来实现效率的提高。一个具有挑战性的任务将是扩展的流体配方湍流，这仍然是开放的探索领域的最小二乘有限元。这包括实施和验证不同的湍流模型，如Spalart-Allmaras和k-milling模型。该产品组合由非牛顿流体的SV-配方与实验数据的同化相结合，以提高高度非线性问题的准确性和鲁棒性。最后，发达国家的方法将比较其效率，完善的方法的基础上复杂的FSI模拟。

In the course of the proposed project, the promising fluid-structure interaction approaches of the first funding period will be further developed to provide reliable and efficient simulation tools for complex and realistic processes. An essential first step for the calculation of realistic problems is the extension of the investigated stress-velocity (SV) formulations to three dimensions. This includes the construction of H(div)-conforming vector-valued interpolation functions of higher order in 3D. In a next step, algorithms for an adaptive mesh generation for time dependent problems are designed. Thus an efficiency increase can be achieved by local mesh refinement as well as coarsening. A challenging task will be the extension of the fluid formulation to turbulent flows, which is still wide open to exploration in the field of least-squares FEM. This includes the implementation and validation of different turbulence models, such as the Spalart-Allmaras and k-epsilon model. The portfolio is completed by a SV-formulation for non-Newtonian fluids combined with the assimilation of experimental data in order to increase accuracy and robustness of highly nonlinear problems. Finally, the developed approaches will be compared regarding their efficiency to well-established methods based on complex FSI-simulations.