Least-squares fluid-structure-interaction for incompressible flows

在拟议的项目过程中，将进一步开发第一个资助期有希望的流固耦合方法，为复杂和现实的过程提供可靠和有效的模拟工具。计算实际问题的重要第一步是将所研究的应力-速度(SV)公式推广到三维。这包括构造三维高阶H(Div)-协调向量值插值函数。在下一步中，设计了时间相关问题的自适应网格生成算法。因此，可以通过局部网格细化和粗化来实现效率的提高。一个具有挑战性的任务将是将流体公式扩展到湍流，这在最小二乘有限元领域仍然是一个开放的探索领域。这包括实施和验证不同的湍流模型，如Spalart-Allmaras和k-epsilon模型。为了提高高度非线性问题的精确度和稳健性，该组合由非牛顿流体的SV公式和实验数据的同化相结合而完成。最后，将所开发的方法与基于复杂FSI仿真的成熟方法的效率进行了比较。

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.