Geometrically exact methods for fluid-structure interaction

在拟议的项目中开发的方法将允许通过实际分区方法解决一类流体-结构-相互作用问题，到目前为止，只能用整体方法解决。这可以通过保证流体侧和结构侧使用相同的边界描述来实现。为此，基于非均匀有理B样条（NURBS）的方法被用于流体和结构侧，并在界面处耦合。除此之外，流体和结构的解算器的分离仍然是可能的。使用分区方法可以将现有的和专门的单字段求解器集成到一个整体解决方案系统中。不幸的是，不同的表面离散化在这样的求解器中提出了挑战。将物理变量从一侧投影到另一侧的必要方法与更精细的整体方法相比降低了分区方法的稳定性。到目前为止，这个问题还没有得到令人满意的解决。通过应用基于NURBS的方法，可以保证两侧湿表面的精确几何形状，并且可以减少或消除传递误差。所提出的概念的灵感来自于等几何分析（伊加），这是近年来越来越流行的结构分析。直接在设计过程中使用的几何公式上执行数值载荷分析是该方法的主要优点，并且该方法用于结构方面的建议项目。由于伊加仅针对相对简单的几何形状实现了合适的体积离散，因此其在流体力学中的应用受到限制。然而，扩展传统的方法与基于NURBS的边界制定可以保留该方法的许多优点。NURBS增强有限元方法（NEFEM）遵循了这一概念，该方法将用于流体侧的拟议项目中。该项目涉及制定基本的转让方法。一个中间步骤是现有方法的扩展，同时在流体或结构方面使用常规方法。所开发的方法的优点将在学术问题和实际应用中得到证明。鲁棒性和准确性的进步，预计将纳入创新的单场解算器和减少错误的转移方法在接口。除了方法开发，还计划举办一个研讨会，以支持关于流体-结构相互作用领域最新技术的科学交流。在这次研讨会上，国际专家将介绍和讨论开创性的方法;研讨会还将为年轻学者提供一个平台。

The methods developed in the proposed project will allow the solution of a class of fluid-structure-interaction problems via practical partitioned methods, which could up to now be solved only with monolithic methods. This can be achieved by guaranteeing that both the fluid and structure sides use an identical boundary description. For this purpose, methods based on Non-Uniform Rational B-Splines (NURBS) are used on both fluid and structural sides and coupled at the interface. Beyond that aspect, the separation of solvers for the fluid and the structure remains possible. Using partitioned approaches allows the integration of existing and specialized single-field solvers into an overall solution system. Unfortunately, different surface discretization in presents a challenge in such solvers. The necessary methods to project physical variables from one side to the other reduce the stability of partitioned approaches compared to more elaborate monolithic approaches. So far this problem has not been addressed satisfactorily. By applying approaches based on NURBS, an exact geometry of the wetted surface on both sides can be guaranteed and the transfer errors can be reduced or eliminated. The proposed concept is inspired by the isogeometric analysis (IGA), which has been gaining popularity in the structural analysis in recent years. Performing the numerical load analysis directly on the geometric formulation used during the design process is the main advantage of this method, and it is used in the suggested project on the structural side. Because the generation of suitable volume discretizations has been achieved in IGA only for relatively simple geometries, its application in fluid mechanics is limited. However, extending conventional methods with a NURBS-based boundary formulation can preserve many advantages of the method. This concept is followed in the NURBS-enhanced Finite-Element Method (NEFEM), which will be used in the proposed project on the fluid side. The project involves the development of the essential transfer methods. One intermediate step is the extension of existing methods while using a conventional method on the other, fluid or structural, side. The advantages of the developed methodology will be demonstrated on academic problems and on real-world applications. Advances in robustness and accuracy are expected by the incorporation of the innovative single-field solvers and by the reduction of errors in the transfer methods at the interface. In addition to the method development, a workshop is planned to support the scientific communication about current state of the art in the field of fluid-structure interaction. During this workshop, groundbreaking methods will be presented and discussed by international experts; the workshop will also provide a platform for young academics.