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用的分割方法来解决一类流-结构-相互作用问题，而到目前为止只能用整体方法来求解。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-Splines(NURBS)的方法在流体侧和结构侧都被使用，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。使用分区方法允许将现有的和专门的单场解算器集成到一个整体解决方案系统中。不幸的是，不同的曲面离散化在这样的求解器中是一个挑战。与更复杂的整体方法相比，将物理变量从一侧投影到另一侧的必要方法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，可以保证两侧湿润表面的精确几何形状，并且可以减小或消除传递误差。提出的概念是受近年来结构分析中流行的等几何分析(IGA)的启发而提出的。这种方法的主要优点是直接对设计过程中使用的几何公式进行数值荷载分析，并在结构端的建议工程中使用。由于IGA只针对相对简单的几何形状实现了合适的体积离散化，其在流体力学中的应用受到了限制。然而，用基于NURBS的边界公式扩展传统方法可以保留该方法的许多优点。NURBS增强有限元方法遵循了这一概念，该方法将用于拟议的流体侧工程。该项目涉及基本转移方法的开发。一个中间步骤是扩展现有的方法，同时在另一个方面使用传统的方法，无论是流体还是结构方法。所开发的方法的优势将在学术问题和现实世界的应用中得到展示。通过采用创新的单场解算器和减少界面传输方法中的错误，预计会在稳健性和准确性方面取得进展。除了方法开发外，还计划举办一次研讨会，以支持关于流体-结构相互作用领域最新技术的科学交流。在这次研讨会期间，国际专家将介绍和讨论开创性的方法；研讨会还将为青年学者提供一个平台。

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.