High-order Geometry, Mesh and Adaptivity for Fluid-Structure Interaction Simulations

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During the last decades, very significant advances have been made in the field of domain representation and discretization for the purpose of simulation-based engineering sciences. These developments have been mostly based on linear representations of domain boundaries and space discretization using low-order elements. Recently, very significant developments have been made towards p-version finite element analysis (FEA), isogeometric analysis (IgA) and high-order (HO) simulations, for several types of partial differential equations, and in particular for structural problems. In these new approaches, HO elements and shape functions are used, thereby increasing the number of degrees of freedom supported by each discrete element, and spatial discretization of boundaries are represented by high degree interpolants that preserve the accuracy of the geometric shapes modeled using CAD systems. Significant reduction in the number of elements and overall computational cost may be achieved, while increasing solution accuracy. A similar trend may be observed in the field of computational fluid dynamics (CFD), where HO methods for fluid flow simulations are also gaining momentum, especially in LES and DNS-type simulations, using various types of Finite Element discretization approaches. A natural extension to these single-discipline advancements involves the development of multi-physics simulation methodologies to model, for instance, the interaction between fluids and solids (FSI). This progress is however hampered by the need for high-quality and robust spatial discretization approaches to generate curved elements which are adapted to the specific features of the physical phenomena being simulated. This research program aims to contribute to the promotion and penetration of HO methods in the practice of engineers and scientists through the development of efficient and robust HO mesh generation and manipulation methods and their validation on test cases representative of real-world applications.