Anna Schwarz

Anna Schwarz, Jens Keim, Christian Rohde et al.

High-order methods offer superior dispersion and dissipation properties compared to low-order schemes but require robust stabilization for discontinuities. To ensure stability, local artificial viscosity is common, but often degrades sub-element resolution. Conversely, subcell resolution preserving limiting strategies such as the finite volume subcell method are typically restricted to uniform topologies, such as purely hexahedral, or simplex meshes. This leaves a significant gap in treating the hybrid-element topologies necessary for complex engineering geometries. This paper presents a robust shock-capturing approach for the discontinuous Galerkin spectral element method on mixed curvilinear meshes containing hexahedral, prismatic, tetrahedral, and pyramid elements. Non-hexahedral elements are handled via collapsed coordinate transformations. The proposed method utilizes an h-adaptive finite volume subcell scheme with arbitrary subcell resolution; 2N + 1 in this work. The schemes essential properties, including conservation, spatial convergence, and the shock capturing capabilities are verified. Finally, the method's applicability to complex configurations is demonstrated through a simulation of the flow around a NACA 0012 airfoil.

Marius Kurz, Rohan Kaushik, Marcel Blind et al.

Reinforcement learning has gained traction for active flow control tasks, with initial applications exploring drag mitigation via flow field augmentation around a two-dimensional cylinder. RL has since been extended to more complex turbulent flows and has shown significant potential in learning complex control strategies. However, such applications remain computationally challenging due to its sample inefficiency and associated simulation costs. This fact is worsened by the lack of generalization capabilities of these trained policy networks, often being implicitly tied to the input configurations of their training conditions. In this work, we propose the use of graph neural networks to address this particular limitation, effectively increasing the range of applicability and getting more value out of the upfront RL training cost. GNNs can naturally process unstructured, threedimensional flow data, preserving spatial relationships without the constraints of a Cartesian grid. Additionally, they incorporate rotational, reflectional, and permutation invariance into the learned control policies, thus improving generalization and thereby removing the shortcomings of commonly used CNN or MLP architectures. To demonstrate the effectiveness of this approach, we revisit the well-established two-dimensional cylinder benchmark problem for active flow control. The RL training is implemented using Relexi, a high-performance RL framework, with flow simulations conducted in parallel using the high-order discontinuous Galerkin framework FLEXI. Our results show that GNN-based control policies achieve comparable performance to existing methods while benefiting from improved generalization properties. This work establishes GNNs as a promising architecture for RL-based flow control and highlights the capabilities of Relexi and FLEXI for large-scale RL applications in fluid dynamics.