Speaker
Antonio Huerta, Polytechnic University of Catalonia
Abstract
Modeling optimal strokes for simplified micro-swimmers requires simulating flow systems in which the geometry is parameterized and plays a central role in determining the hydrodynamic forces acting on the swimmer. Exploring such systems across the relevant parameter space is often prohibitively expensive, as both the flow state and geometric parametrization contribute to a high-dimensional computational model. This challenge becomes even more severe within optimization loops, where multi-query simulations are essential for reliably evaluating the quantities of interest (QoIs) that govern swimmer performance. In this context, continual remeshing is not viable, and reference domain formulations with fitted meshes relying on parameterized geometric mappings offer only offer only limited generalization when confronted with complex or evolving shapes.
By decoupling the exact NURBS-based geometric treatment from the high-order functional approximation, the unfitted Hybridizable discontinuous Galerkin (HDG) method provides an alternative paradigm for high-fidelity simulations in complex domains. When elements are intersected by complex or evolving interfaces, the HDG method naturally fits within a CutFEM-inspired framework due to its hybridization and built-in stabilization mechanisms. By carefully adapting the trace-based formulation, which already localizes most computations to element interiors, to unfitted or cut meshes, the method maintains its inherent robustness. This approach has demonstrated in academic numerical experiments: stability, high-order accuracy, and computational efficiency, making it particularly well suited for simulations with parameterized geometries.