Topology-Preserving Coupling of Compressible Fluids and Thin Deformables

We present a novel discretization of coupled compressible fluid and thin deformable structures that provides sufficient and necessary leakproofness by preserving the path connectedness of the fluid domain. Our method employs a constrained Voronoi-based spatial partitioning combined with Godunov-style finite-volume time integration. The fluid domain is discretized into cells that conform exactly to the fluid-solid interface, allowing boundary conditions to be sharply resolved exactly at the interface. This enables direct force exchange between the fluid and solid while ensuring that no fluid leaks through the solid, even when arbitrarily thin. We validate our approach on a series of challenging scenarios -- including a balloon propelled by internal compressed air, a champagne cork ejecting after overcoming friction, and a supersonic asteroid -- demonstrating bidirectional energy transfer between fluid and solid.