Year: 2025
Type: article
Abstract: We present a geometric reinterpretation of pressure in inviscid potential flows, deriving it from a unified variational principle posed over both the fluid volume and the fluid–solid interface. The bulk action enforces incompressibility via a Lagrange multiplier identified with pressure, while the curvature-dependent boundary action enforces impermeability and yields a surface stress–energy tensor. Its normal–normal projection reproduces the classical wall-pressure distribution. The surface variation also yields a Laplace–Beltrami equation for the boundary potential, whose Green's representation recovers the classical panel-method kernel from first principles. We demonstrate that this framework reproduces canonical solutions for flow around cylinders (with and without circulation) and symmetric airfoils via Joukowski mapping. By unifying the interior and boundary constraints through a single geometric action, this formulation provides a rigorous and extensible foundation for pressure as an emergent curvature-driven quantity.
Source: Physics of Fluids
DOI: 10.1063/5.0286411
Authors: M. Sanchis-Agudo, R. Vinuesa
Institutions: KTH Royal Institute of Technology, University of Michigan
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Funder: European Commission
OpenAlex ID: W4413329622