Full-surface detached vorticity method for solving fluid dynamics

Abstract

A numerical method for solving three-dimensional fluid flow using a velocity-vorticity approach is presented. Within the family of potential flow-based methods, an extension of the vortex lattice method (VLM) has been developed due to its relative simplicity. This extension demonstrates a fully non-linear detached circulation-vorticity hypothesis within the framework of potential flow theory: vorticity is generated at the entire surface, then detached, naturally advected, stretched, and diffused. The results obtained explain and solve fundamental aspects of fluid dynamics, such as the generation of lift (and drag), with outstanding precision, despite relatively coarse discretization and low computational cost. Therefore, it should be considered the cornerstone for future implementations aimed at solving more complex fluid flow phenomena within Lagrangian or meshless Computational Fluid Dynamics (CFD).

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