The Natural Helmholtz-Hodge Decomposition for Open-Boundary Flow Analysis

Area of Science:

• Fluid dynamics
• Computational mathematics
• Scientific computing

Background:

• The Helmholtz-Hodge decomposition (HHD) is crucial for flow analysis, but lacks uniqueness in bounded domains.
• Traditional methods rely on boundary conditions, which may be unknown or unsuitable for open boundary simulations, leading to artifacts.

Purpose of the Study:

• To propose a novel, data-driven Helmholtz-Hodge decomposition (natural HHD) that ensures uniqueness without prior boundary condition assumptions.
• To enable reliable, artifact-free flow analysis for simulations with open or unknown boundary conditions.

Main Methods:

• The natural HHD separates flow fields into internal and external components.
• It employs a data-driven approach to achieve uniqueness, eliminating the need for explicit boundary condition imposition.
• The method computes HHD on a point-wise basis, allowing for local approximations.

Main Results:

• The natural HHD provides a unique decomposition irrespective of boundary conditions.
• It successfully eliminates artifacts and distortions in flow components for open boundary conditions.
• The point-wise computation allows for efficient local approximations within the domain.

Conclusions:

• The natural HHD offers a robust and artifact-free method for flow decomposition, particularly in challenging boundary scenarios.
• Its data-driven and point-wise nature makes it adaptable and computationally efficient for various applications in 2D and 3D.