Visualization of three-dimensional incompressible flows by quasi-two-dimensional divergence-free projections

TL;DR

This paper introduces a method for visualizing 3D incompressible flows through divergence-free quasi-two-dimensional projections, enhancing understanding of flow structures by satisfying boundary conditions and using Galerkin bases.

Contribution

It proposes a novel divergence-free projection technique for 3D flow visualization that ensures boundary condition satisfaction and can be computed with Galerkin bases, improving flow analysis.

Findings

Projection method provides clearer flow structure visualization.

Projections satisfy all boundary conditions and are unique.

Application to natural convection and lid-driven flows demonstrates effectiveness.

Abstract

A visualization of three-dimensional incompressible flows by divergence-free quasi-two-dimensional projections of velocity field on three coordinate planes is proposed. It is argued that such divergence-free projections satisfying all the velocity boundary conditions are unique for a given velocity field. It is shown that the projected fields and their vector potentials can be calculated using divergence-free Galerkin bases. Using natural convection flow in a laterally heated cube as an example, it is shown that the projection proposed allow for a better understanding of similarities and differences of three-dimensional flows and their two-dimensional likenesses. An arbitrary choice of projection planes is further illustrated by a lid-driven flow in a cube, where the lid moves parallel either to a sidewall or a diagonal plane.