On calculation of quasi-two-dimensional divergence-free projections for visualization of three-dimensional incompressible flows

TL;DR

This paper introduces a simplified and faster method for visualizing three-dimensional incompressible flows by computing divergence-free projections using a Chorin projection and SIMPLE-like iteration, applicable to various coordinate systems.

Contribution

It presents an alternative to divergence-free Galerkin bases, enabling easier implementation, faster computation, and generalization to curvilinear coordinates for flow visualization.

Findings

Faster computation of divergence-free projections.

Applicable to cylindrical and spherical coordinates.

Effective post-processing of experimental 3D flow data.

Abstract

A visualization of three-dimensional incompressible flows by divergence-free quasi-two-dimensional projections of the velocity field on three coordinate planes was recently proposed. The projections were calculated using divergence-free Galerkin bases, which resulted in the whole procedure being complicated and CPU-time consuming. Here we propose an alternative way based on the Chorin projection combined with a SIMPLE-like iteration. The approach proposed is much easier in realization, allows for faster computations, and can be generalized for arbitrary curvilinear orthogonal coordinates. To illustrate the visualization method, examples of flow visualization in cylindrical and spherical coordinates, as well as post-processing of experimental 3D-PTV data are presented.