Strain-minimising Stream Surfaces

TL;DR

This paper introduces a method to find and optimize strain-minimising stream surfaces in divergence-free vector fields, enabling realistic visualization of incompressible fluid flows by preserving arc length along seed curves.

Contribution

It presents a novel approach to generate and globally optimize strain-free stream surfaces in divergence-free fields, which was not previously achievable.

Findings

Successfully applied to benchmark datasets

Realistically visualizes flow of flexible objects

Demonstrates applicability to incompressible fluid simulations

Abstract

We study the problem of finding strain-minimising stream surfaces in a divergence-free vector field. These surfaces are generated by motions of seed curves that propagate through the field in a strain minimising manner, i.e., they move without stretching or shrinking, preserving the length of their arbitrary arc. In general fields, such curves do not exist. However, the divergence-free constraint gives rise to these 'strain-free' curves that are locally arc-length preserving when infinitesimally propagated. Several families of strain-free curves are identified and used as initial guesses for stream surface generation. These surfaces are subsequently globally optimised to obtain the best strain-minimising stream surfaces in a given divergence-free vector field. Our algorithm was tested on benchmark datasets, proving its applicability to incompressible fluid flow simulations, where our strain-minimising stream surfaces realistically reflect the flow of a flexible univariate object.