A space-averaged model of branched structures

TL;DR

This paper introduces a simplified one-dimensional space-averaged model for complex branched structures, capturing their geometry and flow dynamics, and applies it to pipe networks and trees under wind forces.

Contribution

It presents a novel space-averaged modeling approach that reduces complex branched systems to a one-dimensional framework using characteristic curves and forcing terms.

Findings

Model accurately captures geometric complexity through characteristic curves.

Successfully applied to mass and momentum balances in practical systems.

Provides a simplified yet effective tool for analyzing branched structures.

Abstract

Many biological systems and artificial structures are ramified, and present a high geometric complexity. In this work, we propose a space-averaged model of branched systems for conservation laws. From a one-dimensional description of the system, we show that the space-averaged problem is also one-dimensional, represented by characteristic curves, defined as streamlines of the space-averaged branch directions. The geometric complexity is then captured firstly by the characteristic curves, and secondly by an additional forcing term in the equations. This model is then applied to mass balance in a pipe network and momentum balance in a tree under wind loading.