A space-averaged model of branched structures

• We present an original space-averaged model for conservation laws in branched systems.
• The system is modeled by one-dimensional equations along characteristic curves related to the initial geometry.
• A geometric forcing term accounts for branching and diameter variations in a continuous way.
• This model accurately predicts mass balance in a pipe network and momentum balance in a tree under wind loading.
• The derivation of this model is general and can be of use in a large variety of branched systems.

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.