A Distributed Parameter Pseudo Bond Graph for Heat Conduction Modelling: Notion of Cellular Bond Graph
A. Nakrachi, G. Dauphin-Tanguy · 2003
The paper presents a new procedure for building a pseudo bond graph model representing 1D and 2D heat conduction phenomena, in their distributed parameter form. The heat conduction equation is written in such a way that conjugate variables, temperature T(t,x,y) and heat flow rate Q⃗˙(t,x,y), and their space derivatives appear explicitly in the equation. New conjugations between variables are introduced as (T,div(Q⃗˙)) and (gradT,Q⃗˙). We define new bond graph elements named “distributed C- and R-elements”, and we build a “Distributed Parameter Bond Graph” (DPBG), with a form slightly different from the classical one. The approximation of the space derivatives leads to submodels we call “cellular bond graphs”, new notion which could be compared to the cellular automata. Moreover, we show how this representation enables to easily build classical finite difference or finite volume schemes.