Bond-graph approach for computational fluid dynamics: a comparison with other numerical methods

This paper shows contributions from a new, bond-graph based, formalism for computational fluid dynamics (CFD) problems, through which the state equations are obtained in terms of nodal vectors of mass, velocity and entropy. The resulting state equations are presented for a 1D problem with constant piecewise shape functions. It is shown that there exist contributions coming from the discontinuities; these contributions can be taken into account in the integration process by using distributional derivatives. Although viscous effects cannot be modeled, heat conduction can be rigorously taken into account with the proper choice of the entropy weight functions. Based on the linearized expressions of the state equations, a comparison is made with a control-volume and with a finite-difference numerical scheme, obtaining an interpretation of the density and entropy weight functions appearing in the bond-graph formalism. Based on the second principle of thermodynamics, it is also shown that the entropy weight functions must decrease as the distance to the corresponding node position increases.