On the 1D modeling of fluid flowing through a Junction

Abstract

Consider a fluid flowing through a junction between two pipes with different sections. Its evolution is described by the 2D or 3D Euler equations, whose analytical theory is far from complete and whose numerical treatment may be rather costly. This note compares different 1D approaches to this phenomenon.

Non Conservative Products in Fluid Dynamics

“…The literature offers a wide range of justifications, often phenomenological, for specific choices of the function Ξ 2 in (3.7), see for instance [8,11,15]. Note that, as soon as Ξ 2 is of class C 2 in all variables, with Ξ 2 a, a, (ρ, q) = 0, and a is in BV(R; R), then Theorem 2.2 applies ensuring the existence of solutions to…”

“…We now test the above condition against various junction condition found in the literature, we refer in particular to [8] for the motivations and further information of the conditions considered below. More precisely, with reference to the labelling in Table 1, we consider definition [L] from [6], condition [p] from [3,4], condition [P] from [6,7] and condition [S] from [11,15].…”

“…The current literature offers a variety of different conditions quantifying the lack in the conservation of linear momentum at a junction where the pipe's section changes, see for instance [3,4,6,7,8,10,11,15]. As a consequence of Theorem 2.2, we can select those conditions that are consistent with the equations for a pipe with smoothly varying section, both in the isentropic and in the full 3 × 3 cases, see § 3.2 and § 3.3 below.…”