A pressurized model for compressible pipe flow.

Mehmet Ersoy (1)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134

We present the full derivation of a compressible model in a thin closed water pipe including friction, changes of section and slope variation. Starting from the compressible 3D Navier-Stokes equation under "thin layer" assumptions with well-suited boundary conditions, we justify the 1D reduced model called pressurized model (also named the \textbf{P}-model). It was introduced in the general framework of unsteady mixed flows in closed water pipes. This model describes the evolution of a compressible flow close to gas dynamics equations in a nozzle. We also propose a class of averaged low Oser compressible models of a general barotropic law $p(\rho) = \rho^{\gamma}$, $\gamma>1$.

Mots clés: pressurized flow; compressible Navier-Stokes; barotropic laws; thin layer; hydrostatic approximation; closed water pipe; friction; viscosity; Oser number

Domaines: Equations aux dérivées partielles [math.AP]

Mehmet Ersoy. A pressurized model for compressible pipe flow.. 2013. ⟨hal-00908965v1⟩