Physical, mathematical, and numerical modeling of a gas flow in pipeline networks with low Mach number expansion

This study aims to investigate gas flows at low velocities through pipeline arrangements. We consider one-dimensional Navier-Stokes equations

averaged over a pipe section to achieve this. In contrast to the classical Boussinesq approximation, we employ the Low Mach Expansion to asymptotically describe compressible effects, obtaining a more accurate representation.

To address the low Mach averaged model, we conceive a numerical method based on the characteristics method and the projection technique. In the initial stage, we present a numerical simulation for the "thermosiphon." This setup consists of two horizontal adiabatic pipes and two vertical pipes with prescribed wall temperatures, resulting in a temperature-driven flow. We incorporate in our algorithm the treatment of Dirac distributions as derivatives of the discontinuous gravity term at the corners and of periodic conditions.

We construct a quasi-exact solution serving as a benchmark for the validation of our numerical results.

Moving forward, we propose laws governing the junctions between multiple pipes and develop an algorithm capable of ensuring proper transmission conditions.

This analysis allows us to present numerical results for more complex pipeline configurations, providing quasi-exact solutions whenever feasible.

Overall, this study investigates further low Mach number gas flows through pipeline networks, employing advanced numerical techniques and validating our findings against established benchmarks.