Isentropic Fluid Dynamics in a Curved Pipe

TL;DR

This paper analyzes how the geometry of a curved pipe influences isentropic fluid flow, providing a solution to the flow dynamics in arbitrarily curved pipes with subsonic initial data.

Contribution

It presents the first comprehensive solution to the Cauchy problem for isentropic flow in arbitrarily curved, piecewise smooth pipes considering subsonic initial conditions.

Findings

Flow solutions exist for subsonic initial data in curved pipes.

The geometry significantly affects flow dynamics.

The front-tracking method effectively solves the problem.

Abstract

In this paper we study isentropic flow in a curved pipe. We focus on the consequences of the geometry of the pipe on the dynamics of the flow. More precisely, we present the solution of the general Cauchy problem for isentropic fluid flow in an arbitrarily curved, piecewise smooth pipe. We consider initial data in the subsonic regime, with small total variation about a stationary solution. The proof relies on the front-tracking method and is based on [1].