Computational and Applied Math Proseminar

Friday, September 29, 1:40 p.m. GWC 604

Michael Herty

Dept. Math., Technical University of Kaiserslautern

Mathematical Properties of Gas Flow in Pipe Networks

Abstract We are interested in gas dynamics in pipe networks. Several models for the dynamics inside the pipe are known which range from partial differential equations to purely algebraic relations. Usually, the dynamics of different pipes is coupled at pipe fittings and we discuss the mathematical and physical reasonable coupling conditions.

We consider questions of well-posedness and existence of solutions near pipe fittings for models based on the nonlinear hyperbolic partial differential equations which are derived from the Euler equations. The problem at hand is an initial and boundary value problem for a system of nonlinear conservation laws coupled by the conditions introduced by the pipe fitting.

The applied techniques are based on considerations on special Riemann problems posed at the pipe fitting. Finally, we present numerical examples showing the dynamics on the pipe and at the pipe fitting.

For further information please contact: mittelmann@asu.edu