An asymptotic‐induced one‐dimensional model to describe fires in tunnels II: the stationary problem

Abstract

SUMMARYWe study stationary solutions of a one-dimensional low-Mach-number model derived in Gasser and Struckmeier (Math. Meth. Appl. Sci. 2002; 25(14): 1231) to describe ÿre events in long tunnels. The existence of solutions of the corresponding stationary model is shown to be equivalent to the existence of solutions of an algebraic problem. Multiple solutions are shown to be possible. The relation between di erent formulations of the problem is analysed. Weak and special distributional solutions are considered. Finally, numerical examples of realistic tunnel data with single and multiple solutions of the stationary problem are given.

On a Model for Fires in Tunnel Network Structures

“…This simplicity guarantees the possibility of fast calculations. Anayltical results on the stationary problem can be found in [3]. A gloabl existence result and stability results on the above model can be found in [4].…”

On the Stability of Solutions of a Tunnel Fire Model

“…We consider a one-dimensional fluid-dynamic model given in [1] developed to describe tunnel fires. Overview articles on this problem are given in [4] and [5]. The model was set up to overcome the main problem, namely to describe a small Mach-number flow with significant energy transport.…”

Modelling and simulation of fires in tunnel networks

“…A good (at least qualitative) agreement with results from experiments has been obtained (see [5,6]). In [4] the stationary model was discussed. In [9] a global existence result of solutions of the transient model was presented and in [10] a bifurcation analysis of the model faces the question on the stability of certain stationary solutions.…”