Note on the Pressure Equations Used in Zone Fire Modeling.
Note on the Pressure Equations Used in Zone Fire
Rehm, R. G.; Forney, G. P.
NISTIR 4906; 34 p. August 1992.
Available from: National Technical Information Service
zone models; equations; fire models; mathematical
models; numerical integration; ordinary differential
equations; phase plane analysis; singular perturbation
Examples of simple zone fire models are analyzed. These
models illustrate the nature of the numerical problems
commonly encountered in zone models of enclosure fires.
Often these difficulties arise in the solution of the
equations for the pressure in connected rooms because
the pressure equilibrates much more rapidly than other
dynamical variables. Since these models are very
simple, analytical techniques can be applied and some
insight gained regarding the nature of these problems.
The models consist of ordinary differential equations
coupled with algebraic equations. Singular perturbation
methods and phase plane analyses, together with
numerical integration of the appropriately
nondimensionalized equations, are employed to examine
the stiff nature of the equations associated with these
models. We conclude that many of the difficulties
associated with numerical integration of zone fire
models in general may be circumvented by appropriate
analysis of the zone fire model equations.