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Note on the Pressure Equations Used in Zone Fire Modeling (NISTIR 4906)



Ronald G. Rehm, Glenn P. Forney


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.
NIST Interagency/Internal Report (NISTIR) - 4906
Report Number


zone models, equations, fire models, mathematical models, numerical integration, ordinary differential equations, phase plane analysis, singular perturbation analysis


Rehm, R. and Forney, G. (1992), Note on the Pressure Equations Used in Zone Fire Modeling (NISTIR 4906), NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed March 2, 2024)
Created August 1, 1992, Updated June 2, 2021