%0 Journal Article
%A David M Lorenzetti
%B Building and Environment
%D 2002
%G eng
%P 1083-1090
%T Computational Aspects of Nodal Multizone Airflow Systems
%V 37
%1 3
%2 LBNL-46949
%X The multizone approach to steady-state airflow problems models a building as a network of discrete mass  flow paths.  A nodal formulation of the problem writes the governing equations in terms of the unknown  pressures at the points where the flow paths connect.  This paper proves conditions under which the nodal  equations yield symmetric positive-definite matrices, guaranteeing a unique solution to the flow network.   It also establishes relaxed conditions under which a nodal airflow system yields asymmetric matrices with  positive eigenvalues, guaranteeing at least one solution.  Properly exploiting the system properties greatly  reduces the cost of numerical solution.  Thus, multizone airflow programs such as Contam and Comis  depend on symmetric positive-definite systems.  However, the background literature neglects or simplifies  the underlying assumptions, does not assert existence and uniqueness, and even contains factual errors.   This paper corrects those errors, states the implicit assumptions made in the programs, and discusses  implications for modelers and programmers.