TY - JOUR
T1 - Implementing state-space methods for multizone contaminant transport
JF - Building and Environment
Y1 - 2014/01//
SP - 131
EP - 139
A1 - Simon T. Parker
A1 - David M. Lorenzetti
A1 - Michael D. Sohn
KW - Concentration solution
KW - Eigenvalue
KW - Indoor dispersion
KW - Multizone models
KW - Numerical methods
KW - State-space
AB - The “well-mixed zone” approximation is a useful model for simulating contaminant transport in buildings. Multizone software tools such as CONTAM [1] and COMIS [2] use time-marching numerical methods to solve the resulting ordinary differential equations. By contrast, the state-space approach solves the same equations analytically [3]. A direct analytical solution, using the matrix exponential, is computationally attractive for certain applications, for example, when the airflows do not change for relatively long periods. However, for large systems, even the matrix exponential requires numerical estimation. This paper evaluates two methods for finding the matrix exponential: eigenvalue decomposition, and the Padé algorithm. In addition, it considers a variation optimised for sparse matrices, and compares against a reference backward Euler time-marching scheme.The state-space solutions can run several orders of magnitude faster than the reference method, with more significant speedups for a greater number of zones. This makes them especially valuable for applications where rapid calculation of concentration and exposure under constant air flow conditions are needed, such as real-time forecasting or monitoring of indoor contaminants. For most models, all three methods have low errors (magnitude of median fractional bias <3·10−5, normalised mean square error <3·10−7, and scaled absolute error <4·10−4). However, for the largest model considered (1701 zones) eigenvalue decomposition showed a dramatic increase in error.
VL - 71
JO - Building and Environment
DO - 10.1016/j.buildenv.2013.09.021
ER -