Spurious Numerical Solutions in Coupled Natural Ventilation and Thermal Analyses

It is well known that iterative solution processes can lead to divergence when dealing with coupled airflow and thermal analyses for buildings ventilated either naturally or by a mixed-mode system. The Newton-Raphson method or its variants are used in almost all existing multi-zone airflow models. This paper discusses the qualitative features of the iterative solution processes of the Newton-Raphson method when used for coupled thermal and ventilation analyses of a simple one-zone building with two openings. Chaotic solutions are obtained for three different coupling strategies in combining the airflow and indoor air temperature calculations. The spurious solutions obtained in this paper are due to the inherent characteristics of the Newton-Raphson method. Our analyses on these spurious numerical solutions are based on a simple dynamical systems approach. Unfortunately, there seems to be no general approach to distinguish the true steady-state solution from the spurious numerical solutions in practical simulations. The fact that chaotic solutions were obtained for a very simple problem in this paper may indicate the need for a further understanding of its implications to more complex multi-zone problems. The findings in this paper may serve as a tool for further development of effective numerical methods for multi-zone airflows and may also provide useful knowledge for interpreting the divergence behaviours of some of the numerical simulations in building ventilation.