Chaotic solution behavior in coupled natural ventilation and thermal analyses

Abstract

The chaotic solution behaviour of the Newton-Raphson method is demonstrated when used in coupled airflow and thermal analyses in natural ventilation. The Newton-Raphson method or its variants are used in almost all existing multi-zone airflow models. Chaotic solutions are obtained when combing the airflow and indoor air temperature calculations in a simple one-zone building with two openings. It is found that the appearance of the spurious solutions is an inherent feature of the Newton-Raphson method. There seems no general approach to distinguish the true steady-state solution from the spurious numerical solutions in practical simulations. The findings may serve as a tool for further development of effective numerical methods for multi-zone airflows and provide useful knowledge for interpreting the divergence behaviors of some of the numerical simulations in building ventilation.