Improved direct solver for building energy simulation

Finite-difference methods, when applied to the differential equations modelling energy flows in buildings, give rise to a system of non-linear difference equations. A frequently used direct solution method involving linearization is analyzed and a related method is proposed. These and one other connected method are compared using a building-related test problem prepared for this purpose. The proposed numerical method is found to produce least error, about 30% less than the commonly used method, and it is recommended for inclusion in building energy simulation software. A fundamental method for estimating the pre-conditioning period of a building, arising from the work, is discussed.