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The stability of numerical methods used for finite-difference thermal modelling of buildings is discussed. A known instability in a commonly used process is described and alternative numerical methods with suitable stability properties are identified. With a view to selecting the optimum numerical method, the building energy simulation problem is characterized mathematically and appropriate implicit solvers are compared on the basis of accuracy and computational effort using a building related test problem prepared for this purpose. A recently developed numerical method with the necessary strong stability is found to possess higher computational efficiency than methods frequently used in this application and it is recommended for inclusion in building energy simulation software.
Crowley, M., Hashmi, S.: Evaluation of implict numerical methods for building energy simulation. Proceedings of the Institution of Mechanical Engineers, Part A, Journal of Power and Energy, vol. 212 no. 5 331-342. August 1, 1998. doi: 10.1177/095765099821200502