Building and Environment 43 (2008) 37–43 A new stable finite volume method for predicting thermal performance of a whole building C. Luo à , B. Moghtaderi, H. Sugo, A. Page School of Engineering, Faculty of Engineering & Built Environment, The University of Newcastle, University Drive, Callaghan NSW 2308, Australia Received 2 August 2006; received in revised form 7 November 2006; accepted 27 November 2006 Abstract Discretised governing equations involving only temperatures and heat fluxes at both surfaces of a solid wall layer were obtained by combining a new stable finite volume scheme for the two inner nodes of the wall layer with the surface diffusion equations (discretised by third order equations). The finite volume scheme for the inner nodes of the layer is proved to be stable with its truncation error being OðDx 4 ; Dx 2 Dt 2 Þ. A special analytical solution for a solid wall was used to evaluate different schemes for the inner nodes, showing that the new proposed scheme performs better than all other schemes for time steps of 3600 and 600 s. Finally, this scheme was used to simulate a whole house and the predicted zonal air temperature, and surface temperatures agreed well with measured values. r 2007 Elsevier Ltd. All rights reserved. Keywords: Finite volume method; Finite difference method; Fourier stability analysis; Thermal zone model; Fourier diffusion equation 1. Introduction A thermal zonal model assumes that all independent variables are distributed uniformly across the building walls and within the zones (such as room air or the air cavity in a cavity wall) and combines the heat balance equations for solid walls with the energy balance equations for the zonal air. To simplify the heat balance equations for solid walls, the response factor method and the conduction transfer function (CTF) method have been adopted in a number of commercial and scientific software programs, such as TRNSYS, Energy Plus (CTF) and AccuRate (Response Factor). To avoid solving the governing equations for the inner nodes of a wall layer, SUNCODE used an explicit difference scheme to solve the wall conduction equations. However, it is well known that the explicit difference scheme has a stability problem. Because of potential stability problems and the storage requirements for the inner nodes, SUNCODE is only suitable for residential or small commercial buildings. The inner node equations prevent researchers using the finite difference method for modelling the thermal performance of buildings. Therefore, to utilise the finite difference method in the thermal performance modelling of buildings, it is necessary to construct a scheme which does not involve the inner nodes. Tsilingiris [1,2] used the Laasonen scheme to develop a finite difference method to study the thermal behaviour of walls. He utilized the effective thermal capacitance and thermal conductivity to simplify the parallel layers of the composite material with Dx ¼ 1 cm and Dt ¼ 60–300 s (or 1–5 min). It is not made clear by the author whether or not the method could be applied to a whole building. The study reported in this paper focuses on a finite difference/finite volume method which can be easily applied to a whole building with reasonable accuracy for time steps ranging from 1 to 3600 s (or 1 h). By using two inner nodes in a construction layer as shown in Fig. 1, all variables from the two inner nodes can be removed by combining the implicit discretised finite difference/finite volume equations for the inner nodes with equations for the two surface nodes. It is shown that this new implicit scheme for the two inner nodes gives better performance than the existing implicit schemes. ARTICLE IN PRESS www.elsevier.com/locate/buildenv 0360-1323/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2006.11.037 à Corresponding author. Department of Chemical Engineering, School of Engineering, The University of Newcastle, University Drive, Callaghan NSW 2308, Australia. Tel.: +61 2 4921 6951; fax: +61 2 4921 8692. E-mail address: Caimao.Luo@newcastle.edu.au (C. Luo).