A new stable finite volume method for predicting thermal performance of a whole building

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 O ( Δ x 4 , Δ x 2 Δ t 2 ) . 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.