Improved finite volume discretisations of entropy generation and turbulence production

The finite volume discretisation of the rates of turbulence production and entropy generation commonly use cell centred differencing schemes. Whilst these are easy to derive they can result in discrepancies in solutions that are otherwise based on gradients approximated at cell faces. For example, a turbulent log law layer calculated using the k–ϵ model can exhibit a spurious peak in the turbulence kinetic energy near the wall, or the volumetric rate of work calculated from entropy generation may not equal energy fluxes through domain boundaries. In this article new discretisations of turbulence production and entropy generation are derived that are based on derivatives centred at cell faces. These do not display the erroneous behaviours of the cell centre discretisations.