A new modelling approach for premixed turbulent combustion has been developed and implemented in computing flow and combustion in axisymmetric engine cylinders. Turbulent transport is treated using a standard second-moment closure model based on Favre density-weighted averaging and the turbulent reaction rate is modelled using a novel laminar flamelet approach. The numerical method is based upon a modified PISO algorithm incorporating second-order bounded spatial differencing. The need for high numerical accuracy is investigated and quantified with reference to engine combustion calculations. The new model for the mean turbulent reaction rate is shown to capture correctly the qualitative behaviour of the flame near to a solid wall, in marked contrast to many existing models. The superiority of the second-moment turbulence model is demonstrated by direct comparison with a standard eddy-viscosity model using an engine combustion test case. A parametric study is carried out to examine the dependence of modelled engine performance on various parameters such as turbulence intensity, compression ratio, engine speed and ignition timing. In every case the expected behaviour is qualitatively well reproduced.