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Advanced diesel engine architectures employing flexible valve trains enable emissions reductions and fuel economy improvements. Flexibility in the valve train allows engine designers to optimize the gas exchange process in a manner similar to how common rail fuel injection systems enable optimization of the fuel injection process. Modulating valve timings directly impacts the volumetric efficiency of the engine since it directly controls how much mass is trapped in the cylinders. In fact, it will be shown that the control authority of valve timing modulation over volumetric efficiency, that is, the range of volumetric efficiencies achievable due to modulation of the valve timing, is three times larger than the range achievable by modulation of other engine actuators such as the exhaust gas recirculation valve or the variable geometry turbocharger. Traditional empirical or regression-based models for volumetric efficiency, while suitable for conventional valve trains, are therefore challenged by flexible valve trains. The added complexity and additional empirical data needed for wide valve timing ranges limit the usefulness of these methods. A simple physically based volumetric efficiency model was developed to address these challenges. The model captures the major physical processes occurring over the intake stroke, and is applicable to both conventional and flexible intake valve trains. The model inputs include temperature and pressure in both the intake and exhaust manifolds, intake and exhaust valve event timings, engine cylinder bore, stroke, connecting rod lengths, engine speed, and effective compression ratio. The model is physically based, requires no regression tuning parameters, is generalizable to other engine platforms, and has been experimentally validated using an advanced multi-cylinder diesel engine equipped with a fully flexible variable intake valve actuation system. Experimental data were collected over a wide range of the operating space of the engine and augmented with air handling actuator and intake valve timing sweeps to maximize the range of conditions used to thoroughly experimentally validate the model for a total of 286 operating conditions. The physically based volumetric efficiency model will be shown to predict the experimentally calculated volumetric efficiency to within 5 per cent for all cases with a root mean square error of less than 2.5 per cent for the entire dataset. The physical model developed differs from previous physical modelling work through the novel application of effective compression ratio, incorporation of no tuning parameters, and extensive validation on a unique engine test bed with fully flexible intake valve actuation. [ABSTRACT FROM PUBLISHER]