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Three different approaches for modelling in-cylinder compression-ignition engine processes for partially premixed combustion modes are compared with experimentally observed cylinder pressure and in-cylinder images of liquid-and vapour-fuel penetration, ignition, combustion, and soot formation in an optically accessible heavy-duty direct injection engine. A multi-dimensional computational fluid dynamics model for engine combustion, KIVA-3V, served as a common platform into which three different combustion submodels were integrated: (1) characteristic time combustion (KIVA-CTC); (2) representative interactive flamelet (KIVA-RIF); and (3) direct integration using detailed chemistry (KIVA-CHEMKIN). Three different engine operating strategies with significant premixing of fuel and air prior to ignition were investigated: low-temperature combustion achieved by charge dilution, with fuel injection either (1) early, or (2) late in the engine cycle, and (3) long ignition delay, hightemperature combustion (i.e. no charge dilution) with fuel injection near top dead centre of the piston stroke.Comparison of simulated cylinder pressure and heat-release rates with the experimental results shows that all the combustion submodels predict the cylinder pressures and heat-release rates reasonably well, but predictions of in-cylinder phenomena were significantly different among the submodels. The KIVA-CHEMKIN submodel predictions agree best with experimental observations of the location of ignition sites and the spatial distribution of soot and OH. The KIVA-RIF model, which uses global quantities to account for turbulence-chemistry interactions, under-predicts the flame lift-off, while ignition sites and species distributions are broader than observed experimentally. The KIVA-CTC submodel greatly over-predicts the spatial extent and total amount of in-cylinder soot.