The combustion processes of homogeneous charge compression ignition (HCCI) engines whose piston surfaces were coated with catalyst (platinum) are numerically investigated. The detailed reaction mechanism of methane oxidation on platinum catalyst is adopted. Mathematical models of three different levels, namely, a single-zone model, a multi-zone model, and a multidimensional one are developed. The effects of catalytic combustion on the ignition timing, the emissions of hydrocarbon (HQ, carbon monoxide (CO) and nitrogen oxide (NOx), and the combustion characteristics of HCCI engines are analyzed through the single- and the multi-zone models. The results show that due to the catalytic coating the ignition timing is advanced, the emissions of HC and CO are decreased, while the emissions of NOx are elevated, and that the indicated fuel conversion rate and the combustion efficiency are increased. Furthermore, through the multidimensional model, the inhomogeneity of the temperature and species concentration fields as well as the turbulence effect are considered. It is shown that the temperature and HC, CO concentration fields in the cylinder are more homogeneous because of the effects of catalytic combustion. Finally, a brief comparison of the above three models is presented. Advantages, drawbacks and applicabilities of each model are discussed. (c) 2006 Elsevier B.V. All rights reserved.