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To further improve the efficiency and emissions profiles of internal combustion engines, many new combustion concepts are currently being investigated. Examples include homogeneous charge compression ignition (HCCI), stratified charge compression ignition (SCCI), lean stratified premixed combustion, and the use of high levels of exhaust gas recirculation (EGR) in diesel engines. The typical combustion temperatures in all of these concepts are lower than those in traditional spark ignition or diesel engines. Most of the combustion models that are currently used in computational fluid dynamics (CFD) simulations were developed to describe either premixed or non-premixed combustion under the assumption of fast chemistry.