Abstract: Flameless oxy-fuel combustion of pulverized coal is one of the development directions of clean coal combustion technology,which can obtain high concentration of CO_2,significantly reduce NO_x emissions,and improve the combustion stability and thermal performance. Computational fluid dynamics( CFD),as one of the important means of combustion research,has the advantages of fast running,low cost,and rich data,which effectively promotes the development of flameless oxy-fuel combustion technology. Based on our long-term research experience on oxy-fuel and flameless combustion of pulverized coal,the CFD simulation method and research progress of flameless oxy-fuel combustion of pulverized coal were summarized. The experimental and mathematical definitions of coal flameless combustion were firstly introduced,which were different from the flameless combustion of gaseous fuels due to the heterogeneous reaction. Then the progress of the CFD methods for flameless oxy-fuel combustion of pulverized coal was discussed in detail,including the sub-models and mechanisms of flow,heat transfer,combustion and pollutant formation. The simulation accuracy and calculation efficiency of flameless oxy-fuel combustion of pulverized coal can be significantly improved by using the realizable k-ε turbulence model considering strong flue gas entrainment,P1 or DO radiation model,WSGG gaseous radiation model modified for oxy-fuel condition,CPD devolatilization model,finite-rate EDC homogeneous combustion model considering turbulence-chemistry interaction,homogeneous reaction mechanisms developed for flameless and oxy-fuel combustion,multi-step surface heterogeneous char burnout model,detailed reaction mechanisms for nitrogen conversion and dynamic adaptive chemistry for calculation acceleration. Next,the numerical studies on flameless oxy-fuel combustion of pulverized coal were reviewed in the aspects of benchmark experiments,micro reaction zone analysis,macro reaction characteristics,pollutant formation and conceptual designs of large-scale boiler. Finally,the development direction of CFD research on flameless oxy-coal combustion were proposed,such as large eddy simulation,combustion models,high-precision detailed reaction mechanisms,dynamic adaptive chemistry modeling,and industrial application optimization.