The coal spontaneous combustion has obvious mesoscale characteristics. The application of the mesoscale science and theory to correlate the microscopic reaction mechanism with the macroscopic properties of coal spontaneous combustion contributes to the in-depth study in the field of coal spontaneous combustion. Firstly,the physical process and the mathematical concept of the coal pile gradation in which the mesoscale II exists are made clear. The differ- ences and interrelationships among the three scales of single coal particle,particle cluster and coal pile are explained in detail. Specifically,multi-scale simulation depends on the reasonable information transfer among scales,which is mainly realized by upscaling method in the study of coal spontaneous combustion. From the point of view of mathemati- cal modeling,it is pointed out that the essence of coal particle cluster is the representative elementary volume (REV) of the coal pile. The REV scale simulation,whose minimum unit is REV,is based on macro-model,which ignores the structural changes in the cluster. Correspondingly,the pore scale simulation,which considers the interaction of individ- ual coal particles inside the REV,is based on micro-model. Secondly,based on the definition of the REV scale,the governing equations,including continuity,momentum,energy and concentration equations,which consider the effects of the transient porosity and high-temperature radiation,are built and the corresponding solving method is briefly de- scribed. Besides,it is pointed out that the parameters including porosity,permeability and heat transfer coefficient,etc. should be obtained from the pore scale simulation. Thirdly,the Lattice Boltzmann equations of pore scale simulation are discussed. A sample is employed to illustrate the procedures for the 3D digital reconstruction and the extraction of the REV. Finally,based on the constitutive relation of parameters between different scales,the upscaling method for obtai- ning parameters,such as porosity,permeability,inertia coefficient and convective heat transfer coefficient in macro- control equation,from the pore scale is proposed,which realizes the information transmission from the pore scale simu- lation with micro-model to the REV scale simulation with macro-model mathematically. Consequently,the multi-scale physical and mathematical modeling from pore scale to REV scale is completed.