**Abstract**

Direct injection diesel engines have high power density with low exhaust emission but suffer from particulate matter (PM). Some new technologies were applied to reduce emissions, but they have not solved the emission problem of diesel engines altogether. The main problem of emissions from diesel engines is the simultaneous process of fuel injection and combustion, so non-homogeneous mixture formation occurs in cylinder space, and non-homogeneity is the main reason for emission generation. The solution to this problem is the separation of injection fuel and combustion processes for homogeneous mixture formation in diesel engines. An applicable practical solution for homogeneous mixture formation is the application of porous media (PM) in diesel engine combustion chambers. PM develops stable ultra-lean combustion and decreases emissions. This chapter has three parts for the mathematical modeling of PM diesel engines. The first part is thermodynamically modeling in a closed cycle. The second is zerodimensional modeling with the chemical kinetics of PM diesel engines, and the third is three-dimensional CFD modeling with the chemical kinetics of PM diesel engines in open or closed cycle. So, mathematical modeling of PM diesel engines, from simple thermodynamically modeling to complicated 3D modeling, is described in this chapter.

**Keywords:** direct injection diesel engine, porous medium, thermodynamic modeling, zero-dimensional modeling, CFD modeling
