Homogeneous and complete combustion in internal combustion engines is advantageous. The use of a porous foam in the exhaust gas in an engine cylinder for heat recovery is examined here with the aim of reducing engine emissions. The internal combustion engine with a porous core regenerator is modeled using SOPHT software, which solved the differential equations for the thermal circuit in the engine. The engine thermal efficiency is observed to increase from 43% to 53% when the porous core regenerator is applied. Further, raising the compression ratio causes the peak pressure and thermal efficiency to increase, e.g., increasing the compression ratio from 13 to 15 causes the thermal efficiency and output work to increase from 53% to 55% and from 4.86 to 4.93 kJ, respectively. The regenerator can also be used as a catalytic converter for fine particles and some other emissions. The regenerator oxidizes unburned hydrocarbons. Meanwhile, heat recovered from the exhaust gases can reduce fuel consumption, further reducing pollutant emissions from the internal combustion engine.