The numerical procedure of combustion modelling by the boundary-domain inte
gral method (BDIM) is presented, based on detailed chemical and physical pr
ocesses of the premixed gaseous fuel. The boundary element method is employ
ed to solve the conservation equations of overall mass, momentum, energy an
d mass species. The law of mass action is applied to determine the chemical
reaction rates representing the basis of the source terms in the conservat
ion equations for mass species. A freely propagating flame including the fo
rced ignition of a homogenous hydrogen-air mixture is calculated as an exam
ple problem of the numerical simulation of the combustion processes.