Abstract <p>A mathematical model and a calculation algorithm for numerical studies of physical and chemical processes in the engines with prechamber ignition have been developed. This type of ignition is currently the subject of active research due to its potential to improve the combustion efficiency, especially in case of the hybrid powertrain configuration. A new approach for modeling the prechamber ignition is proposed, which combines the control-volume method, predefined turbulence parameters, and direct coupling calculations on the basis of the fictitious domain method. This makes it possible to significantly simplify the geometry of the computational domain and the model preparation as well as to reduce the computing time due to the use of a relatively coarse grid. The model of ignition requires only one empirical parameter (if the turbulence field is known) to be tuned up. Modeling is conducted in a direct coupling way. The prechamber, the connecting passage, and the main combustion chamber are considered as a single computational domain. The prechamber volume is separated on the basis of the fictitious domain method. The mesh for the main combustion chamber has a moving boundary. The local flow parameters are calculated using the control volume method with staggered grids for components of the velocity vector and scalar variables. The mathematical model can be used for preliminary planning of three-dimensional calculations of the operating process or their verification in the case when no experimental data are available (at the stage of conceptual design). The results of calculations can be used as initial conditions for estimating the engine knock probability. The model can be used for calibration of the engine control unit.</p>