Computational fluid dynamics of gas-fueled large-bore spark ignition engines with pre-chamber ignition can speed up the design process of these engines provided that 1) the reliability of the results is not affected by poor meshing and 2) the time cost of the meshing process does not negatively compensate for the advantages of running a computer simulation. In this work a flame propagation model that runs with arbitrary hybrid meshes was developed and coupled with the KIVA4-MHI CFD solver, in order to address these aims. The solver follows the G-Equation level-set method for turbulent flame propagation by Tan and Reitz, and employs improved numerics to handle meshes featuring different cell types such as hexahedra, tetrahedra, square pyramids and triangular prisms.Detailed reaction kinetics from the SpeedCHEM solver are used to compute the non-equilibrium composition evolution downstream and upstream of the flame surface, where chemical equilibrium is instead assumed. A generalized least-squares gradient reconstruction algorithm is employed to evaluate spatial derivatives with arbitrary node and cell connectivities, instead of the original ENO scheme. Finally, a new, extended version of the “marching cubes” algorithm for iso-surface tracking was developed and implemented for all four employed cell types.The solver was tested across different cell types and cell resolutions by simulating spherical ignition in a simple cylindrical combustion chamber. Validation was performed against experimental measurements of torch jet ignition with a diaphragm and of prechamber gaseous fuel combustion two-chamber experimental vessel separated by a variable-diameter nozzle, with different grid resolutions.