The present work aims at development and validation of a tool for numerically modeling stratified turbulent combustion in a gasoline direct injection (GDI) engine. For this purpose, an open source code called OpenFOAM (R), which has been attracting growing interests from both industries and academies due to an opportunity to access the source code and to test new models without paying license fees, is further developed by implementing advanced models relevant to stratified turbulent burning. In particular, first, the Flame Speed Closure model of premixed turbulent combustion is implemented in order to simulate flame propagation through inhomogeneously premixed reactants. Second, a newly calculated approximation of the laminar flame speed of gasoline-air mixtures as a function of the equivalence ratio, pressure, and temperature is implemented in order to simulate dependence of burning rate on the local mixture composition. Third, a newly calculated approximation of the combustion temperature of gasoline-air mixtures as a function of the equivalence ratio, pressure, and product enthalpy is implemented in order to allow for dissociation of combustion products and heat losses. Fourth, a presumed mixture-fraction probability density function (PDF) approach is implemented in order to simulate the influence of turbulent fluctuations in the mixture fraction on the local burning rate. In addition to commonly used mass-weighted mixture-fraction PDF, a more consistent model that deals also with the canonical mixture-fraction PDF is developed and the two approaches are compared. Numerical results that show the influence of the aforementioned implementations on computed global characteristics of stratified combustion in a research GDI engine are discussed. The developed numerical tool is quantitatively validated by comparing computed pressure traces in the GDI engine with experimental data obtained in three different cases associated with two different loads, late injection timings, and short time intervals between the injection and spark ignition.