The simulation of chemically reacting flows is computationally challenging and expensive. Much of the difficulty stems from solving the stiff systems of equations that describe the combustion chemistry. As a result, the development of efficient numerical algorithms that reduce the time required to model combustion phenomena are of great interest. In this talk I will present the development and application of an algorithm that accelerates the simulation of laminar flames. This methodology is based on operator-splitting and in-situ adaptive tabulation (ISAT). The scheme is applied to one- and two-dimensional test problems and is applicable to a wide range of flow problems.