Computational fluid dynamics simulations are made possible by the development of numerical schemes that are highly accurate in temporal and spatial discretization and stable at high Reynolds numbers. A fundamental understanding of the stabilization mechanisms of a flame within very small spaces by the cavity method is of both fundamental and practical significance. However, the precise mechanism by which the cavity method generally provides increased flame stability remains unclear and warrants further study. Computational fluid dynamics simulations are performed to understand the overall small-scale combustion characteristics of chemically reacting flow systems. The effects of different design factors on flame stability are investigated. The roles of combustion and transport processes in chemically reacting flow systems are discussed, particularly the transport of momentum, energy, and chemical species in fluids. The results indicate that the cavity structure can induce recirculation of hot products, thereby improving flame stability. The exterior heat loss and wall thermal conductivity are vital in determining the flame stability of the chemically reacting flow system. Further improvement in flame stability can be achieved by using anisotropic walls. A critical issue of fuel-rich cases is the loss of combustion efficiency. Combustion at the microscale can offer many advantages. Faster ignition and more efficient heat transfer can be achieved, but the design is challenging due to the loss of flame stability. The principles developed and illustrated here for combustion systems are important not only for the rational design and development of chemical reactors but also for scientific research involving coupled transport processes and chemical reaction in flow systems.