Controlling light-around and re-light presents design challenges for gas-turbine manufacturers. Researchers have studied the detailed phenomena in laboratory experiments to elucidate controlling factors and modes of behavior. Several groups have reported high-fidelity simulations of the fluid dynamics, turbulent mixing and light-around phenomena using large eddy simulations (LES) on highly refined computational meshes. While such simulations can reproduce experimental observations, they are computationally expensive and tend to be impractical for routine design analyses. In this work, we present a less computationally intensive CFD approach, which has been tested against laboratory experiments using both gaseous-fuel injections and liquid-fuel injections. Results show that a consistent practice of mesh and model settings can be used for all the test cases considered. The simulations generate light-around sequences and total-ignition times that agree well with experimental measurements. Observed trends are predicted when varying burner spacing as well as the fuel and injection method.