In one embodiment, alternative combustion cavity layouts are provided for practicing fuel staging in a trapped vortex (TVC) combustion apparatus comprising an inlet premixer, for injecting fuel-air mixture into the inlet of the combustion apparatus and one or more vortex premixers, for injecting fuel-air mixture into the recirculating vortex within each of one or more trapped vortex cavities. A plurality of TVC cavities, may, for example, be laid out axially, radially, peripherally, internally, or in combinations of such arrangements. These layouts may be used in conjunction with a fuel staging method whereby the relative proportion of mixture introduced through the inlet and the respective vortex premixers can be varied as a function of operating conditions.