Filtration gas combustion in a mesoscale combustor filled with inert fibrous porous media was numerically investigated. Downstream propagating combustion wave and standing combustion wave were obtained in the simulation. The predicted flame stability diagram agrees well with experimental results in the literature. Moreover, it was found that the downstream propagating flame changes its shape and transforms from one stable state to another stable state in a short duration after ignition, while the flame shape of the standing wave remains unchanged. Furthermore, combustion efficiency of both combustion waves increases with time and a nearly complete conversion can be achieved spontaneously due to the strong heat recuperation. It is also demonstrated that heat conduction in the tube wall has a crucial effect on flame behaviors and combustion efficiency. On one hand, for a bigger wall thermal conductivity, the downstream propagating wave moves with a larger speed; on the other hand, a high combustion efficiency can be expected for a smaller thermal conductivity. (C) 2015 Elsevier Ltd. All rights reserved.