The flow physics controlling the stabilisation of a methane/air laminar premixed flame in a narrow channel (internal width with a skeleton mechanism. The quality of the resolution was also assessed from multi-physics budgets derived from first principles, involving upstream-flame heat retrocession by the wall leading to flow acceleration, budgets bringing physical insights into flame/wall interaction. Additional overall mesh convergence tests of the multi-physics solution would have been desirable, but were not conducted due to the high computing cost of these fully compressible simulations, hence also solving for the acoustic field with low convective velocities.