Turbulence and fire-spotting effects into wild-land fire simulators

•A mathematical approach to model the random processes like turbulence and fire-spotting into a DEVS based wildfire model.•Comparison of a Lagrangian and an Eulerian based wildfire models when applied to simulate the random behaviour of wildfires.•The formulation successfully reproduces the realistic situations associated with wildfires.•The model replicates the development of flank fires, back fires, faster spread due to the effect of hot air and firebrands.•Situations involving fire crossing no fuel zones and development of secondary fires due to fire-spotting are reproduced.•The formulation shows potential for implementation in operational wildfire simulators like WRF-SFIRE and ForeFire.