Numerical Modelling of Surface Forest Fire Spread in Nonuniform Woodland

Abstract

The problem of computer modeling of two-dimensional surface forest fire spread is considered. The article describes the initial-boundary value problem in a form of a system of partial differential equations. Presented mathematical model of surface forest fires spread calculates the evolution of the temperature, of combustible forest materials, volume fractions of the multi- phase reactive medium, mass concentration of components of a gas phase. The system of PDEs is solved numerically. Authors explicit numerical schemes with a uniform grid over coordinates and variable steps over time are used. Time steps are selected in accordance with stability conditions of the numerical scheme, and with the speeds of physical and chemical processes at each specific step. Examples illustrate the results of numerical experiments showing how fire front spreads in different directions in windy conditions. Qualitative differences in the geometry and dynamics of temperature density maps are shown for a range of fuelbreak sizes.