Modelling motion of fronts and interfaces is a fundamental task to understand and describe many natural phenomena. The most widely used and successful tool for this purpose is the so called Level-Set Method (LSM). It has been adopted in many different problems, including, for example, turbulent premixed combustion, wildland fire propagation, groundwater infiltration, biology and material science. In many applications the front is embedded into a random environment and therefore the interface gets a random character. The main aim of the present Research Line is the development of a novel approach to track random fronts.

The LSM has been designed to track an interface in frameworks with a clear distinction between the inside and the outside part of a domain. It is a highly robust and accurate method for tracking interfaces with a complex motion and it can be used in the same basic formulation for problems with any spatial dimension. The LSM is particularly useful to handle problems in which the speed of the evolving interface is dependent on the interface properties such as curvature and normal direction, as well as on the boundary conditions at the interface location. Hence, it is suitable for problems in which the topology of the evolving interface changes during the events and for problems in which sharp corners and cusps can be generated.

The proposed approach has been initially derived on the basis of physical arguments for turbulent premixed combustion

[Pagnini & Bonomi, Phys. Rev. Lett. 107, 044503 (2011)] and later it has been applied to wildland fire propagation in collaboration with L. Massidda (CRS4, Pula (CA), Italy) and A. Mentrelli (CIRAM, Bologna, Italy). It is based on the idea to consider the interface embodied by particles with random motion. The average front emerges to be determined by the weighted superpostion of the solutions of the ordinary LSM with the particle probability density function as a weight function. This formulation being based on the LSM has the same striking property of the LSM to be compatible with every type of geometry and flow and to be easily modifiable to include more detailed and correct physics. This approach has emerged to be promising both for its favorably comparison with experimental data (Figure 1) and also for its high potentiality in pattern formation (Figure 2).

Figure 1. Experimental validation of the proposed
approach in turbulent premixed combustion
[Pagnini & Bonomi, Phys. Rev. Lett. 107, 044503 (2011)].

Figure 2. Wildland fire propagation as modelled by the LSM (top) and by the present approach including turbulent heat transfer (middle) and both turbulent heat transfer and fire spotting (bottom); without (left) and with (right) firebreak lines.