Novel Method for Modelling Interface Propagation with Environmental and Engineering Applications

Reference: MTM2016-76016-R
Coordinator: BCAM - Basque Center for Applied Mathematics
Duration: 2017 - 2019
Funding agency: MINECO - Projects R&D&i - Challenges 2016
Type: National Project
Status: Closed


The project aims at introducing a new consolidated methodology based on a novel family of front propagation equations, to study systems characterised by an interface with random motion that neatly separates the spatial domain into inner and outer parts. The breakthrough of the proposed method is that the vitally important inclusion of the effects of random fluctuation allows for preserving the structure of existing operational codes and can be implemented directly as a step-by-step post-processing numerical routine. In particular, this fact preserves the proprietary of the software as in the case of commercial codes used by the industry. The remarkable applicability of the method motivates its use in areas of high interest to society. In this respect the method, after its physical foundation and mathematical investigation, is applied for modelling three phenomena of environmental and engineering interest: wildland fire propagation, turbulent premixed combustion and two-phase flow with application in marine renewable energy. The proposed method is based on the idea to split the motion of the front into a drifting part and a fluctuating part. This splitting allows specific numerical and physical choices that can improve the algorithms and the models. In particular, the drifting part is provided by a chosen existing method (e.g. the level set method (LSM) or the Discrete Event System Specification (DEVS) in the context of wildland fire, the G-equation in turbulent premixed combustion and the LSM in two-phase flow) and this permits the choice for the best drifting part for any specific application. The fluctuating part is the result of a comprehensive statistical description of the physics of the system and includes the random effects embodied in a probability density function accounting for the fluctuations around the front perimeter which is given by the drifting component. As a consequence, the fluctuating part can have a non-zero mean (for example, due to ember jump lengths in wildland fire propagation), which means that the drifting part does not correspond to the average mo- tion. This last fact distinguishes between the present splitting and the well-known Reynolds decomposition adopted in turbulence studies. Owing to the inclusion of random fluctuations, our methodology improves the output of operational front propagation codes by addressing shortcomings faced by them while dealing with random processes. Random fluctuations play an important role for example in the case of turbulent heat transfer and the landing of firebrands in wildfires, the curvature of wrinkled flames in turbulent premixed combustion or the turbulent velocity field of sea water in the case of floating wind turbines. As a further innovation, the derived novel family of equations, which presents a source term that was never considered previously in literature, shows characteristic aspects of both moving interface schemes (which generate a sharp function that is non zero inside a bounded domain and zero outside) and reaction-diffusion equations (whose solution is generally a continuous smooth function that has an exponential decay, and it is non zero in an infinite domain) and hence reconciles the two approaches which are considered alternative to each other.