Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
A fast level set method for propagating interfaces
Journal of Computational Physics
Numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains
Journal of Computational Physics
The fast construction of extension velocities in level set methods
Journal of Computational Physics
IEEE Transactions on Image Processing
Error correction for fire growth modeling
ICCSA'13 Proceedings of the 13th international conference on Computational Science and Its Applications - Volume 1
Journal of Computational Physics
Hi-index | 0.09 |
Level set methods are versatile and extensible techniques for general front tracking problems, including the practically important problem of predicting the advance of a fire front across expanses of surface vegetation. Given a rule, empirical or otherwise, to specify the rate of advance of an infinitesimal segment of fire front arc normal to itself (i.e., given the fire spread rate as a function of known local parameters relating to topography, vegetation, and meteorology), level set methods harness the well developed mathematical machinery of hyperbolic conservation laws on Eulerian grids to evolve the position of the front in time. Topological challenges associated with the swallowing of islands and the merger of fronts are tractable. The principal goals of this paper are to: collect key results from the two largely distinct scientific literatures of level sets and fire spread; demonstrate the practical value of level set methods to wildland fire modeling through numerical experiments; probe and address current limitations; and propose future directions in the simulation of, and the development of, decision-aiding tools to assess countermeasure options for wildland fires. In addition, we introduce a freely available two-dimensional level set code used to produce the numerical results of this paper and designed to be extensible to more complicated configurations.