High-Resolution Numerical Scheme for Simulating Wildland Fire Spread

Vasileios G. Mandikas () and Apostolos Voulgarakis
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Vasileios G. Mandikas: School of Production Engineering and Management, Technical University of Crete, 73100 Chania, Greece
Apostolos Voulgarakis: School of Chemical and Environmental Engineering, Technical University of Crete, 73100 Chania, Greece

Mathematics, 2025, vol. 13, issue 22, 1-21

Abstract: Predicting wildland fire spread requires numerical schemes that can resolve sharp gradients at the fireline while remaining stable and efficient on practical grids. We develop a compact high-order finite-difference scheme for Hamilton–Jacobi level-set formulations of wildfire propagation, based on the anisotropic spread law of Mallet and co-authors. The spatial discretization employs a compact finite-difference derivative scheme to achieve spectral-like resolution with narrow stencils, improving accuracy and boundary robustness compared with wide-stencil ENO/WENO reconstructions. To control high-frequency artifacts intrinsic to non-dissipative compact schemes, an implicit high-order low-pass filter is incorporated and activated after each Runge–Kutta stage. Convergence is verified on the eikonal expanding-circle benchmark, where the method attains the expected high-order spatial accuracy as the grid is refined. The proposed scheme is then applied to wind-driven wildfire simulations governed by Mallet’s non-convex Hamiltonian, including a single ignition under moderate and strong wind. A complex topology test case is also considered, involving two ignitions that merge into a single front with the evolution of an internal unburnt island. The results demonstrate that the proposed method accurately reproduces fireline evolution even on coarse grids, achieving accuracy comparable to fifth-order WENO while maintaining superior fidelity in complex fireline topologies, where it better resolves multi-front interactions and topological changes in the fireline. This makes the method an efficient, accurate alternative for level-set wildfire modeling and readily integrable into existing frameworks.

Keywords: wildland fire spread; front propagation; level set method; Hamilton–Jacobi equations; compact finite differences; low-pass high-order filter (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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