NUMERICAL RESOLUTION OF A FREE BOUNDARY PROBLEM IN A HETEROGENEOUS MEDIUM
Keywords:
free boundary problem, heterogeneous medium, traveling wave solution, system of parabolic/Hamilton-Jacobi equations, numerical resolution, finite elementDOI:
https://doi.org/10.17654/0975045225007Abstract
This paper investigates the propagation of a flame front in a periodic heterogeneous solid medium under the effect of temperature. The system of PDEs for the temperature and the interface form a free boundary system composed of a parabolic equation coupled with a Hamilton-Jacobi type equation. We propose a monotonous and stable numerical scheme and verify numerically that the numerical solution converges to a traveling wave solution for large time.
Received: November 6, 2024
Revised: December 20, 2024
Accepted: December 25, 2024
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