In this work a class of finite volume schemes is proposed to numerically solve equations involving propagating fronts. They fall into the class of Hamilton-Jacobi equations. Finite volume schemes based on staggered grids and initially developed to compute fluid flows, are adapted to the G-equation, using the Hamilton-Jacobi theoretical framework. The designed scheme has a maximum principle property and is consistent and monotonous on Cartesian grids. A convergence property is then obtained for the scheme on Cartesian grids and numerical experiments evidence the convergence of the scheme on more general meshes.
Classification: 35F21, 65N08, 65N12
Keywords: Finite volumes, Hamilton-Jacobi, Stability, Convergence
@article{SMAI-JCM_2018__4__375_0,
author = {Nicolas Therme},
title = {A class of robust numerical schemes to compute front propagation},
journal = {The SMAI journal of computational mathematics},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {4},
year = {2018},
pages = {375-397},
doi = {10.5802/smai-jcm.39},
language = {en},
url={smai-jcm.centre-mersenne.org/item/SMAI-JCM_2018__4__375_0/}
}
Therme, Nicolas. A class of robust numerical schemes to compute front propagation. The SMAI journal of computational mathematics, Volume 4 (2018) , pp. 375-397. doi : 10.5802/smai-jcm.39. https://smai-jcm.centre-mersenne.org/item/SMAI-JCM_2018__4__375_0/
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