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.
DOI: 10.5802/smai-jcm.39
Keywords: Finite volumes, Hamilton-Jacobi, Stability, Convergence
CC-BY-NC-ND 4.0
@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},
pages = {375--397},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {4},
year = {2018},
doi = {10.5802/smai-jcm.39},
mrnumber = {3883674},
zbl = {1416.65299},
language = {en},
url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.39/}
}
TY - JOUR AU - Nicolas Therme TI - A class of robust numerical schemes to compute front propagation JO - The SMAI Journal of computational mathematics PY - 2018 SP - 375 EP - 397 VL - 4 PB - Société de Mathématiques Appliquées et Industrielles UR - https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.39/ DO - 10.5802/smai-jcm.39 LA - en ID - SMAI-JCM_2018__4__375_0 ER -
%0 Journal Article %A Nicolas Therme %T A class of robust numerical schemes to compute front propagation %J The SMAI Journal of computational mathematics %D 2018 %P 375-397 %V 4 %I Société de Mathématiques Appliquées et Industrielles %U https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.39/ %R 10.5802/smai-jcm.39 %G en %F SMAI-JCM_2018__4__375_0
Nicolas Therme. 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/articles/10.5802/smai-jcm.39/
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