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: https://doi.org/10.5802/smai-jcm.39
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}, pages = {375--397}, publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles}, volume = {4}, year = {2018}, doi = {10.5802/smai-jcm.39}, zbl = {1416.65299}, mrnumber = {3883674}, language = {en}, url = {smai-jcm.centre-mersenne.org/item/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/item/SMAI-JCM_2018__4__375_0/
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