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A class of robust numerical schemes to compute front propagation
Nicolas Therme1
1 Université de Nantes, Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629, 2 rue de la Houssinière, BP 92208, 44322 Nantes, France
The SMAI Journal of computational mathematics, Volume 4 (2018), pp. 375-397.

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.

Published online:
DOI: 10.5802/smai-jcm.39
Classification: 35F21, 65N08, 65N12
Keywords: Finite volumes, Hamilton-Jacobi, Stability, Convergence

Nicolas Therme 1

1 Université de Nantes, Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629, 2 rue de la Houssinière, BP 92208, 44322 Nantes, France 
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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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