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1 LMJL - Laboratoire de Mathématiques Jean Leray

Abstract : 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 an 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.

Keywords : Finite volume Hamilton-Jacobi MUSL Stability Convergence





Author: Nicolas Therme -

Source: https://hal.archives-ouvertes.fr/



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