Year: 2013
Author: S. Clain, M. Djenno Ngomanda
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 1 : pp. 99–115
Abstract
The paper is dedicated to the construction of an analytic solution for the level set equation in $R^2$ with an initial condition constituted by two half-planes. Such a problem can be seen as an equivalent Riemann problem in the Hamilton-Jacobi equation context. We first rewrite the level set equation as a non-strictly hyperbolic problem and obtain a Riemann problem where the line sharing the initial discontinuity corresponds to the half-planes junction. Three different solutions corresponding to a shock, a rarefaction and a contact discontinuity are given in function of the two half-planes configuration and we derive the solution for the level set equation. The study provides theoretical examples to test the numerical methods approaching the solution of viscosity of the level set equation. We perform simulations to check the three situations using a classical numerical method on a structured grid.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-IJNAM-560
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 1 : pp. 99–115
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Riemann problem Cauchy problem level set equation analytical solution half-planes problem.