A fast-marching like algorithm for geometrical shock dynamics

We develop a new algorithm for the computation of the Geometrical Shock Dynamics (GSD) model. The method relies on the fast-marching paradigm and enables the discrete evaluation of the first arrival time of a shock wave and its local velocity on a Cartesian grid. The proposed algorithm is based on a...

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Bibliographic Details
Published in:Journal of computational physics 2015-03, Vol.284, p.206-229
Main Authors: Noumir, Y., Le Guilcher, A., Lardjane, N., Monneau, R., Sarrazin, A.
Format: Article
Language:English
Subjects:
Algorithms
Computation
Dynamical systems
Fast-marching method
Finite difference method
Geometrical shock dynamics
Level set method
Mathematical analysis
Mathematical models
Nonlinear dynamics
p-system
Riemann problem
Shock wave
Singularities
Two dimensional
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Summary:We develop a new algorithm for the computation of the Geometrical Shock Dynamics (GSD) model. The method relies on the fast-marching paradigm and enables the discrete evaluation of the first arrival time of a shock wave and its local velocity on a Cartesian grid. The proposed algorithm is based on a first order upwind finite difference scheme and reduces to a local nonlinear system of two equations solved by an iterative procedure. Reference solutions are built for a smooth radial configuration and for the 2D Riemann problem. The link between the GSD model and p-systems is given. Numerical experiments demonstrate the efficiency of the scheme and its ability to handle singularities.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2014.12.019