Prépublication du DMI numéro 00-01 (15/03/2000)

A SPLITTED GODUNOV SCHEME FOR SOLVING A SYSTEM OF ELASTICITY IN A NONCONSERVATIVE FORM.
MOPHOU, Gisèle - Groupe de Recherche de Mathématiques, Université des Antilles et de la Guyane, Pointe-à-Pitre, F-97159 cedex
POULLET, Pascal - Groupe de Recherche de Mathématiques, Université des Antilles et de la Guyane, Pointe-à-Pitre, F-97159 cedex

In this paper, we develop a theoretical study for a modeling of elasticity in one dimension, in order to construct a numerical scheme for solving the Riemann problem. The nonconservative form of our model system requires the use of a well adapted theory for giving sense to our problem. We choose a framework of generalized functions for solving a scalar hyperbolic equation with a discontinuous coefficient $ \,\,\sigma_t +u\sigma_x \approx 0,\,\,$ where $\,\,u\,\,$ is the velocity, solution of Burgers equation. After an explicit solution of the Riemann problem, we derive a Godunov splitted scheme for computing an approximate solution of the Cauchy problem. We prove some stability properties for the scheme and its convergence to a generalized solution.