NUMERICAL-METHODS FOR THE SOLUTION OF NONLINEAR PARTIAL-DIFFERENTIAL EQUATIONS INVOLVING PRODUCTS OF DISTRIBUTIONS - HYDRODYNAMICS AND ELASTOPLASTICITY

We develop numerical methods of Godunov or Lax-Friedrichs type adapted to the case of ''nonconservative'' systems. These methods (even nonconservative Lax-Friedrichs) are based upon explicit solutions of the Riemann problem (quite rigorous from the mathematical viewpoint); one is confronted with ''products of distributions '' of the kind Y. delta (where Y is the Heaviside function and delta the Dirac measure). From a solution of the Riemann problem, we build numerical schemes for the solution of the Cauchy problem. We apply these techniques in the case of hydrodynamics and of elastoplasticity, that are treated by convection/propagation splittings.