A NOTE ON THE EFFECT OF ARTIFICIAL VISCOSITY ON SOLUTIONS OF CONSERVATION-LAWS

We consider central difference schemes with artificial viscosity terms for nonlinear hyperbolic systems. We analyze the influence of artific ial viscosity on solutions with shocks of nonlinear hyperbolic problem s in one dimension. Both stationary and moving shocks are considered. The analysis shows that for the Euler equations one can obtain well be haved (sharp) shock layers when a scalar viscosity coefficient is used . This is not true for a general system. Numerical computations of Bur gers' equation and the Euler equations are presented. They support the results from the linear theory.