Approximate Riemann solvers and waves on a nonlinear elastic string

If variable boundary conditions are imposed on a stretched nonlinear elastic string, elementary methods of solution fail, in general. If shocks develope, characteristic theory cannot be used after the shock forms. In the present note we examine the behaviour of the resultant wave motion using Godunov type numerical schemes with various Riemann solvers. Approximate Riemann solvers of the form suggested by Harten, Lax, and Van Leer [6] are compared with an exact solver. Up to the first breakdown time, the solutions may be compared to the solution obtained from characteristic theory. © 1991.