A ROUGH GODUNOV SCHEME

We introduce a new finite volume scheme for 1D conservation systems. T his scheme, VFRoe, is based on the local resolution of linearized Riem ann problems. Unlike the well known Roe scheme, we don't prescribe to carry out any consistency relation with the conservation system. The n umerical flux is also defined by taking the physical flux at the inter face value of the linearized Riemann solver. This ensures that the sch eme is in conservation form and with consistent flux. We present some numerical tests.