A contribution to multidimensional upwinding and fluctuation splitting - Nonlinear matrix schemes

This paper provides a contribution towards developing robust and accurate multidimensional upwind schemes based on a characteristic decomposition of the Euler equations and a fluctuation splitting space discretization. A new nonlinear matrix scheme is presented which extends the concept of nonlinear advection velocity to the Euler system. The scheme is shown to provide second-order-accurate results for subsonic, transonic and supersonic flows, while capturing shocks monotonically.