High-order residual distribution and error estimation for steady and unsteady compressible flow

In the first part, an extension of upwind residual distribution schemes for high-order accurate solution of hyperbolic problems is introduced, based on the use of spatially varying distribution matrices. Following this, the application to adjoint-based error estimation for steady compressible flow is presented. Finally the resolution of acoustic wave propagation by a space-time residual distribution is discussed. The accuracy of the methodology is demonstrated on several test cases.