On uniformly high-order accurate residual distribution schemes for advection-diffusion.
Abstract
We discuss preliminary results on the construction of uniformly high-order residual distribution $(\cal RD)$ type discretizations for steady advection-diffusion on unstructured grids. A properly designed scaling of the $(\cal RD)$ upwind stabilization with the physical viscosity allows to obtain schemes with uniform and arbitrary accuracy, on a very compact stencil. Second- and third-order examples are given to illustrate the potential of the approach.