Characteristic-type formulation of the Navier-Stokes equations for high order upwind schemes

We propose a formulation of the three-dimensional Navier-Stokes equations, which expresses the inviscid part of the equations as a decomposition into several plane waves which are aligned with the numerical grid. The resulting equations are very well suited to numerical solution using compact high order upwind schemes. Boundary conditions and blockwise decomposition of the computational domain are particularly straightforward. Such advantages make the formulation attractive, even when using central or pseudospectral differencing methods. Numerical examples are presented.