Designing an efficient solution strategy for fluid flows. I - A stable high order finite difference scheme and sharp shock resolution for the Euler equations

The numerical method presented underlies a novel general solution strategy for solving flows governed by the compressible Euler or Navier-Stokes equations, and gives attention to the treatment of discontinuities which lead to sharp shock resolution. Symmetrization of the equations, canonical splitting of the flux derivative vector, and difference operators satisfying a discrete analog of the integration-by-parts procedure are used in the formulation of the semidiscrete energy estimate. The positioning of the subgrids used around discontinuities or sharp gradients, and the computation of the viscosity, are effected by a multiscale wavelet analysis-based detection algorithm for the pressure grid function. (AIAA)