A discontinuous hp finite element method for the Euler and Navier-Stokes equations

This paper introduces a new method for the solution of the Euler and Navier -Stokes equations, which is based on the application of a recently develope d discontinuous Galerkin technique to obtain a compact, higher-order accura te and stable solver. The method involves a weak imposition of continuity c onditions on the state variables and on inviscid and diffusive fluxes acros s inter-element and domain boundaries. Within each element the field variab les are approximated using polynomial expansions with local support; theref ore, this method is particularly amenable to adaptive refinements and polyn omial enrichment. Moreover, the order of spectral approximation on each ele ment can be adaptively controlled according to the regularity of the soluti on. The particular formulation on which the method is based makes possible a consistent implementation of boundary conditions, and the approximate sol utions are locally (elementwise) conservative. The results of numerical exp eriments for representative benchmarks suggest that the method is robust, c apable of delivering high rates of convergence, and well suited to be imple mented in parallel computers. Copyright (C) 1999 John Wiley & Sons, Ltd.