Unified construction of finite element and finite volume discretizations for compressible flows

A framework for the construction of node-centred schemes to solve the compressible Euler and Navier-Stokes equations is presented. The metric quantities are derived by exploiting some properties of CO finite element shape functions. The resulting algorithm allows to implement both artificial diffusion and one-dimensional upwind-type discretizations. The proposed methodology adopts a uniform data structure for diverse grid topologies (structured, unstructured and hybrid) and different element shapes, thus easing code development and maintenance. The final schemes are well suited to run on vector/parallel computer architectures. In the case of linear elements, the equivalence of the proposed method with a particular finite volume formulation is demonstrated