A finite element formulation of compressible flows using various sets of independent variables Original Research Article

This paper presents a finite element method for the simulation of compressible flows. The Navier–Stokes and Euler equations are solved in the conservation form using various sets of independent variables. A variational formulation is developed based upon a variant of the Petrov–Galerkin method, and uses a shock-capturing operator. An adaptive algorithm based on a particular residual norm is proposed. Several numerical examples are presented to demonstrate the performances of each set of variables in solving compressible high-speed flows.