Finite element solution of compressible viscous flows using conservative variables Original Research Article

A finite element method for solving the compressible Navier-Stokes equations is presented. These equations are solved in conservation form and using conservative variables. Appropriate finite element approximations are discussed when a Galerkin variational formulation is used. For high-speed flows, the formulation is stabilized using the stream line upwind Petrov-Galerkin method for which we propose an analytical expression for the matrix τ. A new discontinuity-capturing operator is also proposed to accurately solve flow problems exhibiting sharp gradients. The non-linear systems of equations arising from the discretization are solved using an iterative strategy based on the generalized minimal residual (GMRES) algorithm. Numerical results for transonic and supersonic flows are presented that demonstrate the effectiveness of the proposed finite element method.