Petrov‐Galerkin finite element model for compressible flows

Abstract

Abstract A Petrov‐Galerkin method for the solution of the compressible Euler and Navier‐Stokes equations is presented. It is based on the introduction of an anisotropic blancing diffusion in the direction of the local direction of propagation of the scalar variables. The local direction in which the anisotropic diffusion is introduced is uniquely determined, and the magnitude of the balancing diffusion is automatically calculated locally using a criterion that is optimal for one‐dimensional transport equations. The algorithm has been implemented using four‐noded bilinear elements with forward Euler and second‐order Runge‐Kutta methods of integration in time. Several applications are presented and show the stability and approximation properties of the method.