A Petrov-Galerkin Technique for the Solution of Transonic and Supersonic Flows

Abstract

This paper is both the description of a streamline-upwid/Petrov-Galerking (SUPG) formulation and the documentation of the devopment of a code for the finite element solution of transonic and supersonic flows. The aim of this work is to present a formulation to be able to treat domanins of any configuration and to use the appropriate physical boundary conditions, which are the major stumbling blocks of the finite difference schemes.
The implemented code has the following features: The Hughes SUPG-type formulation with an oscillation-free shock-capturing operator, adaptive refinement, explicit integration with local time-step and hourglassing control. An automatic scheme for dealing with slip boundary conditions and a boundary-augmented lumped mass matrix for speeding up convergence.
In Section 1 we will describe briefly the theoretucak background of the SUPG formulation. In Section 2 it is described how the foregoing formulation was used in the finite element code and which are the appropriate boundary conditions to be used. Finally in Section 3 we will show some results obtained with this code.