A stabilized Powell-Sabin finite-element method for the 2D Euler equations in supersonic regime

摘要

In this paper is presented a Powell-Sabin finite-elements scheme (PS-FEM) for the solution of the 2D Euler equations in supersonic regime. The spatial dis-cretization is based on PS splines, that are piecewise quadratic polynomials with a global C 1 continuity, defined on conforming triangulations. Some geometrical issues related the practical construction of the PS elements are discussed, in particular, the generation of the control triangles and the imposition of the boundary conditions. A stabilized formulation is considered, and a novel shock-capturing technique in the context of continuous finite-elements is proposed to reduce oscillations around the discontinuity, and compared with the classic technique proposed by Tedzuyar [1]. The code is verified using manufactured solutions and validated using two challenging numerical examples, which allows to evaluate the performance of the PS discretization in capturing the shocks.