A new upwind finite element formulation is presented for the two dimensional compressible Euler equations with unstructured mesh. The basis of formulation is the exponential weighting function derived from the variational principle by Shen. A new mesh Peclet number is defined for each edge of the triangular element using the Jacobian of flux vector and edge length. To prevent spurious oscillation around shock a shock capturing term is included. A newly developed FCT technique suitable for Petrov-Galerkin type FEM and an edge-swapping technique are introduced to enhance its discontinuity capturing ability. Also an adaptive remeshing is applied to reduce computing time and memory requirements.
The accuracy and the discontinuity capturing ability of present method are demonstrated in test cases of supersonic flows over ramp and wedge, reflecting shock and a transonic flow over NACA0012 airfoil.
