A recent adaptive finite element algorithm classified as Runge-Kutta FEM, formulated for Euler equations, has been reproduced in this paper to investigate scheme properties as well as performance. The procedures described herein is based on the Standard Galerkin Method for two space dimensions. Two schemes are presented for error estimation associated with mesh refinement strategy. The capability of unrefinement (adaptively coarsening the mesh) is also included. The methods do not require a structured mesh and are therefore applicable to quite general geometries.
Numerical application includes four basic compressible flow problems formulated on structured meshes and scramjet inlet flow problem on unstructured meshes. supersonic flow over a 20 degree ramp, supersonic flow over a 4% circular arc bump, transonic flow over a 10% circular arc bump, and impingement of shock on leading edge of cowl lip constitutes the first four test problems. The scramjet inlet flow is solved, on the other hand, for the inlet Mach number 2.85 and 5.0.
