Paper presented at the 8th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Mauritius, 11-13 July, 2011.
We consider the classical Scramjet test problem for the compressible
Euler equations. Our objective is the comparison
of different mesh refinement techniques: on the one hand hierarchical
refinement of quadrilateral meshes with hanging
nodes, on the other hand isotropic and anisotropic triangular
meshes. Discretization of the Euler equations written in conservative
variables is done by a standard discontinuous finite
element (Galerkin) method. In each step of the algorithm, an
error indicator is used to guide the mesh modification. Here
we implemented as criterion for quadrilateral mesh refinement,
indicators based on the physical variables jumps, as
they are usually used in practice. Comparison is done with
respect to the resolution of certain physical features, and also
with respect to CPU-time, which appears to be fair, since the
different algorithms are programmed within the same program
handling the different ingredients in a uniform manner.
For the anisotropic mesh refinement algorithm we use
BAMG. All other algorithms have been implemented by the
authors in the C++-library Concha.