An adaptive Cartesian grid method for unsteady compressible flow in irregular regions (Q1902384)

The authors describe an explicit adaptive Cartesian grid method for the solution of the Euler equations for two- and three-dimensional compressible flows in irregular domains. In each cell the surface elements of the body are treated as an interface. A single grid algorithm and a coupling with a mesh refinement scheme are presented, and results are shown for comparison with a Prandtl-Meyer flow, an unsteady shock reflection, an axisymmetric flow past a cone, and a three-dimensional flow past a cone-cylinder combination. The paper ends with an outlook on future work, in which a method is sketched out, through which current limitations on geometric complexities can be overcome.