Fully conservative overset mesh to overcome the blunt body metric singularity in finite difference methods

Abstract

A fully conservative overset mesh method is proposed and applied to overcome the metric singularity at the symmetry line for blunt bodies, e.g., capsules and blunted cones, in general curvilinear coordinates. The overset mesh is placed automatically at the symmetry line by avoiding the collapse of the grid lines using a hexahedral structure in contrast to the prismatic structure of a body-orientated mesh. In addition, the grid points of the overset mesh coincide with those of the body-orientated mesh to avoid interpolation techniques to interchange the flow variables between the two meshes. This coincidence ensures the conservation of the flow variables and avoids uncertainties at the shock as the method is naturally conservative. The thin-layer Navier–Stokes equations for high Reynolds number flows are solved using an AUSM+ or an AUSMPW+ flux vector splitting in combination with a mesh adaption to capture the shock accurately. For verification purposes of the proposed method, a supersonic 2D-axisymmetric hemisphere cylinder is chosen and the results along the wall are verified. Furthermore, the conservative properties of the applied overset mesh method are shown and the results on the stagnation line are presented. In addition, a supersonic 3D calculation is investigated to show the applicability of the presented method for simulations with an angle of attack.