High-order immersed boundary method for inviscid flows applied to flux reconstruction method on a hierarchical Cartesian grid

We propose novel high-order immersed boundary methods for simulating inviscid flows on hierarchical Cartesian grids using the flux reconstruction (FR) method. A high-order distribution of physical quantities derived from the FR method is utilized to interpolate flow variables to maintain the same order near the wall as the interior domain. In particular, the wall's curvature effect is investigated in depth. We validate the accuracy through basic 2-D and 3-D simulations of inviscid flows. Consequently, the same accuracy as the order of the FR method (up to the fourth order) is achieved, including in the near-wall region.