Adaptively-refined Cartesian-mesh approaches were employed for the computation of Euler equations

solid wall boundary was introduced by a discrete forcing immersed boundary approach

and shape of cut cell kept in accordance with that in the flow field

which efficiently relieved the time step restriction of small cut cell.To remedy the numerical suction peak

a novel method for reflection of ghost point along with interpolation scheme were devised which were applied for adaptively-refined Cartesian-mesh.Inviscid flows around RAE2822 airfoil

double NACA0012 airfoil and Suddhoo three-element airfoil were simulated and compared with published theoretical and single/multi domain structured mesh results.The results show that solid wall is efficiently resolved by the current discrete forcing immersed boundary approach and flows around complex geometries are adequately simulated by adaptively-refined Cartesian-mesh approaches.