A high-resolution numerical method for flow computations using Building-Cube Method (BCM) is developed. BCM is a block structured Cartesian mesh approach proposed as the next generation CFD algorithm by one of the authors. One of the critical problem of conventional Cartesian mesh approach is the wall boundary treatment. The gridless-type boundary treatment is construcrted to resolve boundary layer efficiently in a Cartesian grid. One of the attractive features of BCM is easy construction of high-order computational schemes. Compact differencing scheme with low-pass filtering and high-order Lagrange interpolation for the communication between cube blocks are constructed and the capability of the developed approach is demonstrated through a 2-D inviscid vortex advection problem. The proposed method is applied to the aeroacoustic problem.