Despite the high cost of memory and CPU time required to resolve the boundary layer, a viscous unstructured grid solver has many advantages over a structured grid solver such as the convenience in automated grid generation and vortex capturing by solution adaption. In present study, an unstructured Cartesian grid solver is developed on the basis of the existing Euler solver, NASCART-GT. Instead of cut-cell approach, immersed boundary approach is applied with ghost cell boundary condition, which can be easily applied to a moving grid solver. The standard $k-{varepsilon}$ model by Launder and Spalding is employed for the turbulence modeling, and a new wall function approach is devised for the unstructured Cartesian grid solver. Developed approach is validated and the efficiency of the developed boundary condition is tested in 2-D flow field around a flat plate, NACA0012 airfoil, and axisymmetric hemispheroid.