Nomenclature Cd Drag coefficient C f Skin friction coefficient Cl Lift coefficient

This work presents a new viscous wall boundary condition technique for embedded Cartesian grid schemes in order to model laminar viscous flows. The development of viscous effects modeling using pure Cartesian grids with cut cells at the surface has been hampered by the widely varying control volume sizes associated with the mesh refinement and the cut cells associated with the solid surface. This scheme removes the cells adjacent to the surface from the control volume formulation. These cells are instead solved via an interpolation technique which utilizes the wall boundary conditions to build the interpolating functions. Two different interpolation techniques are presented, one without considering wall curvature and one considering wall curvature. Results are compared to subsonic and supersonic two-dimensional airfoil cases