**3.1.3 Artificial dissipation**

In the cell-centered spatial discretization schemes, such as the one described above which is non-dissipative, therefore, artificial dissipation terms are added. The approach of (Jameson et al., 1981) is adopted to construct the dissipative terms consisting of blend of second and fourth differences of the vector conserved variables. Fourth differences are added everywhere in the flow domain where the solution is smooth, but are 'switched off' in the region of shock waves. A term involving second differences is then 'switched on' to damp oscillations near shock waves. This switching is achieved by means of a shock sensor based on the local second differences of pressure. Since the computational domain is structured. The scaling quantity confirms the inclusion of the cell volume in the dependent variable. The blend of second and fourth differences provides third-order back ground dissipation in smooth region of the flow and first-order dissipation in shock waves.
