The numerical solution of impact problems are oftentimes problematic due to the presence of spurious oscillations in the resulting functions. Eliminating these oscillations is complicated and requires a damping effect to be exerted in the solution. In the proposed method, viscous damping has been applied with a special damping character. Using this scheme, the numerical solution of 2D impact problems contains significantly less oscillations compared to other widely applied methods. In quantitative terms, an improvement of 2.42% and 9.29% or more can be achieved in the time evolution of the velocity and the pressure, respectively.