**7. Conclusions**

406 Computational Simulations and Applications

Figure 12 presents the pressure coefficient contour around the ship hull at the level of the free surface. The low pressure regions can be seen in blue at the wave crests of the divergence wave and the high pressure regions can be seen in red at the bow of the ship and

Fig. 12. Free-surface elevation around the Series-60 hull, *RL*=1.0x103, *Fn*=0.25 and pressure

Fig. 13. Drag coefficient on the Series-60 hull, *RL*=1.0x103, *Fn*=0.25.

Figure 13 shows the total (in red), frictional (in black), and pressure (in blue) drag coefficients on the ship hull. After time=4, the steady state is obtained and the drag

at the wave trough.

field.

coefficients are constant.

An upwind and TVD numerical scheme was implemented to solve the unsteady slightly compressible Navier-Stokes equations for the free-surface flow around ship hulls. The physical domain is discretized in a Cartesian grid and the boundary condition on the body surface is implemented using the Immersed Boundary Method (IBM).

The implemented code is parallelized using MPI to be run in an arbitrary number of computers of a cluster. The numerical code was verified for the flow around a sphere, and a Series-60 hull.

The results obtained for the sphere were compared to numerical and experimental data from literature showing the good quality of the numerical results. The numerical results obtained for the ship hull were not compared to other numerical and experimental data because of the difficulty to find those data for lower Reynolds number. However, the numerical results agree qualitatively well to experiments.

Next phase of development will include the implementation of the *k-* turbulence model and validation of the numerical code for higher Reynolds numbers and configurations of practical interest, such as, resistance to motion, moonpool – free decay and forced motion, wave run-up and air gap, and wake and shadow flows.
