3.1.2. Computational Mesh

The computational mesh is generated entirely within the automatic facilities of Star-CCM+. As stated earlier, the near-wall mesh is generated so that *y*<sup>+</sup> < 1 over the wetted area of the ship. This is achieved via the prism layer mesher, offered by Star-CCM+. It should be noted that no prism layer refinement has been applied to the side walls and canal bottom. Therefore, wall functions are employed on these boundaries. The choice of background and overset mesh is of critical importance. This must be done in a way that enables the solver to adequately capture flow properties as they transition from the background into the overset mesh. The cell distribution of each domain is depicted graphically in Figure 4, whereas Figure 5 depicts the *y*<sup>+</sup> distribution on the hull at a physical time of 40 s for the *Fh* = 0.77 case.

**Figure 4.** Three-dimensional depiction of the computational mesh.

**Figure 5.** The *y*<sup>+</sup> distribution on the ship hull at *Fh* = 0.77, sampled at 40 s physical time.

The arrangement of the mesh does not vary across case studies; the total cell numbers for each canal are shown in Table 3. The circa 8 million cell difference between the two adopted canals is a direct result of the smaller wetted volume occupied by the Suez Canal.


Figure 4 also depicts the manner in which the mesh coarsens as the distance from the waterline is increased. This gradual coarsening is implemented to reduce the overall number of computational cells.

#### 3.1.3. Time-Step Selection

Time-step selection is of high importance in CFD. In this respect, the Courant–Friedrichs–Lewy (CFL) number may be used as an assessment criterion. The CFL number is defined as the product of the flow speed and time-step, divided by the mesh size [29]. As a fluid parcel propagates through the mesh, one would ideally aim to capture its properties at each cell. This is satisfied when CFL < 1. Since the mesh is kept identical for all cases, the highest speed can be used to assess the CFL condition. Moreover, a CFL condition onto the background domain is not a meaningful metric, since the majority of the fluid is static. Instead, the CFL number within the overset box is monitored throughout the duration of the simulation.

Typically, when solid body motion is present, the time-step requirements are relatively low. In this work, a trial with a time-step of 0.0035*L*/*U*, where *L* is the ship length and *U* is the ship speed in m/s was used. The results indicated satisfactory agreement with experimental data, as will be demonstrated in the following section. For this reason, the time-step is set at 0.0035*L*/*U* for all simulations. For the highest speed, the average CFL within the overset domain did not exceed 0.7, which is considered adequate for a first-order temporal discretisation scheme. It should also be borne in mind that if the time-step is too low, severe numerical noise may be noticed in the solution time-history [38].
