# Numerical Study of Wave Effect on Aircraft Water-Landing Performance
## 3 Validation of Numerical Model  
### Validation of Numerical Wave  
The regular wave case is carried out to validate the accuracy of the numerical wavemaker. The wave parameters used in this section are based on the hypotheses of non-breaking wave [38] and intermediate water depth [39]. Specifically, as detailed in Section 2.3, wave height is 2.0 m, wave length is 40 m, wave period is 5.06 s and water depth is 10 m. Accordingly, the wave steepness \(H/L\) (the ratio of wave height to wavelength) and \(d/L\) (the ratio of water depth to wavelength) are approximately 0.05 and 0.25. Thus, the wave is non-breaking and the wave phase speed has only a negligible influence due to the water depth. The methodology given in Section 2 is applied to derive the analytical regular wave components. These wave components are used to determine the wave elevation at the inlet boundary, as given by Equation (4), and the corresponding horizontal and vertical water particle velocities are given by Equations (5) and (6). These quantities are then inputted into the CFD simulation through STAR CCM+ package.  
Figure 3 shows the computational grid of regular wave case. The grid used in this section is structured and locally refined at the air-water two-phase interface to improve the accuracy of wave simulation. Particularly, a very fine grid is equally discretized in \(x\),  
Figure 2: Computational domain and initial flow field of aircraft water-landing simulation: (**a**) calm water-landing; (**b**) regular wave landing.  
and \(z\) directions within the region of wave elevated from \(z=-H\) to \(z=H\) as shown in Figure 3b. Furthermore, a cell size growth rate of 1.2 along the wave propagated direction is adopted in the absorbing zone, thus reducing the total cell number and computational cost. Based on the mesh and time step independence studies by [28; 33], the refined grid resolution near the interface and time step in this section are adopted as \(L/\triangle x=60\), \(L/\triangle y=60\), \(H/\triangle z=40\) and \(T/dt=1000\). Three wave elevation probes are set up at different distances from the inlet of the domain with an interval distance \(L=40\) m, as shown in Figure 3a.  
The comparisons between the wave elevations obtained by the CFD simulation and the analytical calculation are shown in Figure 4. The target wave elevations colored by black lines are the resolved waves given by the aforementioned analytical wave in Section 2.2, and the wave elevation depicted with red curves are the result of numerical simulation. The numerical wave elevations at probe P1-P3 match well with the analytical values. Therefore, the combination of the wavemaker and selected grid resolution and time step is able to meet the requirements of numerical wave generation.  
Figure 4: Comparison of 3D regular wave elevations in time: (**a**) probe P1 (\(x=0\) m); (**b**) probe P2 (\(x=40\) m); (**c**) probe P3 (\(x=80\) m).  
Figure 3: Computational grid of regular and unidirectional wave cases: (**a**) domain grid and position of wave elevation probe; (**b**) local refined grid near the air-water interface, green surface and curve showing the desired wave.