## 5 Choosing the Proper Mesh Element  
Modeling tasks using acoustic elements requires a properly defined shape of elements and mesh density. This has a significant impact on the task size, time and accuracy of calculations. The FEM mesh should be chosen in the right way to reflect the waveform. Otherwise, the wave may be omitted in the calculation. A large variety of finite elements allows you to define the acoustic medium in the right way to get the results most similar to reality [1]. Analyzing the available literature and documentation [17; 18; 36; 37], it can be stated that for elements with linear shape functions, it is recommended to take their size at least six times smaller than the wavelength, while for square functions the element size should be taken about three times smaller than the wavelength. Calculations related to underwater explosions should be made using square shape functions. The length of the shock wave necessary to determine the size of the element can be determined by the relationship:  
\[l=c_{o}t_{i} \tag{15}\]  
where:  
\(c_{o}\)--sound speed in medium, m/s  
\(t_{i}\)--time of the pressure pulse, s  
However, during an underwater explosion, acoustic elements interact with structural elements. Then numerous wave reflections are created that can interfere with each other. In this case, it is difficult to determine the length of the newly formed wave. The density of finite elements should then be selected by subsequent iterations [3]. The study analyzes how the size and type of the FEM element affects pressure values and the pressure pulse waveform. For this purpose, the cubic geometry of the acoustic medium with a length of 0.4 m was modeled (Figure 10). Then, using the formula for the pressure waveform developed by Geers & Hunter, the acoustic medium was loaded with the shock wave. During the research, the mesh density and shape functions of FEM elements were changed to check the impact of these changes on the incident wave. Acoustic medium were modeled using the AC3D8R (3D acoustic hexagonal 8-nodes)  
Figure 9: Acoustic medium subregions used in in computer aided engineering (CAE) programs. Figure 11 shows pressure waves simulated as a 100 kg TNT underwater explosion incident on various FEM elements 10 m away from the epicenter. A comparison of the incident wave on the hexagonal and tetragonal mesh with a density of 0.1 m is presented. The graph shows that in both cases the pressure waveform is significantly disturbed. Maximum pressure value according to the mathematical model has not been reached. In addition, the wave was distributed in time, which ceased to be a pressure impulse. The difference can also be seen depending on the type of FEM element used. For hexagonal elements, the wave is significantly flattened, and the maximum pressure is underestimated more than for tetragonal elements. In both cases, the pressure wave was not reflected satisfactorily. This means that in strength calculations using a mesh with a density greater than 0.1 m, the structure may be loaded with incorrect pressure. It is worth noting that despite loading only by the positive phase pressure pulse, a negative phase also appeared in the FEM mapping, which is a desirable effect for this type of phenomenon. Figure 12 presents a comparison of the incident wave and its mapping by 0.005 m hexagonal and tetragonal elements. In analyzing the chart, it can be noticed that both the maximum value of the incident pressure and its time course is preserved. In the case of tetragonal elements, the pressure in the acoustic medium is even higher than the incident wave. The most accurate wave mapping was obtained by using a FEM hexagonal mesh with a density of 0.005 m. Further reduction of the mesh size causes a significant increase in the calculation time; however, it does not affect the results obtained. In this case, a negative phase was also noted in the response of the acoustic medium. It was also analyzed how the shape and size of elements affect the nature of the incident wave.