*2.6. Convergence Tests*

Before conducting parametric studies of the wave-induced dynamic response in a porous seabed under wave loading, it is necessary to check the convergence of a newly proposed numerical model. The convergence tests are carried out in regards of the nodes distance size (∆*x*), shape factor (*c*) and the node number of the local region (*K*), which could have an influence on the numerical accuracy and computational efficiency.

Firstly, the small node distance size makes the results more accurate, however, it will result in enormous computational cost. As shown in Figure 2, the ∆*x* is equal to *L*/50, *L*/100, and *L*/200 respectively (*L* is the wavelength). The non-dimensional pore water pressures (*ps*/*p*0) are depicted, *p*<sup>0</sup> represents the amplitude of linear wave pressure at the seabed surface. From the figure, the result for the case of ∆*x* equal to *L*/50 is slightly difference from the others, while the results are almost the same for ∆*x* equal to *L*/100 and *L*/200, which indicate the model is convergent with a node distance that is smaller than *L*/100.

**Figure 2.** Time variation of dynamic pore water pressure in porous seabed under wave loading for different mesh conditions.

Next, the convergence test of shape factor is conducted.The shape factor is generally equal to 15–60 times the maximum Euclidean distance between two adjacent nodes by convention. The *c* adopts 3.975 (15 × ∆*x*), 7.95 (30 × ∆*x*), and 15.9 (60 × ∆*x*) separately. From the Figure 3, it can be conclude that the numerical results are not sensitive to the affect the shape factor on the consequence of the almost the same results obtained for this set of shape factors.

**Figure 3.** Time variation of dynamic pore water pressure in porous seabed under wave loading for different shape factors.

Moreover, the effect of the number of nearest neighbour nodes in a local region is examined. The dynamic pore water responses in a seabed are depicted in Figure 4 regards for the different numbers of neighbour nodes in the local region, which are 5, 9 and 13, respectively. From the figure, the result shows a good tendency during the whole process when *K* = 9. It also can be seen that for *K* = 5, the amplitude of the result is slightly different with the result of *K* = 9. When *K* = 13, the value of |*p<sup>s</sup>* |/*p*<sup>0</sup> is even beyond 1 after 2 s, which is obviously wrong. This condition might be the ill-condition in this case. Thus, the number of the nodes located in the local region is 9 in this study.

**Figure 4.** Time variations of dynamic pore water pressure in porous seabed under wave loading for different local region nodes number.
