## 3 Applications
### Numerical Parameters
#### 3.2.2 Eulerian Model Parameters  
Among the most important parameters in the simulation of wave propagation, breaking and run-up using the non-hydrostatic D/C Galerkin model are the breaking waves parameters. Wave overturning and small-scale processes related to wave breaking cannot be reproduced in depth-averaged models, consequently some kind of closure is required. Usually, this closure involves two steps. The first is a trigger mechanism to locate in space and time the limits of breaking. The second is a mechanism that generates the dissipation of energy in the model. The dissipation of energy is accomplished by shifting locally to the depth-integrated hydrostatic shallow water Equations, modeling breaking wave fronts as shocks. This procedure was firstly presented by [PERSON] et al. (2018) as the hydrostatic front approximation (HFA) method for the modeling of wave breaking. For the trigger mechanism of wave breaking, two different criteria are used. The first criterion is used for solitary waves and establish that wave breaking occurs when \(\frac{\kappa}{\mathrm{h}}>0.8\)([PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2018). This criterion is referred to as the local criterion in [PERSON] et al. (2018). All of the elements containing a node with the wave breaking condition \(\frac{\kappa}{\mathrm{h}}>0.8\) are shifted to the hydrostatic mode by making \(\mathrm{q}_{\mathrm{b}}^{n+1}\,=0\), \(\frac{\partial\mathrm{q}_{\mathrm{b}}^{n+1}}{\partial\kappa}=0\), \(\frac{\partial\mathrm{q}_{\mathrm{b}}^{n+1}}{\partial y}=0\) and \(\mathrm{w}_{\xi}=\mathrm{w}_{\mathrm{b}}=0\) in the element. The second criterion is used for regular waves and was first introduced by [PERSON] et al. (2014)([PERSON] et al., 2018) as the surface variation criterion. A node is flagged if \(\frac{\frac{\omega_{\mathrm{f}}}{\mathrm{h}}}{\sqrt{\mathrm{g}\mathrm{h}} \mathrm{h}}>G\), with \(G\in[0.3,\,0.65]\) depending on the type of breaker. Flagged nodes are clustered to form a breaking region. All of the elements containing a flagged node are shifted in the element to hydrostatic mode by making \(\mathrm{q}_{\mathrm{b}}^{n+1}\,=0\), \(\frac{\partial\mathrm{q}_{\mathrm{b}}^{n+1}}{\partial\kappa}=0\), \(\frac{\partial\mathrm{q}_{\mathrm{b}}^{n+1}}{\partial y}=0\) and \(\mathrm{w}_{\xi}=\mathrm{w}_{\mathrm{b}}=0\). More details regarding the implementation of this detection criterion can be found in [PERSON] et al. (2018)([PERSON] et al., 2018). The boundaries conditions in all tests are: at wall boundaries the gradients of water elevations and the velocities normal to the boundary are set to zero; at open boundaries, the water elevations are determined by a Sommerfeld radiation condition; at wave inflow boundaries, the water elevations and velocities are calculated with the corresponding inflow wave analytical formula; no boundary conditions are required for the non-hydrostatic pressure. In the simulation of tests T1 and T2, the experiments of [PERSON] and [PERSON] (2018) were replicated with a numerical domain of 32 m long and 0.24 m wide and the initial water depth was 0.70 m. Square elements with sizes \(\Delta\mathrm{x}=\Delta\mathrm{y}=0.04\) m were considered, resulting in 5607 nodes. The surface variation criterion was used as the trigger mechanism of wave breaking. The parameter ywas chosen to replicate the waves before and after the breaking zone (consequently trying to match the total energy dissipation of wave breaking with the HFA method). In test T3, we analyzed the tests of [PERSON] (2018) and [PERSON] et al. (2018) with a numerical domain of 45 m long and 0.2 m wide and a water depth of 1 m. Square elements with \(\Delta\mathrm{x}=\Delta\mathrm{y}=0.05\) m were used, leading to 4505 nodes. A Manning coefficient of \(n=0.01\) was established to represent the finished concrete surface of the reef model. The local criterion was utilized as the trigger mechanism of wave breaking.