## 5 Conclusions  
The most widely used CFD approaches, namely the Eulerian and Lagrangian methods, are characterized by specific advantages and disadvantages. The most relevant advantages of Lagrangian approaches over Eulerian methods are the exact conservation of mass and momentum and the meshless properties. Moreover, the Lagrangian method gives detailed information of individual particles that can be crucial in many applications. In terms of computing cost, the Eulerian method was faster than the Lagrangian method. In fact, tracking a sufficient number of particles and analyzing them in the Lagrangian approach required more time than the Eulerian iterations.  
New research challenges on Computational Fluid Dynamics (CFD) are constantly on-going; in particular, recently, research has focused on coupling the Eulerian-Lagrangian techniques to combine the advantages of the individual models in a single model, thus increasing the accuracy, efficiency and regime of validity.  
The present study dealt with the comparison of the Lagrangian and Eulerian approaches in the simulation of regular breaking waves on a plane slope and solitary waves transformation, breaking and run-up. The performance of the numerical models was evaluated in accordance with experimental data.  
Both Eulerian and Lagrangian approaches were capable of simulating the analysed phenomena. However, the Lagrangian method showed more accuracy to reproduce the wave shape, both in deep waters and shoaling zones right up to the breaking region. Eulerian models cannot reproduce wave overturning exactly (e.g., only one water surface elevation value is permitted). Additionally, when using the HFA method in the case of regular waves, a high vertical resolution multilayer model is required to capture the hydrostatic shock of a breaking wave [91].  
For the tests T3-T4, the numerical results demonstrated that the Eulerian and Lagrangian methods have similar accuracy on predicting the solitary wave transformation, breaking and run-up processes.  
In this study, the hardware accelerated DualSPHysics code on a GPU was used; the new DualSPHysics code is a user-friendly platform designed to encourage researchers to use the SPH technique to investigate novel and real CFD problems that are beyond the scope of classical models. In recent years, DualSPHysics code has been shown to be accurate for simulating coastal engineering problems, with a continuous improvement in efficiency thanks to the exploitation of hardware such as GPUs for scientific computing.  
In this study, this important acceleration of the code using the new GPU technology has been observed by comparing its performance against the classic version of SPHysics code using a single core.  
[PERSON], [PERSON], [PERSON] performed the numerical modeling and analysed the results; [PERSON] conceived and coordinated the experiments; [PERSON] wrote the manuscript; [PERSON], [PERSON], [PERSON] and [PERSON] discussed and revised the paper. All authors have read and agreed to the published version of the manuscript.  
[PERSON] participated in this research thanks to the support of the Sistema Nacional de Investigacion (SNI), of Secretaria Nacional de Ciencia, Tecnologia e Innovacion (SENACYT), Panama.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no competing interests.