A Particle Finite Element approach to model sediment transport and erodible surfaces

  • Martini, Simone (Politecnico di Milano)
  • Corigliano, Alberto (Politecnico di Milano)
  • Cremonesi, Massimiliano (Politecnico di Milano)

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Land protection has always been and still remains an important topic to avoid environmental disasters. The last examples are the flood events in the Marche region on September 2022, in which there were 12 victims, 50 injured and 150 people displaced. In total, the monetary damage amounted to approximately EUR 2 billion. In this context, floods are a term that refers to the overflowing of a river that brings with it debris and sediment with the serious risk of damaging everything around it. The objective of this work is to simulate erosion and sediment transport to help studying the risks and consequences of such an event. To this purpose, the Navier-Stokes equations for the fluid are solved using the Particle Finite Element Method [1], integrating the sediment information as a scalar concentration variable. This addition was done in the form of a diffusion-transport equation, creating a mixture model [3]. The PFEM is based on the Lagrangian description of the domain: the mesh follows the movement of the particles and so the position of the nodes is continuously updated. The main obstacle of this method is related to the deterioration of the grid due to the movement of the particles. To overcome this problem, a remeshing phase is considered by changing the connectivity of the grid when needed. In this context, the equation for the sediment is solved on the fluid mesh, thus avoiding considering a new mesh for the sediment. Then an erosion model based on the scouring Shields criterion [2] has been added to the proposed approach. Exploiting sediment transport and erosion models, dune erosion and marine erosion of beaches have been numerically solved. This research field is crucial for analyzing the possibility of beaches disappearing. Due to the hypothesis of the chosen mixture model, the applications are limited to flows where the concentration of sediment is quite low. The numerical tests proved that the proposed model is accurate and robust making it usable for real engineering problems. Future developments include the extension to 3D in order to create a tool that could be beneficial for land protection.