A coupled approach to the large scale simulation of incompressible flows

  • Montanino, Andrea (University of Naples Federico II)
  • Franci, Alessandro (Universidad Politècnica de Catalunya (UPC))
  • Masò, Miguel (Universidad Politècnica de Catalunya (UPC))
  • de-Pouplana, Ignasi (Universidad Politècnica de Catalunya (UPC))
  • Zuccaro, Giulio (University of Naples Federico II)

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In this work, we present a methodology for the fast and robust solution of large-scale wave propagation and wave-structure interaction problems. The approach consists in adopting and coupling two different formulations: an Eulerian Shallow Water (SW) approach and a Lagrangian Navier-Stokes formulation. The SW formulation assumes that the pressure distribution is hydrostatic, and the velocity in the vertical direction is negligible compared to the other two directions. This allows to solve large three-dimensional problems by practically using a 2D approach, making it particularly useful for simulating wave propagation problems in large domains. When the hypotheses underlying the SW formulation are no longer valid (i.e. in the near-field), the complete Navier-Stokes problem must be solved. Here, for this purpose, we use the Particle Finite Element Method (PFEM), a Lagrangian numerical approach particularly suited for free-surface flows and fluid-structure interaction problems [1]. The two different methods are coupled with a one-way approach. In particular, first, a SW simulation is run, and information in terms of fluid horizontal velocity (averaged on the water depth) and water level is stored; in a second step, the Navier-Stokes problem is solved with the PFEM, using as input the information stored during the SW solution. This scheme is mirroring the one recently proposed in [2]. The proposed algorithm allows a significant reduction in computational costs due to the adoption of the SW formulation in the far-field domain without a loss of accuracy in the near-field zone. The resulting methodology can be employed for different risk assessment analyses, including, for example, the study of coastal water run-up due to sea-storms. REFERENCES [1] M. Cremonesi, A. Franci, S.R. Idelsohn, E. Oñate, A state of the art review of the Particle Finite Element Method (PFEM), Archives of Computational Methods in Engineering, 17:1709-1735, (2020). [4] M. Masó, A. Franci, I. de-Pouplana, A. Cornejo, E. Oñate, A Lagrangian-Eulerian procedure for the coupled solution of the Navier-Stokes and shallow water equations for landslide-generated waves, Advanced Modeling and Simulation in Engineering Sciences, 9 (15), 2022.