The possibility to use a Lagrangian frame to solve problems with large time-steps was successfully explored previously by the authors for the solution of homogeneous incompressible fluids and also for solving multi-fluid problems [28][29][30]
This paper describes a strategy to solve multifluid and Fluid Structure Interaction (FSI) problems using Lagrangian particles combined with a fixed Finite Element (FE) mesh . The method is an extension from the fluid-only PFEM-2 [14] [15], which uses explicit integration over the streamlines to improve accuracy. As a result, the convective term does not appear in the set of equations solved in the fixed mesh. Enrichments in the pressure and field are used to improve the description of the interface between phases.
The application of the semi-Lagrangian Particle Finite Element Method (SL-PFEM) for the seakeeping simulation of the Wave Adaptive Modular Vehicle under spray generating conditions is presented. The time integration of the Lagrangian advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL-PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented. Keywords Particle Finite Element Method • semi-Lagrangian formulations • seakeeping 1 Introduction The Particle Finite Element Method (PFEM) [18] is a versatile framework for the analysis of fluid-structure interaction problems. The PFEM combines Lagrangian particle-based techniques with the advantage of the integral formulation of the Finite Element Method (FEM). It has been shown [14, 15,21, 28, 13, 27] to successfully simulate a wide variety of complex engineering problems, e.g., free-surface/multi-fluid flows with violent interface motions, multi-fluid mixing and
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