This paper describes a strategy to solve multi-fluid and fluid–structure interaction (FSI) problems using Lagrangian particles combined with a fixed finite element (FE) mesh. Our approach is an extension of the fluid-only PFEM-2 (Idelsohn et al., Eng Comput 30(2):2–2, 2013; Idelsohn et al., J Numer Methods Fluids, 2014) 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 on the fixed mesh. Enrichments in the pressure field are used to improve the description of the interface between phases.
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This research has been partly funded by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007-2013/ under REA Grant agreement no. 289911. This work was also supported by the ERC Advanced Grant REALTIME Project (AdG-2009325), the ERC Advanced Grant SAFECON Project (AdG-26752) and the HFLUIDS Project of the National RTD Plan of the Spanish Ministry of Science and Innovation (BIA2010-15880). The authors would also like to thank Dr. Riccardo Rossi for suggesting the special shape functions used in this work.
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