Published in *Int. J. Numer. Meth. Fluids* Vol. 75 (9), pp. 621-644, 2014

doi: 10.1002/fld.3908

Multifluids are those fluids in which their physical properties (viscosity or density) vary internally and abruptly forming internal interfaces that introduce a large nonlinearity in the Navier–Stokes equations. For this reason, standard numerical methods require very small time steps in order to solve accurately the internal interface position. In a previous paper, the authors developed a particle‐based method (named particle finite element method (PFEM)) based on a Lagrangian formulation and FEM for solving the fluid mechanics equations for multifluids. PFEM was capable of achieving accurate results, but the limitation of small time steps was still present. In this work, a new strategy concerning the time integration for the analysis of multifluids is developed allowing time steps one order of magnitude larger than the previous method. The advantage of using a Lagrangian solution with PFEM is shown in several examples. All kind of heterogeneous fluids (with different densities or viscosities), multiphase flows with internal interfaces, breaking waves, and fluid separation may be easily solved with this methodology without the need of small time steps.

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