Unified one-fluid formulation for incompressible flexible solids and multiphase flows: Application to hydrodynamics using the Immersed Structural Potential Method (ISPM)

In this paper, we present a two-dimensional computational framework for the simulation of fluid-structure interaction problems involving incompressible flexible solids and multiphase flows, further extending the application range of classical immersed computational approaches to the context of hydrodynamics. The proposed method aims to overcome shortcomings such as the restriction of having to deal with similar density ratios among different phases or the restriction to solve single-phase flows. First, a variation of classical immersed techniques, pioneered with the Immersed Boundary Method [1], is presented by rearranging the governing equations which define the behaviour of the multiple physics involved. The formulation is compatible with the 'one-fluid' formulation for two phase flows and can deal with large density ratios with the help of an anisotropic Poisson solver. Second, immersed deformable structures and fluid phases are modelled in an identical manner except for the computation of the deviatoric stresses. The numerical technique followed in this paper builds upon the Immersed Structural Potential Method [2] developed by the authors, by adding a Level Set based method for the capturing of the fluid-fluid interfaces and an interface Lagrangian based meshless technique for the tracking of the fluid-structure interface. The spatial discretisation is based on the standard Marker-and-Cell method used in conjunction with a fractional step approach for the pressure/velocity decoupling, a second order time integrator and a fixed point iterative scheme. The paper presents a wide range of two-dimensional applications involving multiphase flows interacting with immersed deformable solids, including benchmarking against both experimental and alternative numerical schemes.