Interaction of Multiphase Fluids and Solid Structures

  • Hector GomezEmail author
  • Jesus Bueno
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


Fluid–Structure Interaction (FSI) problems are ubiquitous in almost every branch of engineering and science. Their nonlinear and time-dependent nature makes usually the analytical solution very difficult or even impossible to obtain, requiring the use of experimental analysis and/or numerical simulations. This fact has prompted the development of a great variety of numerical methods for FSI. However, most of the efforts have been focused on classical fluids governed by the Navier–Stokes equations, which cannot capture the physical mechanisms behind multiphase fluids. Here, we present several models for the interplay of solids and multiphase flows, which we apply to particular problems such as phase-change-driven implosion, droplet motion, and elastocapillarity.

In this work, the behavior of the structure is described by the nonlinear equations of elastodynamics and treated as a hyperelastic solid. In particular, we employ a Neo-Hookean and a Saint Venant–Kirchhoff model. Our approach for the multiphase fluid is based on the diffuse-interface or phase-field method. The Navier–Stokes–Korteweg equations are used to describe compressible fluids that are composed of two phases of the same component, which may undergo phase transformation. The Navier–Stokes–Cahn–Hilliard equations are used to describe two-component immiscible flows with surface tension. As FSI technique, we adopt a boundary-fitted approach with matching discretization at the interface. This choice leads to a natural monolithic FSI coupling with strong, exact enforcement of the kinematic conditions. We use the Lagrangian description to derive the semidiscrete form of the solid equations and the Arbitrary Lagrangian–Eulerian description for the fluid domain. For the spatial discretization we adopt isogeometric analysis based on Non-Uniform Rational B-Splines. Regarding the time integration, we use a generalized-α scheme. The nonlinear system of equations is solved using a Newton–Raphson iteration procedure, which leads to a two-stage predictor-multicorrector algorithm. A quasi-direct monolithic formulation is adopted for the solution of the FSI problem.


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Authors and Affiliations

  1. 1.School of Mechanical EngineeringPurdue UniversityWest LafayetteUSA
  2. 2.Departamento de MatemáticasUniversidade da CoruñaA CoruñaSpain

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