Eulerian Method for FSI Based on the Reference Map

Abstract eng:
We present a new method for FSI based on discretizing the inverse of the motion function, known as the reference map. By storing and updating this field, finite-deformation solid constitutive relations can be implemented numerically in Eulerian frame. Together with an Eulerian-frame method for the fluid motion, the two phases can be represented on a single, fixed background grid, with interfaces between phases resolved using level-sets. The universally Eulerian nature of the method removes certain computational costs and simplifies issues such as resolving contact between (submerged) solids and as well as implementation of incompressibility conditions. We demonstrate the method in problems involving one to twenty submerged hyperelastic solids interacting within low and moderate Reynolds fluid flows, both compressible and incompressible. We demonstrate the ability to model plastic media and capture shocks by way of discretizing the system in conservative form.

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