Eulerian method for multiphase interactions of soft solid bodies in fluids

TL;DR

This paper presents an Eulerian computational method for simulating interactions between multiple soft solids and fluids, enabling stable, efficient, and accurate modeling of complex multiphase behaviors including solid contact.

Contribution

The authors develop a novel, faster, and more stable coupling approach for fluid-solid interactions using a reference map variable on a fixed grid, capable of handling multiple phases and solid contact.

Findings

The method demonstrates convergence with a weakly compressible Navier-Stokes fluid and neo-Hookean solids.

It enables simulation of both fluid-solid and solid-solid interactions.

The approach improves computational stability and efficiency over previous methods.

Abstract

We introduce an Eulerian approach for problems involving one or more soft solids immersed in a fluid, which permits mechanical interactions between all phases. The reference map variable is exploited to simulate finite-deformation constitutive relations in the solid(s) on the same fixed grid as the fluid phase, which greatly simplifies the coupling between phases. Our coupling procedure, a key contribution in the current work, is shown to be computationally faster and more stable than an earlier approach, and admits the ability to simulate both fluid--solid and solid--solid interaction between submerged bodies. The interface treatment is demonstrated with multiple examples involving a weakly compressible Navier--Stokes fluid interacting with a neo-Hookean solid, and we verify the method's convergence. The solid contact method, which exploits distance-measures already existing on the grid, is demonstrated with two examples. A new, general routine for cross-interface extrapolation is introduced and used as part of the new interfacial treatment.