# A conservative and non-dissipative Eulerian formulation for the simulation of soft solids in fluids

## TL;DR

This paper introduces a conservative, non-dissipative Eulerian finite volume method using the reference map technique for simulating incompressible hyperelastic solids in fluids, improving robustness and interface smoothness without artificial viscosity.

## Contribution

The authors develop a robust Eulerian formulation with modifications that eliminate artificial viscosity and interface wrinkles, enhancing simulation accuracy for soft solids in fluids.

## Key findings

- Elimination of artificial viscosity in solid regions.
- Reduction of interface wrinkles and improved smoothness.
- Enhanced numerical robustness and stability.

## Abstract

Soft solids in fluids find wide range of applications in science and engineering, especially in the study of biological tissues and membranes. In this study, an Eulerian finite volume approach has been developed to simulate fully resolved incompressible hyperelastic solids immersed in a fluid. We have adopted the recently developed reference map technique (RMT) by Valkov et. al (J. Appl. Mech., 82, 2015) and assessed multiple improvements for this approach.These modifications maintain the numerical robustness of the solver and allow the simulations without any artificial viscosity in the solid regions (to stabilize the solver). This has also resulted in eliminating the striations ("wrinkles") of the fluid-solid interface that was seen before and hence obviates the need for any additional routines to achieve a smooth interface. An approximate projection method has been used to project the velocity field onto a divergence free field. Cost and accuracy improvements of the modifications on the method have also been discussed.