Monolithic framework to simulate fluid-structure interaction problems using geometric volume-of-fluid method

TL;DR

This paper presents a monolithic Eulerian framework using the geometric volume-of-fluid method for simulating fluid-structure interactions involving incompressible flow and hyperelastic solids, verified through benchmarks and turbulent flow simulations.

Contribution

It introduces a novel VOF/PLIC-based FSI framework that accurately captures interfaces and solid deformation on a fixed grid, with demonstrated stability and efficiency on coarse meshes.

Findings

Stable and accurate interface capturing despite discontinuities

Comparable accuracy on coarse grids to finer diffusive methods

Successful simulation of turbulent flow with deformable walls

Abstract

We develop a three-dimensional Eulerian framework to simulate fluid-structure interaction (FSI) problems on a fixed Cartesian grid using the geometric volume-of-fluid (VOF) method. The coupled problem involves incompressible flow and viscous hyperelastic solids. A VOF-based one-continuum formulation is used to describe the unified momentum conservation equations with incompressibility constraints that are solved using the finite volume method (FVM). In the geometric VOF interface-capturing (IC) approach, the PLIC method is used to reconstruct the interface, and the Lagrangian Explicit (LE) method is used in the directionally split advection procedure. To model the hyperelastic behavior of the solid, we consider Mooney-Rivlin material models, where we use the left Cauchy-Green deformation tensor (B) to account for the solid deformation on an Eulerian grid and the fifth-order WENO-Z reconstruction method is utilized to treat the advection terms involved in the transport equation of B. Multiple benchmark problems are considered to verify the accuracy of the approach. Furthermore, to demonstrate the capability of the solver to handle turbulent interactions, we perform direct numerical simulation (DNS) of turbulent channel flow with a deformable compliant bottom wall and a rigid top wall; our observations align well with previous experimental and numerical works. The detailed numerical experiments show that: (i) Despite the discontinuity of the interface across the cell boundaries and stress discontinuity across the interface, a VOF/PLIC-based FSI framework can provide stable and accurate solutions that significantly minimizes numerical artifacts (e.g., flotsam and spurious currents) while maintaining a sharp interface. (ii) The accuracy of a VOF/PLIC-based FSI approach on coarse grids is comparable to the accuracy of a diffusive IC method-based FSI approach on much finer grids.