Benchmarking the Immersed Boundary Method for Viscoelastic Flows

TL;DR

This paper benchmarks the immersed boundary method's accuracy and convergence for viscoelastic flows around complex geometries, comparing it with other solvers and analyzing numerical parameter choices.

Contribution

It provides the first systematic benchmarking of the immersed boundary method for viscoelastic flows using Oldroyd-B and Rolie-Poly models, including parameter analysis.

Findings

IB method shows good accuracy for viscoelastic flow simulations.

Optimal numerical parameters depend on flow regime.

Comparison with finite element and finite volume methods highlights strengths and limitations.

Abstract

We present and analyze a series of benchmark tests regarding the application of the immersed boundary (IB) method to viscoelastic flows through and around non-trivial, stationary geometries. The IB method is widely used for the simulation of biological fluid dynamics and other modeling scenarios where a structure is immersed in a fluid. Although the IB method has been most commonly used to model systems with viscous incompressible fluids, it also can be applied to visoelastic fluids, and has enabled the study of a wide variety of dynamical problems including the settling of vesicles and the swimming of elastic filaments in fluids modeled by the Oldroyd-B constuitive equation. However, to date, relatively little work has explored the accuracy or convergence properties of the numerical scheme. Herein, we present benchmarking results for an IB solver applied to viscoelastic flows in and around non-trivial geometries using the idealized Oldroyd-B and more realistic, polymer-entanglement-based Rolie-Poly constitutive equations. We use two-dimensional numerical test cases along with results from rheology experiments to benchmark the IB method and compare it to more complex finite element and finite volume viscoelastic flow solvers. Additionally, we analyze different choices of regularized delta function and relative Lagrangian grid spacings which allow us to identify and recommend the key choices of these numerical parameters depending on the present flow regime.